mpdl-xml-content: texts/XML/echo/en/Harriot_Add_MS_6782

annotate texts/XML/echo/en/Harriot_Add_MS_6782_HSPGZ0AE.xml @ 6:22d6a63640c6

moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/

author	casties
date	Fri, 07 Dec 2012 17:05:22 +0100
parents
children	568e026bb6d6

rev	line source
6 22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1 <?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2 <metadata>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3 <dcterms:identifier>ECHO:HSPGZ0AE.xml</dcterms:identifier>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4 <dcterms:creator>Harriot, Thomas</dcterms:creator>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5 <dcterms:title xml:lang="en">Mss. 6782</dcterms:title>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6 <dcterms:date xsi:type="dcterms:W3CDTF">o. J.</dcterms:date>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7 <dcterms:language xsi:type="dcterms:ISO639-3">eng</dcterms:language>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8 <dcterms:rights>CC-BY-SA</dcterms:rights>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9 <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10 <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11 <echodir>/permanent/library/HSPGZ0AE</echodir>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12 <log>Automatically generated by bare_xml.py on Tue Nov 15 14:20:53 2011</log>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13 </metadata>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15 <text xml:lang="eng" type="free">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16 <div xml:id="echoid-div1" type="bundle" level="1" n="1">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17 <pb file="add_6782_f001" o="1" n="1"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	18 <div xml:id="echoid-div1" type="page_commentary" level="2" n="1">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	19 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	20 <s xml:id="echoid-s1" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	21 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	22 <s xml:id="echoid-s1" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	23 Lists of powers of two up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mn>2</mn><mrow><mn>2</mn><mn>9</mn></mrow></msup></mrow></mstyle></math>, in standard denary (right) and in octonary (left).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	24 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	25 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	26 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	27 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	28 <head xml:id="echoid-head1" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	29 Octonaria. Denaria.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	30 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	31 Octonary. Denary
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	32 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	33 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	34 <pb file="add_6782_f001v" o="1v" n="2"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	35 <pb file="add_6782_f002" o="2" n="3"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	36 <pb file="add_6782_f002v" o="2v" n="4"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	37 <pb file="add_6782_f003" o="3" n="5"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	38 <pb file="add_6782_f003v" o="3v" n="6"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	39 <pb file="add_6782_f004" o="4" n="7"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	40 <pb file="add_6782_f004v" o="4v" n="8"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	41 <pb file="add_6782_f005" o="5" n="9"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	42 <pb file="add_6782_f005v" o="5v" n="10"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	43 <pb file="add_6782_f006" o="6" n="11"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	44 <pb file="add_6782_f006v" o="6v" n="12"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	45 <pb file="add_6782_f007" o="7" n="13"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	46 <pb file="add_6782_f007v" o="7v" n="14"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	47 <pb file="add_6782_f008" o="8" n="15"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	48 <pb file="add_6782_f008v" o="8v" n="16"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	49 <pb file="add_6782_f009" o="9" n="17"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	50 <pb file="add_6782_f009v" o="9v" n="18"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	51 <pb file="add_6782_f010" o="10" n="19"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	52 <pb file="add_6782_f010v" o="10v" n="20"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	53 <pb file="add_6782_f011" o="11" n="21"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	54 <pb file="add_6782_f011v" o="11v" n="22"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	55 <pb file="add_6782_f012" o="12" n="23"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	56 <pb file="add_6782_f012v" o="12v" n="24"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	57 <pb file="add_6782_f013" o="13" n="25"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	58 <pb file="add_6782_f013v" o="13v" n="26"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	59 <pb file="add_6782_f014" o="14" n="27"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	60 <pb file="add_6782_f014v" o="14v" n="28"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	61 <pb file="add_6782_f015" o="15" n="29"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	62 <pb file="add_6782_f015v" o="15v" n="30"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	63 <pb file="add_6782_f016" o="16" n="31"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	64 <pb file="add_6782_f016v" o="16v" n="32"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	65 <pb file="add_6782_f017" o="17" n="33"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	66 <pb file="add_6782_f017v" o="17v" n="34"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	67 <pb file="add_6782_f018" o="18" n="35"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	68 <pb file="add_6782_f018v" o="18v" n="36"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	69 <pb file="add_6782_f019" o="19" n="37"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	70 <pb file="add_6782_f019v" o="19v" n="38"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	71 <pb file="add_6782_f020" o="20" n="39"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	72 <pb file="add_6782_f020v" o="20v" n="40"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	73 <pb file="add_6782_f021" o="21" n="41"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	74 <pb file="add_6782_f021v" o="21v" n="42"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	75 <pb file="add_6782_f022" o="22" n="43"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	76 <pb file="add_6782_f022v" o="22v" n="44"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	77 <pb file="add_6782_f023" o="23" n="45"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	78 <pb file="add_6782_f023v" o="23v" n="46"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	79 <pb file="add_6782_f024" o="24" n="47"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	80 <pb file="add_6782_f024v" o="24v" n="48"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	81 <pb file="add_6782_f025" o="25" n="49"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	82 <pb file="add_6782_f025v" o="25v" n="50"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	83 <pb file="add_6782_f026" o="26" n="51"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	84 <pb file="add_6782_f026v" o="26v" n="52"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	85 <pb file="add_6782_f027" o="27" n="53"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	86 <div xml:id="echoid-div2" type="page_commentary" level="2" n="2">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	87 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	88 <s xml:id="echoid-s3" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	89 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	90 <s xml:id="echoid-s3" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	91 A word square based on the words HENRICUS PRINCEPS FECIT (Prince Henry made it). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	92 The number 184,756 appears four times in the bottom right.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	93 In each quarter of the square, there are 184,756 ways of reading HENRICUS PRINCEPS FECIT,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	94 starting from the centre and ending at a corner. Thus there are 739,024 ways in total.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	95 This number may have been written on the page but has now disappeared (see Add MS 6782, f. 28 for a similar calculation).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	96 For the calculations leading to 184,756 see Add MS 6782, f. 57 and f. 58.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	97 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	98 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	99 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	100 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	101 <pb file="add_6782_f027v" o="27v" n="54"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	102 <pb file="add_6782_f028" o="28" n="55"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	103 <div xml:id="echoid-div3" type="page_commentary" level="2" n="3">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	104 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	105 <s xml:id="echoid-s5" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	106 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	107 <s xml:id="echoid-s5" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	108 A word square based on the words SILO PRINCEPS FECIT (Prince Henry made it). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	109 A <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>5</mn><mo>×</mo><mn>1</mn><mn>9</mn></mstyle></math> rectangular version of this arrangement, carved in stone, is to be found in the church of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	110 San Juan Apostol y Evangelista in Santianes de Pravia, northern Spain,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	111 commemorating Silo, king of Asturias (774 to 783). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	112 The number 12,780 appears four times in the bottom right hand corner of the page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	113 In each quarter of the square, there are 12,780 ways of reading SILO PRINCEPS FECIT,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	114 starting from the centre and ending at a corner. Thus there are 51,480 ways in total.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	115 For the calculations leading to 12,780 see Add MS 6782, f. 57 and f. 58.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	116 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	117 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	118 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	119 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	120 <pb file="add_6782_f028v" o="28v" n="56"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	121 <pb file="add_6782_f029" o="29" n="57"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	122 <div xml:id="echoid-div4" type="page_commentary" level="2" n="4">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	123 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	124 <s xml:id="echoid-s7" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	125 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	126 <s xml:id="echoid-s7" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	127 This folios shows calculations for solving the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>z</mi><mo>+</mo><mn>3</mn><mi>a</mi><mo>=</mo><mn>2</mn><mn>7</mn><mn>6</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	128 (in modern notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mn>3</mn><mi>x</mi><mo>=</mo><mn>2</mn><mn>7</mn><mn>6</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	129 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	130 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	131 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	132 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	133 <pb file="add_6782_f029v" o="29v" n="58"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	134 <div xml:id="echoid-div5" type="page_commentary" level="2" n="5">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	135 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	136 <s xml:id="echoid-s9" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	137 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	138 <s xml:id="echoid-s9" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	139 Triangular numbers arranged as dot patterns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	140 The arrangement of Pascal's triangle on the right shows how each row is obtained
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	141 by summing two copies of the preceding row.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	142 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	143 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	144 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	145 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	146 <pb file="add_6782_f030" o="30" n="59"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	147 <div xml:id="echoid-div6" type="page_commentary" level="2" n="6">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	148 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	149 <s xml:id="echoid-s11" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	150 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	151 <s xml:id="echoid-s11" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	152 The upper left quarter of the page contains two versions of Pascal's triangle, in different layouts. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	153 The upper right quarter shows the entries of the triangle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	154 generated by successive multiplications of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	155 The lower right quarter shows the entries of the triangle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	156 generated by successive multiplications of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo maxsize="1">)</mo></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	157 The lower left quarter demonstrates, following from the multiplications on the right,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	158 that the entries in each row sum to a power of 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	159 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	160 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	161 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	162 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	163 <head xml:id="echoid-head2" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	164 De combinationibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	165 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	166 On combinations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	167 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	168 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	169 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	170 <s xml:id="echoid-s13" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	171 To serve ones turne. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	172 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	173 <s xml:id="echoid-s14" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	174 To do one a sound turne.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	175 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	176 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	177 <pb file="add_6782_f030v" o="30v" n="60"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	178 <div xml:id="echoid-div7" type="page_commentary" level="2" n="7">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	179 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	180 <s xml:id="echoid-s15" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	181 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	182 <s xml:id="echoid-s15" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	183 This page includes numerals from 1 to 9 written with a medieval form for '4',
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	184 and also with characters composed only of straight lines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	185 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	186 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	187 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	188 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	189 <pb file="add_6782_f031" o="31" n="61"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	190 <div xml:id="echoid-div8" type="page_commentary" level="2" n="8">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	191 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	192 <s xml:id="echoid-s17" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	193 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	194 <s xml:id="echoid-s17" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	195 The reference to 'Saxton's great map' is to Christopher Saxton's county maps for England and Wales,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	196 published from 1579 onwards. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	197 Units of measurement:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	198 a pase or pace (from Latin passus) was the length of a double stride, about 5 feet or 1.5 metres.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	199 Thus one square pase was 25 square feet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	200 The Roman mile was 1000 pases. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	201 For some rough working for this page see Add MS 6788, f. 547v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	202 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	203 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	204 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	205 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	206 <head xml:id="echoid-head3" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	207 An æstimable reckoning how many persons <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	208 may inhabit the whole world.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	209 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	210 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	211 <s xml:id="echoid-s19" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	212 Supositions.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	213 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	214 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	215 <s xml:id="echoid-s20" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	216 [1]. The semiperimeter of a circle. 31,415,926
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	217 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	218 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	219 <s xml:id="echoid-s21" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	220 [2]. The semidiameter. 10,000,000
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	221 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	222 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	223 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	224 <s xml:id="echoid-s22" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	225 The compasse of the earth <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	226 after the rate of 60 miles <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	227 to a degree. 21,600 miles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	228 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	229 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	230 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	231 <s xml:id="echoid-s23" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	232 Ergo: The halfe compasse. 10,300 miles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	233 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	234 The figure 10,300 is a copying error for 10,800.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	235 The correct figure has been used in the subsequent calculations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	236 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	237 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	238 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	239 <s xml:id="echoid-s24" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	240 The semidiameter of the earth. 3,437 miles. 747 pases.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	241 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	242 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	243 <s xml:id="echoid-s25" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	244 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mo>,</mo><mn>4</mn><mn>3</mn><mn>7</mn><mo>,</mo><mn>7</mn><mn>4</mn><mn>7</mn><mo>×</mo><mn>1</mn><mn>0</mn><mo>,</mo><mn>3</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>=</mo><mn>3</mn><mn>5</mn><mo>,</mo><mn>4</mn><mn>0</mn><mn>8</mn><mo>,</mo><mn>7</mn><mn>9</mn><mn>4</mn><mo>,</mo><mn>1</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>=</mo></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	245 plano circuli. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	246 quod <reg norm="aequatur" type="abbr">æquat</reg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	247 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	248 <reg norm="superficies" type="abbr">superf</reg>: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	249 terræ et aquæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	250 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	251 a plane circle which equals <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> the surface of land and water.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	252 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	253 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	254 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	255 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	256 <s xml:id="echoid-s26" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	257 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>5</mn><mo>,</mo><mn>4</mn><mn>0</mn><mn>8</mn><mo>,</mo><mn>7</mn><mn>9</mn><mn>4</mn><mo>,</mo><mn>1</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>4</mn><mo>=</mo></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	258 141,635,176,400,000
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	259 <reg norm="superficies" type="abbr">superf:</reg> maris et terræ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	260 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	261 The surface of sea and land.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	262 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	263 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	264 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	265 <s xml:id="echoid-s27" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	266 70,817,588,200,000 =
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	267 <reg norm="superficies" type="abbr">superf:</reg> Terræ: vel maris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	268 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	269 The surface of land or sea.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	270 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	271 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	272 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	273 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	274 <s xml:id="echoid-s28" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	275 49,987 miles square in England
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	276 (<foreign xml:lang="lat">ut aliby</foreign> by Saxtons <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	277 great map) after the rate of 60 miles to a degree <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	278 including rivers & all wastes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	279 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	280 'aliby' is a copying error for 'alibi' (see Add MS 6788, f. 547v). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	281 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	282 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	283 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	284 <s xml:id="echoid-s29" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	285 It lacketh but 13 miles of 50,000.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	286 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	287 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	288 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	289 <s xml:id="echoid-s30" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	290 50,000 miles. 5,000,000 persons. supposed. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	291 1 mile. 100 persons. 70,817,588 miles. 7,081,758,800. persons in the earth.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	292 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	293 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	294 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	295 <s xml:id="echoid-s31" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	296 This subcalculation gives 10,000 square pases per person,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	297 converted next to 250,000 square feet, then to 5 and 8/11 acres.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	298 </emph>]</s><lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	299 <s xml:id="echoid-s32" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	300 1,000,000 pp. 100 persons. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	301 10000 pp. 1 person. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	302 10000 [square pases] = <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	303 250,000 [square feet] = <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mfrac><mrow><mn>8</mn></mrow><mrow><mn>1</mn><mn>1</mn></mrow></mfrac></mstyle></math> acres.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	304 (note rivers & waste included <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	305 as above.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	306 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	307 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	308 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	309 <s xml:id="echoid-s33" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	310 6 men may stand in a pase square. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	311 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	312 <s xml:id="echoid-s34" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	313 Therefore 6,000,000 in one mile square. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	314 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>,</mo><mn>0</mn><mn>8</mn><mn>1</mn><mo>,</mo><mn>5</mn><mn>8</mn><mo>,</mo><mn>8</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>6</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>4</mn><mn>2</mn><mo>,</mo><mn>4</mn><mn>9</mn><mn>0</mn><mo>,</mo><mn>5</mn><mn>5</mn><mn>2</mn><mo>,</mo><mn>8</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	315 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	316 <s xml:id="echoid-s35" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	317 The number of persons yt may stand on ye earth.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	318 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	319 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	320 <pb file="add_6782_f031v" o="31v" n="62"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	321 <div xml:id="echoid-div9" type="page_commentary" level="2" n="9">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	322 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	323 <s xml:id="echoid-s36" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	324 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	325 <s xml:id="echoid-s36" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	326 For some of the calculations behind this page see Add MS 6788, f. 536, f. 537, f. 541.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	327 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	328 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	329 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	330 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	331 <head xml:id="echoid-head4" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	332 The issue from one man & one woman in 240 yeares may be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	333 more then can inhabit the whole earth.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	334 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	335 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	336 <s xml:id="echoid-s38" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	337 Supposing.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	338 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	339 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	340 <s xml:id="echoid-s39" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	341 1. That the first man & woman have a child every yeare <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	342 one yeare male & in other <emph style="super">yeare</emph> female
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	343 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	344 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	345 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	346 <s xml:id="echoid-s40" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	347 2. That the children when they are 20 yeares old & upward <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	348 do also every yeare beget a child one yeare male & an <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	349 other yeare female
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	350 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	351 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	352 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	353 <s xml:id="echoid-s41" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	354 3. That all are living at the end of 240 yeares. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	355 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	356 <s xml:id="echoid-s42" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	357 The number of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	358 males, 5,034,303,437. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	359 females, 5,034,303,437. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	360 persons, 10,068,606,874. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	361 (recconed in <foreign xml:lang="lat">charta</foreign> c)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	362 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	363 Sheet c) is almost certainly Add MS 6788, f. 537,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	364 where the same suppositions appear and this calculation is carried out,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	365 but unfortunately the lettering of that page is obscured in the binding.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	366 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	367 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	368 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	369 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	370 <s xml:id="echoid-s43" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	371 That in 400 yeares upon the former suppositions <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	372 there would be more men then can stand on the face <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	373 of the whole <emph style="st">yeare</emph> earth.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	374 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	375 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	376 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	377 <s xml:id="echoid-s44" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	378 (In <foreign xml:lang="lat">charta</foreign> db) I find that in 340 yeares they will make <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	379 a number of 14 places.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	380 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	381 Sheet db) is probably Add MS 6788, f. 541, but the lettering of that page is unfortunately obscured in the binding.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	382 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	383 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	384 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	385 <s xml:id="echoid-s45" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	386 Therefore in 400 yeares they will make a number of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	387 16 places which is more then can stand on the face of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	388 the earth (<foreign xml:lang="lat">ut versa pagina</foreign>.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	389 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	390 'ut versa pagina' (as the other side of the page); see Add MS 6782, f. 31.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	391 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	392 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	393 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	394 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	395 <s xml:id="echoid-s46" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	396 How many persons have had being in 6000, yeares <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	397 and in what roome they may stand.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	398 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	399 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	400 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	401 <s xml:id="echoid-s47" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	402 Supposing <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	403 1. That <emph style="st">in 40 yeares</emph> the world when it was replenished <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	404 to the number of 7,000,000,000.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	405 (<foreign xml:lang="lat">ut versa pagina</foreign>) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	406 they were alwayes one time with an other the same number.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	407 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	408 'ut versa pagina' (as the other side of the page); see Add MS 6782, f. 31.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	409 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	410 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	411 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	412 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	413 <s xml:id="echoid-s48" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	414 2. That in <emph style="st">every</emph> 40 yeares there is (one time with an other) as <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	415 I have proved in an other page (& agreeth with Nombers .26.64 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	416 a new generation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	417 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	418 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	419 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	420 <s xml:id="echoid-s49" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	421 Therefore in 6000 yeares there are 150 generations. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	422 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	423 <s xml:id="echoid-s50" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	424 Therefore there have been of persons in 6000 yeres <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	425 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><mn>5</mn><mn>0</mn><mo>=</mo><mn>1</mn><mo>,</mo><mn>0</mn><mn>5</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn></mstyle></math>. persons. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	426 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	427 <s xml:id="echoid-s51" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	428 There being 50,000 miles square in England; <emph style="st">therefore</emph> there <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	429 may stand in England 300,000,000,000. persons. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	430 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	431 <s xml:id="echoid-s52" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	432 The former number is three times greater, & therefore <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	433 there place of standing must be also 3 times greater then England.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	434 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	435 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	436 <pb file="add_6782_f032" o="32" n="63"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	437 <div xml:id="echoid-div10" type="page_commentary" level="2" n="10">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	438 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	439 <s xml:id="echoid-s53" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	440 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	441 <s xml:id="echoid-s53" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	442 Another copy of the table shown on Add MS 6782, f. 63.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	443 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	444 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	445 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	446 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	447 <pb file="add_6782_f032v" o="32v" n="64"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	448 <pb file="add_6782_f033" o="33" n="65"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	449 <div xml:id="echoid-div11" type="page_commentary" level="2" n="11">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	450 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	451 <s xml:id="echoid-s55" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	452 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	453 <s xml:id="echoid-s55" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	454 This folio gives systematic lists of all combinations (without repetition) of the letters
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	455 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	456 In each case the combinations are listed as single letters, pairs, triples, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	457 Combinations of the same size are listed alphabetically, thus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>d</mi></mstyle></math>, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	458 (In the final column the triples are to be read downwards from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>e</mi><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	459 then back up from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>f</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi><mi>f</mi></mstyle></math>.) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	460 Numbers written to the right of the columns show the number of combinations in each part of the list.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	461 Totals are given at the bottom. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	462 A table mid-left lists numbers of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></mrow></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow><mo>-</mo><mn>1</mn></mstyle></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>=</mo><mn>1</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	463 The latter are the numbers that appear as totals. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	464 A table lower left shows how combinations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math> may be derived from those for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	465 by adding <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> to the end of each of them and then also listing <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> as a singleton.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	466 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	467 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	468 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	469 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	470 <head xml:id="echoid-head5" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	471 Of combinations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	472 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	473 <pb file="add_6782_f033v" o="33v" n="66"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	474 <pb file="add_6782_f034" o="34" n="67"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	475 <div xml:id="echoid-div12" type="page_commentary" level="2" n="12">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	476 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	477 <s xml:id="echoid-s57" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	478 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	479 <s xml:id="echoid-s57" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	480 This folio gives systematic lists of all combinations (without repetition) of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	481 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	482 In each case the combinations are listed as single letters, pairs, triples, nd so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	483 Combinations of the same kind are listed alphabetically, thus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>d</mi></mstyle></math>, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	484 Numbers written to the right of the columns show the number of combinations in each part of the list.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	485 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	486 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	487 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	488 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	489 <head xml:id="echoid-head6" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	490 Of combinations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	491 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	492 <pb file="add_6782_f034v" o="34v" n="68"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	493 <pb file="add_6782_f035" o="35" n="69"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	494 <div xml:id="echoid-div13" type="page_commentary" level="2" n="13">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	495 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	496 <s xml:id="echoid-s59" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	497 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	498 <s xml:id="echoid-s59" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	499 This folio shows combinations (without repetition) of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	500 with each list constructed from the previous one.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	501 Combinations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>, for example, are found from combinations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	502 by adding <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> to each of them, together with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> as a singleton. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	503 Numbers to the right of each column show the number of combinations in each part of the list.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	504 Totals are given at the bottom. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	505 Harriot uses the word 'complications' for combinations of more than one letter,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	506 and 'simples' for single letters. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	507 At the end of the page Harriot reaches the conclusion that if null combinations are counted,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	508 then the total number of combinations will be a power of 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	509 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	510 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	511 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	512 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	513 <head xml:id="echoid-head7" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	514 Of combinations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	515 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	516 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	517 <s xml:id="echoid-s61" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	518 By this manner of construction & <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	519 generation of the variety of combinations <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	520 or complications: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	521 these propositions are manifest:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	522 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	523 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	524 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	525 <s xml:id="echoid-s62" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	526 The nomber of complications with the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	527 nomber of there simples: is double to the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	528 nomber of complications with there simples, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	529 of the next praecedent order: & one more.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	530 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	531 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	532 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	533 <s xml:id="echoid-s63" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	534 In any order of complications:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	535 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	536 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	537 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	538 <s xml:id="echoid-s64" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	539 The nomber of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	540 Bynaryes Ternaryes Quaternaries &c. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	541 is æquall to the nomber, in the precedent order, of: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	542 Binaryes & Simples.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	543 Ternary<emph style="super">es</emph>s & Binaryes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	544 Quaternaryes & Ternaryes. & c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	545 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	546 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	547 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	548 <s xml:id="echoid-s65" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	549 Hereby is <emph style="st">[???]</emph> also manifest, the reason & order <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	550 of the construction of the table of combinations by nombers <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	551 which <emph style="st">followeth</emph> <emph style="super">is set downe</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	552 in an other paper.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	553 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	554 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	555 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	556 <s xml:id="echoid-s66" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	557 In some cases rationall or negative <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	558 is <emph style="st">[???]</emph> added: as of the species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	559 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. question may be made whether an other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	560 thing hath acte upon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. or both <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	561 that is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. or neither.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	562 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	563 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	564 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	565 <s xml:id="echoid-s67" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	566 And such negatives may be understode <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	567 of all the rest.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	568 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	569 <s xml:id="echoid-s68" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	570 And thus the sommes of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	571 every order wilbe one more; and there <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	572 progression wilbe. 2. 4. 8. 16. 32. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	573 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	574 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	575 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	576 <s xml:id="echoid-s69" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	577 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, or not. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	578 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	579 <s xml:id="echoid-s70" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	580 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. or not. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	581 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	582 <s xml:id="echoid-s71" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	583 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	584 or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>. or not. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	585 &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	586 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	587 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	588 <pb file="add_6782_f035v" o="35v" n="70"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	589 <pb file="add_6782_f036" o="36" n="71"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	590 <div xml:id="echoid-div14" type="page_commentary" level="2" n="14">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	591 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	592 <s xml:id="echoid-s72" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	593 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	594 <s xml:id="echoid-s72" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	595 Columns 1 to 10 of Pascal's triangle, continued in the lower half of the page as far as column 18. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	596 The table is continued to column 24 on Add MS 6782, f. 37.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	597 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	598 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	599 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	600 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	601 <head xml:id="echoid-head8" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	602 Of combinations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	603 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	604 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	605 <s xml:id="echoid-s74" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	606 These nombers are also the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	607 nombers which are used for the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	608 extraction of rootes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	609 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	610 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	611 <pb file="add_6782_f036v" o="36v" n="72"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	612 <pb file="add_6782_f037" o="37" n="73"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	613 <div xml:id="echoid-div15" type="page_commentary" level="2" n="15">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	614 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	615 <s xml:id="echoid-s75" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	616 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	617 <s xml:id="echoid-s75" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	618 Pascal's triangle as far as column 24, continued from Add MS 6782, f. 36.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	619 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	620 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	621 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	622 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	623 <head xml:id="echoid-head9" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	624 Of combinations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	625 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	626 <pb file="add_6782_f037v" o="37v" n="74"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	627 <pb file="add_6782_f038" o="38" n="75"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	628 <div xml:id="echoid-div16" type="page_commentary" level="2" n="16">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	629 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	630 <s xml:id="echoid-s77" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	631 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	632 <s xml:id="echoid-s77" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	633 On this page, as on Add MS 6782, f. 36, Harriot recognizes the usefulness of the triangular numbers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	634 both for calculating numbers of combinations and for extraction of roots. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	635 In the note in the bottom right hand corner of the page, Harriot mentions Boethius, Jordanus, and Maurolico
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	636 as writers on figurate numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	637 His source for both Boethius and Jordanus was probably Jacques Lefevre d'Etaples (Jacob Faber Satuplensis),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	638 <emph style="it">Epitome, compendiosaque introductio in libros arithmeticos diui Severini Boetij</emph> (1503, 1522),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	639 which includes a comparison of the 'De instituione' of Boethius with the 'De arithmetica' of Jordanus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	640 His source for Maurolico was the <emph style="it">Arithmeticorum libri duo</emph> (1575),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	641 which he cited several times elsewhere.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	642 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	643 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	644 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	645 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	646 <head xml:id="echoid-head10" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	647 Of combinations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	648 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	649 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	650 <s xml:id="echoid-s79" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	651 A Generall rule to get the mayne summe of all the complications <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	652 of any Nomber of Species without the table of combinations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	653 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	654 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	655 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	656 <s xml:id="echoid-s80" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	657 According to the nomber of species: understand as many termes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	658 to be gotten in continuall proportion or progression, beginning at <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	659 a unite & making every terme double to his precedent: the
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	660 <emph style="super">double of the</emph> last <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	661 terme lesse by a unite is the summe desired. or the somme of the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	662 progression.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	663 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	664 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	665 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	666 <s xml:id="echoid-s81" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	667 As for example.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	668 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	669 <s xml:id="echoid-s82" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	670 I wold know all the complications <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	671 of 6. species. together with the nomber of the simples. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	672 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	673 <s xml:id="echoid-s83" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	674 the sixth terme of such a progression I spake of, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	675 is 32.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	676 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	677 <s xml:id="echoid-s84" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	678 <emph style="st">therefore</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	679 <emph style="super">The double lesse by a unite is</emph> 63,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	680 <emph style="st">is</emph> the summe of all the <emph style="st">the</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	681 complications with the nomber of simples which were <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	682 sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	683 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	684 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	685 <s xml:id="echoid-s85" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	686 If the number of species be greate; the last terme <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	687 desired is to be gotten by <emph style="super">the</emph> rule of progression in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	688 arithmeticke.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	689 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	690 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	691 <s xml:id="echoid-s86" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	692 The reason of the rule is easily to be conceaved <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	693 out of the particular constructions in an other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	694 paper annexed.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	695 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	696 The 'other paper' referred to here is probably Add MS 6782, f. 331.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	697 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	698 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	699 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	700 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	701 <s xml:id="echoid-s87" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	702 A Generall methode for the particular summes of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	703 complications :
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	704 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	705 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	706 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	707 <s xml:id="echoid-s88" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	708 As for example of 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	709 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	710 <s xml:id="echoid-s89" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	711 <emph style="st">I would know all</emph> first in 6 there are <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	712 6 diverse simple species.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	713 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	714 <s xml:id="echoid-s90" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	715 Then I wold know how many <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	716 complications of 2 wilbe found in 6; also how many of 3. & 4. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	717 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	718 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	719 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	720 <s xml:id="echoid-s91" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	721 The Theoreme for the rule is this: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	722 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	723 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	724 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	725 <s xml:id="echoid-s92" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	726 As 2 hath in proportion to the second nomber from the nomber <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	727 of species towardes a unite: so hath the nomber of variety of unites <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	728 to the somme of the complications of 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	729 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	730 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	731 <s xml:id="echoid-s93" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	732 And as 3 hath in proportion to the third nomber from the nomber <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	733 of species towardes a unite: so hath the nomber of <emph style="st">variety of</emph> compli-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	734 cations of 2, last gotten; to the somme of the complications of 3. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	735 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	736 <s xml:id="echoid-s94" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	737 & so forth, <emph style="st">generally</emph> as wilbe manifest by the example following.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	738 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	739 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	740 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	741 <s xml:id="echoid-s95" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	742 An example for 20.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	743 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	744 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	745 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	746 <s xml:id="echoid-s96" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	747 The practice is playne. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	748 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	749 <s xml:id="echoid-s97" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	750 The theoreme is to be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	751 demonstrated out of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	752 Boetius or Maurolicus, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	753 & I thinke Jordanus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	754 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	755 <s xml:id="echoid-s98" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	756 by the doctrine of genera- <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	757 ting triangular nombers <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	758 & of triangular, piramidal. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	759 & of piramidal, triangle- <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	760 pyramidal &c. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	761 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	762 <s xml:id="echoid-s99" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	763 And is worth the noting <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	764 for some other respects <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	765 especially <emph style="st">of generating</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	766 for getting the nomber <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	767 of [¿]complicity[?] that <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	768 belongs to any dignityes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	769 for extracting there roote; <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	770 seeing those nombers are <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	771 the very same.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	772 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	773 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	774 <pb file="add_6782_f038v" o="38v" n="76"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	775 <pb file="add_6782_f039" o="39" n="77"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	776 <div xml:id="echoid-div17" type="page_commentary" level="2" n="17">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	777 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	778 <s xml:id="echoid-s100" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	779 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	780 <s xml:id="echoid-s100" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	781 By 'transpositions' Harriot means what we would now call permutations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	782 His 'single variations' are what we would now call cyclic permutations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	783 For simple diagrams illustrating cyclic permutations see Add MS 6782, f. 43v and f. 225v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	784 On this folio he lists all possible permutations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	785 and begins a list for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	786 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	787 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	788 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	789 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	790 <head xml:id="echoid-head11" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	791 Of Transpositions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	792 </head>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	794 <s xml:id="echoid-s102" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	795 Single variations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	796 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	797 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	798 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	799 <s xml:id="echoid-s103" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	800 They are <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	801 so many as <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	802 there are <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	803 species.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	804 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	805 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	806 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	807 <s xml:id="echoid-s104" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	808 The nomber of transpositions of any nomber of species being given: The nomber <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	809 of transpositions of the next nomber of species, is a nomber that riseth of there <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	810 multiplication.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	811 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	812 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	813 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	814 <s xml:id="echoid-s105" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	815 For: suppose the nomber of transpositions of 3 species, that is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, to be 6. The <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	816 next nomber to be transposed is 4. which let be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	817 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	818 <s xml:id="echoid-s106" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	819 Now <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, in respect of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	820 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math> hath foure places. that is he may be next after <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>: after <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>: after <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>: or <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	821 before <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	822 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	823 <s xml:id="echoid-s107" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	824 So many places it hath with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi><mi>b</mi></mstyle></math>, & the rest of the 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	825 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	826 <s xml:id="echoid-s108" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	827 Therefore 4 times <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	828 6, which is 24. is the nomber of transpositions of 4 species.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	829 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	830 <s xml:id="echoid-s109" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	831 The like reason <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	832 is of all others that <emph style="st">may</emph> follow
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	833 <foreign xml:lang="lat">in infinitum</foreign>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	834 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	835 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	836 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	837 <s xml:id="echoid-s110" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	838 Transpositions of:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	839 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	840 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	841 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	842 <s xml:id="echoid-s111" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	843 Number of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	844 Termes of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	845 variations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	846 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	847 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	848 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	849 <s xml:id="echoid-s112" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	850 Sume of the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	851 species totall
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	852 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	853 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	854 <pb file="add_6782_f039v" o="39v" n="78"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	855 <pb file="add_6782_f040" o="40" n="79"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	856 <div xml:id="echoid-div18" type="page_commentary" level="2" n="18">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	857 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	858 <s xml:id="echoid-s113" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	859 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	860 <s xml:id="echoid-s113" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	861 This small table shows all the combinations and permutations of up to 7 letters.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	862 The figures in the column under 7, for example, show all the combinations of 7 single letters (7),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	863 all the combinations of 2 letters (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>×</mo><mn>6</mn><mo>=</mo><mn>4</mn><mn>2</mn></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	864 of 3 letters (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>×</mo><mn>6</mn><mo>×</mo><mn>5</mn><mo>=</mo><mn>2</mn><mn>1</mn><mn>0</mn></mstyle></math>), and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	865 Lines drawn between columns show how figures in a given column are obtained
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	866 from those in the preceding column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	867 The figures in column 7, for example, are obtained from those in column 6 by multiplying by 7.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	868 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	869 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	870 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	871 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	872 <head xml:id="echoid-head12" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	873 combinations & transpositions together.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	874 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	875 <pb file="add_6782_f040v" o="40v" n="80"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	876 <div xml:id="echoid-div19" type="page_commentary" level="2" n="19">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	877 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	878 <s xml:id="echoid-s115" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	879 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	880 <s xml:id="echoid-s115" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	881 Tables showing the most likely sums on 5 dice, or on 6 dice (totals only). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	882 The left hand table is a frequency table for the sums on five dice,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	883 constructed by adding copies of the columns of table (v) from Add MS 6782, f. 40
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	884 (just as table (v) there was constructed from table (iv). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	885 The two right hand columns are a frequency table for the sums on six dice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	886 Here the individual columns that make up the sum have not been written down but
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	887 the additions have been carried out in the working at the bottom of the page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	888 In the table itself Harriot has written only the totals. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	889 As on Add MS 6782, f. 40, the most likely sums are marked with crosses.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	890 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	891 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	892 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	893 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	894 <pb file="add_6782_f041" o="41" n="81"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	895 <div xml:id="echoid-div20" type="page_commentary" level="2" n="20">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	896 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	897 <s xml:id="echoid-s117" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	898 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	899 <s xml:id="echoid-s117" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	900 The two words 'on dice' in the title are written in Harriot's Algonquin alphabet
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	901 (see Add MS 6782, f. 337). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	902 The two tables at the top of the page show the sums that can be obtained on
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	903 (i) two dice (sums ranging from 2 to 12) or (ii) three dice (sums ranging from 3 to 18). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	904 The three tables in the lower part of the page are frequency tables for the sums on
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	905 (iii) two dice; (iv) three dice ; (v) four dice. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	906 Tables (iii) and (iv) can be calculated directly from (i) and (ii).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	907 However, the layout shows that (iv) can also be calculated by taking copies of the totals from (iii),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	908 staggering their starting position, and then adding;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	909 this is equivalent to taking the totals from (iii)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	910 and then adding 1, 2, 3, 4, 5, 6, in turn to represent the throw of the third dice. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	911 For each of (iii), (iv), and (v) the most likely sums are marked with a small cross.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	912 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	913 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	914 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	915 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	916 <head xml:id="echoid-head13" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	917 Of combinations & transpositions of the numbers [on diz]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	918 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	919 <pb file="add_6782_f041v" o="41v" n="82"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	920 <pb file="add_6782_f042" o="42" n="83"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	921 <div xml:id="echoid-div21" type="page_commentary" level="2" n="21">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	922 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	923 <s xml:id="echoid-s119" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	924 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	925 <s xml:id="echoid-s119" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	926 Another version of the tables from the lower half of Add MS 6782, f. 81.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	927 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	928 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	929 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	930 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	931 <pb file="add_6782_f042v" o="42v" n="84"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	932 <div xml:id="echoid-div22" type="page_commentary" level="2" n="22">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	933 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	934 <s xml:id="echoid-s121" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	935 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	936 <s xml:id="echoid-s121" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	937 The word 'diz' (dice) is written at the top of the page in Harriot's Algonquin alphabet
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	938 (see Add MS 6782, f. 337.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	939 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	940 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	941 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	942 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	943 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	944 <s xml:id="echoid-s123" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	945 [diz]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	946 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	947 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	948 <pb file="add_6782_f043" o="43" n="85"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	949 <pb file="add_6782_f043v" o="43v" n="86"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	950 <pb file="add_6782_f044" o="44" n="87"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	951 <div xml:id="echoid-div23" type="page_commentary" level="2" n="23">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	952 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	953 <s xml:id="echoid-s124" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	954 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	955 <s xml:id="echoid-s124" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	956 This folio quotes some text from Girolam Cardano, <emph style="it">Opus novum de proportionibus</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	957 (1570), page 187, Proposition 170. The copy is in an unknown hand.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	958 The table below the text is exactly as given by Cardano.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	959 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	960 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	961 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	962 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	963 <head xml:id="echoid-head14" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	964 Cardanus de proportionibus. prop. 170.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	965 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	966 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	967 <s xml:id="echoid-s126" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	968 Ut autem habeas numeros singulorum ordinum, in quavis multitudino, deducito <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	969 numerum ordinis a primo, & divide per numerum ordinis ipsius reliquum, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	970 et illud quod proventi, ducito in numerum maximum praecedentis ordinis, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	971 et habebis numerum quaesitum. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	972 <s xml:id="echoid-s127" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	973 Velut si sint undecim, volo scire breviter numeros, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	974 qui fiunt ex variatione trium. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	975 <s xml:id="echoid-s128" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	976 Primum deduco pro secundo ordine 1 ex 11 fit 10, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	977 divido per 2 numerum ordinis, exit 5, duco in 11 fit 55 numerus secundi ordinis. Inde <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	978 detraho 2, qui est numerus differentiae ordinis totij a primo ex 11, relinquitur 9, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	979 divido 9 per 3 numerum ordinis exit 3, duco 3 in 55 numerum secundi fit 165, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	980 numerus totij ordinis. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	981 <s xml:id="echoid-s129" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	982 Similiter volo numerum variatione quatuor, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	983 dedco 3 differentiam 4 a primo ordine ab 11 relinquitur 8, divido 8 per 4 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	984 numero ordinis, exit 2, duco 2 in 195 fit 330, numeri quarti ordinis. </s><lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	985 <s xml:id="echoid-s130" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	986 Similiter pro quinto detraho 4 differentiam a primo ordine, relinquitur 7, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	987 divido per 5 numerum ordinis exit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>, duco in 330 numero praecedentis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	988 ordine, fit 462 numerus quinti ordinis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	989 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	990 As moreover you have the numbers of a single row, of any size,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	991 you can derive the numbers of each place from the first,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	992 and divide by the number of the place, and what arises multiply by the greatest number
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	993 of the preceding place,and you will have the number sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	994 Thus if there are eleven [objects],
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	995 I want to know quickly the number that arises for three choices. First, for the second place,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	996 I take 1 from 11 which makes 10, I divide by 2, the number of the place, there comes out 5,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	997 I multiply by 11 to make 55, the number of the second place. Next I subtract 2,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	998 which is the number of the difference of all the places from the first, from 11, there remains 9,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	999 I divide 9 by 3,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1000 the number of the place, there comes out 3, I multiply 3 by 55, the second number, to make 165,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1001 the number in the third place. Similarly if I want the number for four choices, I take 3,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1002 the difference of 4 from the first place, from 11, there is left 8, I divide 8 by 4,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1003 the number of the place, there comes out 2, I multiply 2 by 165 to make 330,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1004 the number of the fourth place.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1005 Similarly for the fifth I subtract 4, the difference from the first place, there remains 7, I divide by 5,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1006 the number of the place, there comes out <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>, I multiply by 330,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1007 the number of the previous place, to make 462, the number of the fifth place.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1008 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1009 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1010 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1011 <pb file="add_6782_f044v" o="44v" n="88"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1012 <pb file="add_6782_f045" o="45" n="89"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1013 <div xml:id="echoid-div24" type="page_commentary" level="2" n="24">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1014 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1015 <s xml:id="echoid-s131" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1016 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1017 <s xml:id="echoid-s131" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1018 This folio appears to deal with 6 dice numbered as follows:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1019 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1020 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1021 <s xml:id="echoid-s132" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1022 first die: 0 0 0 0 0 1 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1023 second die: 0 0 0 0 0 2 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1024 third die: 0 0 0 0 0 3 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1025 fourth die: 0 0 0 0 0 4 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1026 fifth die: 0 0 0 0 0 5 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1027 sixth die: 0 0 0 0 0 6
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1028 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1029 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1030 <s xml:id="echoid-s133" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1031 The tables show the possible outcomes of throwing the first, then the first and the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1032 then the first and the second and the third, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1033 In the table for six dice, for example, we see that combinations with one 0 and five other numbers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1034 can appear in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mo>×</mo><mn>6</mn><mo>=</mo><mn>3</mn><mn>0</mn></mstyle></math> ways (since any of the five zeros can appear in any of the six positions). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1035 Squeezed below and between the main tables are frequency tables showing how many times each sum can appear.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1036 For six dice, for example, we see that the total 3 can arise in two ways (as 1 + 2 or as 0 + 3)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1037 giving 3,750 possibilities in total.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1038 In each of these tables the number of possibilites is summed, giving the appropriate power of 6 in each case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1039 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1040 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1041 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1042 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1043 <pb file="add_6782_f045v" o="45v" n="90"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1044 <pb file="add_6782_f046" o="46" n="91"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1045 <pb file="add_6782_f046v" o="46v" n="92"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1046 <pb file="add_6782_f047" o="47" n="93"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1047 <pb file="add_6782_f047v" o="47v" n="94"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1048 <pb file="add_6782_f048" o="48" n="95"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1049 <pb file="add_6782_f048v" o="48v" n="96"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1050 <div xml:id="echoid-div25" type="page_commentary" level="2" n="25">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1051 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1052 <s xml:id="echoid-s135" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1053 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1054 <s xml:id="echoid-s135" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1055 Combinations of quantities generated by multiplication. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1056 The letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> stand for
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1057 <foreign xml:lang="lat">pondus</foreign> (weight),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1058 <foreign xml:lang="lat">magnitudo</foreign> (magnitude),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1059 <foreign xml:lang="lat">figura</foreign> (area),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1060 <foreign xml:lang="lat">situs</foreign> (place),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1061 <foreign xml:lang="lat">altitudo</foreign> (altitude)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1062 (see Add MS 6786, f. 291).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1063 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1064 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1065 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1066 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1067 <pb file="add_6782_f049" o="49" n="97"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1068 <div xml:id="echoid-div26" type="page_commentary" level="2" n="26">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1069 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1070 <s xml:id="echoid-s137" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1071 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1072 <s xml:id="echoid-s137" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1073 The tables on this folio appear to have been begun at the top left
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1074 but then re-started and continued along the right-hand edge. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1075 The tables are calculated in turn for 1, 2, 3, 4, 5, 6 throws of a die. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1076 Take, for example, the fourth table, for four throws of a die. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1077 The first row indicates that the combination 1111 can occur in only one way. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1078 The next two rows indicate how many ways only 1 and 2 can occur, distributed as either
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1079 3 + 1 (thus, 1112, 1121, 1211, 2111, 2221, 2212, 2122, 1222), that is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mo>×</mo><mn>4</mn><mo>=</mo><mn>8</mn></mstyle></math> ways in total,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1080 or as
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1081 2 + 2 (thus, 1122, 1212, 1221, 2112, 2121, 2211), that is, 3 + 3 = 6 ways in total.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1082 These two calculations are shown in full on Add MS 6782, f. 50v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1083 The fourth row indicates how many ways only 1, 2, and 3 can occur,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1084 with any one of them appearing twice (thus 1123, 1132, 1212, 3112, ...), that is,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1085 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>3</mn><mo>=</mo><mn>3</mn><mn>6</mn></mstyle></math> ways in total.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1086 Further details of the calculation are shown on Add MS 6782, f. 50v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1087 The fifth and final row indicates how many ways 1, 2, 3, 4 can appear, that is,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1088 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>4</mn><mo>=</mo><mn>2</mn><mn>4</mn></mstyle></math> ways in total. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1089 All the other tables are calculated in a similar way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1090 Several of the calculations can be seen on Add MS 6782, f. 50v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1091 Below the line (still reading the page sideways) are two further tables;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1092 for the continuation of these, see Add MS 6782, f. 50. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1093 Harriot also includes some brief notes to explain how the tables have been derived.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1094 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1095 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1096 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1097 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1098 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1099 <s xml:id="echoid-s139" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1100 11112 variatur per:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1101 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1102 11112 may be varied by:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1103 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1104 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1105 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1106 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1107 <s xml:id="echoid-s140" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1108 conversionem, ut
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1109 22221.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1110 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1111 conversion, as 22221.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1112 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1113 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1114 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1115 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1116 <s xml:id="echoid-s141" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1117 transpositionem, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1118 11112, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1119 11121, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1120 11211, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1121 12111, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1122 21111
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1123 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1124 transposition, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1125 11112, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1126 11121, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1127 11211, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1128 12111, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1129 21111
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1130 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1131 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1132 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1133 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1134 <s xml:id="echoid-s142" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1135 coniugationum ut <emph style="st">supra</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1136 sunt 2 ex 6; sunt 15<emph style="super">ies</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1137 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1138 conjugation, as there are 2 out of 6, there are 15 ways
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1139 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1140 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1141 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1142 <pb file="add_6782_f049v" o="49v" n="98"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1143 <pb file="add_6782_f050" o="50" n="99"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1144 <div xml:id="echoid-div27" type="page_commentary" level="2" n="27">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1145 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1146 <s xml:id="echoid-s143" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1147 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1148 <s xml:id="echoid-s143" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1149 On this folio Harriot uses the totals he has arrived at on Add MS 6783, f. 49,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1150 but now extends the calculations to all six numbers on the die. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1151 As for Add MS 6783, f. 49, we will once again examine the fourth table. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1152 The first row indicates that a given number can be appear four times in just one way;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1153 but the given number can be chosen in six ways, so there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>×</mo><mn>6</mn><mo>=</mo><mn>6</mn></mstyle></math> such combinations in total. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1154 The second row indicates that any two numbers can occur together, with 3 of one and 1 of the other, in 8 ways
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1155 (as calculated on Add MS 6783, f. 49,);
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1156 but two numbers can be chosen from six in 15 ways (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>6</mn><mo>×</mo><mn>5</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>1</mn></mrow></mfrac></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1157 so there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>8</mn><mo>×</mo><mn>5</mn><mo>=</mo><mn>1</mn><mn>2</mn><mn>0</mn></mstyle></math> such combinations in total. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1158 The third row indicates that any two numbers can occur together, with 2 of one and 2 of the other, in 6 ways
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1159 (as calculated on Add MS 6783, f. 49,);
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1160 but two numbers can be chosen from six in 15 ways (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>6</mn><mo>×</mo><mn>5</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>1</mn></mrow></mfrac></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1161 so there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mo>×</mo><mn>1</mn><mn>5</mn><mo>=</mo><mn>9</mn><mn>0</mn></mstyle></math> such combinations in total. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1162 The fourth row indicates that any three numbers can occur together in 36 ways
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1163 (as calculated on Add MS 6783, f. 49,);
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1164 but three numbers can be chosen from six in 20 ways (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>6</mn><mo>×</mo><mn>5</mn><mo>×</mo><mn>4</mn></mrow><mrow><mn>3</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>1</mn></mrow></mfrac></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1165 so there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>6</mn><mo>×</mo><mn>2</mn><mn>0</mn><mo>=</mo><mn>7</mn><mn>2</mn><mn>0</mn></mstyle></math> such combinations in total. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1166 The fifth row indicates that any four numbers can occur together in 24 ways
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1167 (as calculated on Add MS 6783, f. 49,);
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1168 but four numbers can be chosen from six in 15 ways (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>6</mn><mo>×</mo><mn>5</mn><mo>×</mo><mn>4</mn><mo>×</mo><mn>3</mn></mrow><mrow><mn>4</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>1</mn></mrow></mfrac></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1169 so there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>4</mn><mo>×</mo><mn>1</mn><mn>5</mn><mo>=</mo><mn>3</mn><mn>6</mn><mn>0</mn></mstyle></math> such combinations in total. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1170 As a check on the calculations, Harriot has calculated powers of 6 on the same page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1171 It is easily seen from this that each table includes all the possibilities for that number of throws.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1172 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1173 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1174 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1175 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1176 <pb file="add_6782_f050v" o="50v" n="100"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1177 <div xml:id="echoid-div28" type="page_commentary" level="2" n="28">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1178 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1179 <s xml:id="echoid-s145" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1180 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1181 <s xml:id="echoid-s145" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1182 Calculations for Add MS 6782, f. 97.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1183 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1184 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1185 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1186 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1187 <pb file="add_6782_f051" o="51" n="101"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1188 <pb file="add_6782_f051v" o="51v" n="102"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1189 <pb file="add_6782_f052" o="52" n="103"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1190 <pb file="add_6782_f052v" o="52v" n="104"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1191 <pb file="add_6782_f053" o="53" n="105"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1192 <pb file="add_6782_f053v" o="53v" n="106"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1193 <pb file="add_6782_f054" o="54" n="107"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1194 <pb file="add_6782_f054v" o="54v" n="108"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1195 <pb file="add_6782_f055" o="55" n="109"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1196 <div xml:id="echoid-div29" type="page_commentary" level="2" n="29">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1197 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1198 <s xml:id="echoid-s147" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1199 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1200 <s xml:id="echoid-s147" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1201 For the definition of binomes of the third kind, see Add MS 6782, f. 267. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1202 On this page, Harriot shows that the cube of a binome of the third kind is again a binome of the third kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1203 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1204 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1205 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1206 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1207 <head xml:id="echoid-head15" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1208 De cubo binomij 3<emph style="super">i</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1209 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1210 On the cube of a third binome
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1211 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1212 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1213 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1214 <s xml:id="echoid-s149" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1215 <reg norm="binomij" type="abbr">bin</reg>. 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1216 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1217 a binome of the third kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1218 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1219 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1220 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1221 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1222 <s xml:id="echoid-s150" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1223 <reg norm="binomij" type="abbr">bin</reg>. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1224 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1225 a binome of the first kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1226 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1227 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1228 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1229 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1230 <s xml:id="echoid-s151" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1231 Ergo cubus: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>5</mn><mn>4</mn><mn>0</mn><mn>8</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>5</mn><mn>4</mn><mn>0</mn><mn>0</mn></mrow></msqrt></mstyle></math>. <reg norm="binomij" type="abbr">bin</reg>. 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1232 <reg norm="differentia" type="abbr">diff</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1233 <reg norm="quadrati" type="abbr">quad</reg>: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1234 8. cubus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1235 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1236 Therefore the cube <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>5</mn><mn>4</mn><mn>0</mn><mn>8</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>5</mn><mn>4</mn><mn>0</mn><mn>0</mn></mrow></msqrt></mstyle></math> is a binome of the third kind;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1237 the difference of the squares <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1238 is 8, a cube.</emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1239 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1240 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1241 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1242 <pb file="add_6782_f055v" o="55v" n="110"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1243 <pb file="add_6782_f056" o="56" n="111"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1244 <div xml:id="echoid-div30" type="page_commentary" level="2" n="30">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1245 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1246 <s xml:id="echoid-s152" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1247 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1248 <s xml:id="echoid-s152" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1249 For the definition of binomes of the fourth kind, see Add MS 6782, f. 267. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1250 On this page, Harriot shows that the cube of a binome of the fourth kind is again a binome of the fourth kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1251 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1252 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1253 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1254 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1255 <head xml:id="echoid-head16" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1256 De cubo binomij 4<emph style="super">i</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1257 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1258 On the cube of a fourth binome
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1259 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1260 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1261 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1262 <s xml:id="echoid-s154" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1263 <reg norm="binomij" type="abbr">bin</reg>. 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1264 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1265 a binome of the fourth kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1266 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1267 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1268 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1269 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1270 <s xml:id="echoid-s155" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1271 <reg norm="binomij" type="abbr">bin</reg>. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1272 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1273 a binome of the first kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1274 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1275 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1276 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1277 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1278 <s xml:id="echoid-s156" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1279 Ergo cubus <reg norm="binomij" type="abbr">bin</reg>. 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1280 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1281 Therefore the cube is a binome of the fourth kind;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1282 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1283 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1284 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1285 <s xml:id="echoid-s157" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1286 512. <reg norm="differentia" type="abbr">dra</reg> <reg norm="quadrati" type="abbr">quad</reg>: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1287 cub
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1288 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1289 512. the difference of the squares, is a cube.</emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1290 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1291 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1292 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1293 <s xml:id="echoid-s158" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1294 Aliter
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1295 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1296 Another way
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1297 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1298 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1299 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1300 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1301 <s xml:id="echoid-s159" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1302 Ergo cubus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1303 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mn>2</mn><mn>0</mn><mo>+</mo><msqrt><mrow><mn>5</mn><mn>1</mn><mn>7</mn><mo>,</mo><mn>8</mn><mn>8</mn><mn>8</mn></mrow></msqrt></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1304 Ut supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1305 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1306 Therefore the cube is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mn>2</mn><mn>0</mn><mo>+</mo><msqrt><mrow><mn>5</mn><mn>1</mn><mn>7</mn><mo>,</mo><mn>8</mn><mn>8</mn><mn>8</mn></mrow></msqrt></mstyle></math>. As above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1307 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1308 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1309 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1310 <pb file="add_6782_f056v" o="56v" n="112"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1311 <pb file="add_6782_f057" o="57" n="113"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1312 <div xml:id="echoid-div31" type="page_commentary" level="2" n="31">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1313 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1314 <s xml:id="echoid-s160" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1315 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1316 <s xml:id="echoid-s160" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1317 The table at the top left shows the number of pathways from centre to corner
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1318 for squares of size <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>1</mn><mo>×</mo><mn>2</mn><mn>1</mn></mstyle></math>. For a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mo>×</mo><mn>5</mn></mstyle></math> square, for instance,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1319 there are 20 pathways to each corner, and so 80 in all.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1320 (There is an error in the calculation for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>9</mn><mo>×</mo><mn>9</mn></mstyle></math> squares, where there are 70 pathways to each corner,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1321 making a total of 280 in all, not 240.) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1322 Below the table are the numbers of pathways for the squares on Add MS 6782, f. 28 and f. 27,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1323 SILO PRINCEPS FECIT (17 letters, 51,480 pathways) and HENRICUS PRINCEPS FECIT (21 letters, 739,024 pathways). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1324 The calculations down the right hand side of the page show the multiplication
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1325 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>1</mn><mo>×</mo><mn>1</mn><mn>2</mn><mo>×</mo><mn>1</mn><mn>3</mn><mo>×</mo><mo>…</mo><mo>×</mo><mn>2</mn><mn>1</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1326 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1327 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1328 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1329 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1330 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1331 <s xml:id="echoid-s162" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1332 Silo princeps fecit (17) 51,480
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1333 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1334 Prince Silo made it
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1335 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1336 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1337 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1338 <s xml:id="echoid-s163" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1339 Jacobus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1340 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1341 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1342 <s xml:id="echoid-s164" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1343 Henricus princeps fecit (21) 739,024
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1344 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1345 Prince Henry made it
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1346 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1347 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1348 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1349 <s xml:id="echoid-s165" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1350 Carolus princeps fecit (20)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1351 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1352 Prince Charles made it
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1353 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1354 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1355 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1356 <pb file="add_6782_f057v" o="57v" n="114"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1357 <div xml:id="echoid-div32" type="page_commentary" level="2" n="32">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1358 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1359 <s xml:id="echoid-s166" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1360 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1361 <s xml:id="echoid-s166" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1362 The upper half of the page shows calculations of the number of pathways through a quarter square
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1363 for up to 9 letters. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1364 The calculation in the lower half of the page arrives at the total 705,432.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1365 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1366 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1367 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1368 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1369 <pb file="add_6782_f058" o="58" n="115"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1370 <div xml:id="echoid-div33" type="page_commentary" level="2" n="33">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1371 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1372 <s xml:id="echoid-s168" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1373 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1374 <s xml:id="echoid-s168" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1375 This folios shows a version of Pascal's triangle, with the numbers 1, 2, 6, 20, 70, ...
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1376 along the diagonal emphasized. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1377 Here the numbers represent the number of pathways through a square with up to 144 cells,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1378 from the starting point (marked 0) to any cell in the grid.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1379 The numbers along the diagonal show the number of pathways from corner to corner,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1380 as required on Add MS 6782, f. 27 and f. 28.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1381 The numbers 12,870 and 184,756 from f. 28 and f. 27 appear on this diagonal,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1382 as does the number 705,432 calculated on Add MS 6782, f. 57v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1383 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1384 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1385 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1386 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1387 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1388 <s xml:id="echoid-s170" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1389 <reg norm="examinatur" type="abbr">examinat</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1390 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1391 examined
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1392 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1393 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1394 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1395 <pb file="add_6782_f058v" o="58v" n="116"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1396 <pb file="add_6782_f059" o="59" n="117"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1397 <pb file="add_6782_f059v" o="59v" n="118"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1398 <pb file="add_6782_f060" o="60" n="119"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1399 <div xml:id="echoid-div34" type="page_commentary" level="2" n="34">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1400 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1401 <s xml:id="echoid-s171" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1402 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1403 <s xml:id="echoid-s171" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1404 Quarter squares, completed with numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1405 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1406 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1407 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1408 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1409 <pb file="add_6782_f060v" o="60v" n="120"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1410 <pb file="add_6782_f061" o="61" n="121"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1411 <pb file="add_6782_f061v" o="61v" n="122"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1412 <pb file="add_6782_f062" o="62" n="123"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1413 <pb file="add_6782_f062v" o="62v" n="124"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1414 <pb file="add_6782_f063" o="63" n="125"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1415 <div xml:id="echoid-div35" type="page_commentary" level="2" n="35">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1416 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1417 <s xml:id="echoid-s173" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1418 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1419 <s xml:id="echoid-s173" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1420 The table on this folio shows the same information as Add MS 6782, f. 58,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1421 but now in the form of one quarter of a word square.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1422 The 'letters' in each cell are the upper entries, in slightly heavier ink.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1423 The lower entry in each cell is the number of pathways to that square, starting from the top left hand corner. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1424 Grid squares along the diagonal have been slightly shaded for emphasis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1425 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1426 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1427 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1428 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1429 <pb file="add_6782_f063v" o="63v" n="126"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1430 <pb file="add_6782_f064" o="64" n="127"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1431 <div xml:id="echoid-div36" type="page_commentary" level="2" n="36">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1432 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1433 <s xml:id="echoid-s175" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1434 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1435 <s xml:id="echoid-s175" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1436 Squares of size <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mo>×</mo><mn>3</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mo>×</mo><mn>5</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>×</mo><mn>7</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>9</mn><mo>×</mo></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1437 completed with numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1438 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1439 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1440 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1441 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1442 <pb file="add_6782_f064v" o="64v" n="128"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1443 <pb file="add_6782_f065" o="65" n="129"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1444 <pb file="add_6782_f065v" o="65v" n="130"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1445 <pb file="add_6782_f066" o="66" n="131"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1446 <pb file="add_6782_f066v" o="66v" n="132"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1447 <pb file="add_6782_f067" o="67" n="133"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1448 <div xml:id="echoid-div37" type="page_commentary" level="2" n="37">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1449 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1450 <s xml:id="echoid-s177" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1451 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1452 <s xml:id="echoid-s177" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1453 In this page. Harriot begins by constructing a table of the interest paid after seven years
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1454 on a capital sum of £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math> at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1455 The first row shows the total if the interest is paid yearly (7 payments). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1456 The second row shows the total if interest is paid twice a year (14 payments). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1457 The third row shows the total if interest is paid three times a year (21 payments). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1458 From here, Harriot immediately generalizes to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> payments per year.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1459 He then (implicitly) allows <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> to become very large, indeed infinitely large,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1460 so that the fractions <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mo maxsize="1">(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo maxsize="1">)</mo><mi>n</mi></mrow><mrow><mi>n</mi><mi>n</mi></mrow></mfrac></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mo maxsize="1">(</mo><mi>n</mi><mo>-</mo><mn>2</mn><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo maxsize="1">)</mo><mi>n</mi></mrow><mrow><mi>n</mi><mi>n</mi><mi>n</mi></mrow></mfrac></mstyle></math>, ... can all be taken to be 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1461 Harriot then substitutes <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>1</mn><mn>0</mn></mstyle></math> to obtain the interest on £100 at a rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1462 paid continuously over seven years. The total comes to £201 7 shillings and 6 pence,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1463 plus a further fraction that he estimates is not quite <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>7</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mstyle></math> pence.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1464 (There were 20 shillings (s) to £1, and 12 pence (d) to 1 shillling.) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1465 This page combines the calculations on the nearby f. 68
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1466 (interest on £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>, paid at decreasing intervals)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1467 with those f. 69
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1468 (interest on £100 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math> paid at decreasing intervals and taken to a limit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1469 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1470 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1471 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1472 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1473 <head xml:id="echoid-head17" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1474 Interest upon interest for 7 yeares.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1475 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1476 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1477 <s xml:id="echoid-s179" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1478 The sum of interest upon interest <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1479 continually for every instant <emph style="super">in</emph> seven <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1480 yeares with the principall of 100£ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1481 after the rate of 10 in the 100 for <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1482 a yeare.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1483 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1484 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1485 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1486 <s xml:id="echoid-s180" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1487 201£ + 7s + 6d + <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>0</mn><mn>6</mn><mn>2</mn><mn>0</mn><mn>5</mn><mi>a</mi></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn><mn>0</mn><mn>0</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1488 not <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>7</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1489 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1490 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1491 <pb file="add_6782_f067v" o="67v" n="134"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1492 <pb file="add_6782_f068" o="68" n="135"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1493 <div xml:id="echoid-div38" type="page_commentary" level="2" n="38">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1494 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1495 <s xml:id="echoid-s181" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1496 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1497 <s xml:id="echoid-s181" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1498 Below the rough work crossed out at the top are calculations of interest on £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1499 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1500 The first table shows the interest paid every year for seven years.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1501 The words <foreign xml:lang="lat">continue proportionales</foreign> (continued proportionals)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1502 indicate that each row is obtained by multiplication from the previous row.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1503 The multiplier from each row to the next is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac><mo maxsize="1">)</mo></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1504 The second table shows a similar calculation but now interest is added twice yearly
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1505 and the multiplier is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>b</mi></mrow></mfrac><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1506 The table shows only the first four entries and then the total after 7 years. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1507 The third table repeats the calculation but now interest is added three times yearly
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1508 and the multiplier is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn><mi>b</mi></mrow></mfrac><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1509 The table shows only the first three entries and then the total after 7 years.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1510 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1511 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1512 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1513 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1514 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1515 <s xml:id="echoid-s183" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1516 yeres
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1517 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1518 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1519 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1520 <s xml:id="echoid-s184" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1521 continue proportionales
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1522 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1523 continued proportionals
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1524 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1525 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1526 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1527 <pb file="add_6782_f068v" o="68v" n="136"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1528 <pb file="add_6782_f069" o="69" n="137"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1529 <div xml:id="echoid-div39" type="page_commentary" level="2" n="39">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1530 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1531 <s xml:id="echoid-s185" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1532 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1533 <s xml:id="echoid-s185" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1534 After the rough work crossed out at the top,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1535 the table show the calculation of interest on £100 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1536 paid every year for five years. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1537 The next section is crossed out but the reader is referred by asterisk to an expression lower down the page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1538 Here Harriot has written a general formula for the interest paid on £100
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1539 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math> after <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> years. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1540 In the next calculation Harriot has assumed that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> is infinitely large,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1541 so that the fractions <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mo maxsize="1">(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo maxsize="1">)</mo><mi>n</mi></mrow><mrow><mi>n</mi><mi>n</mi></mrow></mfrac></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mo maxsize="1">(</mo><mi>n</mi><mo>-</mo><mn>2</mn><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo maxsize="1">)</mo><mi>n</mi></mrow><mrow><mi>n</mi><mi>n</mi><mi>n</mi></mrow></mfrac></mstyle></math>, ... can all be taken to be 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1542 Thus he obtains the interest on £100 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math> paid continuously. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1543 In calculating the sum, Harriot has drawn a vertical line that cuts off the calculation after 6 terms.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1544 He notes underneath that £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mn>4</mn></mstyle></math>d (4 pence), that £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mn>4</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math>d,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1545 and that the sum of all the remaining terms will not make up as much as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math>d.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1546 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1547 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1548 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1549 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1550 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1551 <s xml:id="echoid-s187" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1552 yeares
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1553 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1554 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1555 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1556 <s xml:id="echoid-s188" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1557 The summe of interest upon interest <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1558 continually for every instant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1559 the whole yeare with the principall <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1560 of 100£ after the rate of 10 in ye 100 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1561 for the yeare.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1562 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1563 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1564 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1565 <s xml:id="echoid-s189" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1566 not <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math> d
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1567 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1568 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1569 <pb file="add_6782_f069v" o="69v" n="138"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1570 <pb file="add_6782_f070" o="70" n="139"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1571 <div xml:id="echoid-div40" type="page_commentary" level="2" n="40">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1572 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1573 <s xml:id="echoid-s190" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1574 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1575 <s xml:id="echoid-s190" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1576 The tables in the first row show the calculation of interest on £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1577 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math> for four years. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1578 The tables in the second row show the calculation of interest on £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1579 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mn>0</mn></mrow></mfrac></mstyle></math> for four years. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1580 The tables in the third row show the calculation of interest on £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1581 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn><mn>0</mn></mrow></mfrac></mstyle></math> for four years. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1582 The tables in the last row show the calculation of interest on £<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1583 at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mi>c</mi></mrow></mfrac></mstyle></math> for seven years. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1584 The words <foreign xml:lang="lat">continue proportionales</foreign> (continued proportionals)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1585 next to the final table indicate that each row is obtained by multiplication from the previous row.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1586 The multiplier from each row to the next is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>c</mi></mrow></mfrac><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1587 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1588 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1589 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1590 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1591 <pb file="add_6782_f070v" o="70v" n="140"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1592 <pb file="add_6782_f071" o="71" n="141"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1593 <pb file="add_6782_f071v" o="71v" n="142"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1594 <pb file="add_6782_f072" o="72" n="143"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1595 <pb file="add_6782_f072v" o="72v" n="144"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1596 <div xml:id="echoid-div41" type="page_commentary" level="2" n="41">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1597 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1598 <s xml:id="echoid-s192" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1599 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1600 <s xml:id="echoid-s192" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1601 A list of texts and page numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1602 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1603 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1604 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1605 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1606 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1607 <s xml:id="echoid-s194" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1608 Compendium Avicennæ. 17. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1609 Brevi Breviarum pro Baconis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1610 ad <emph style="super">[???]</emph> [???]. 95. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1611 Verbum abreviatum [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1612 Raymondi de Leone Vividi. 26A. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1613 Secretum secretorum naturæ de lazuli <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1614 lapidis philosphonum. 285 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1615 Tractatus trium Bretonum Br. Baconis. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1616 Epistola prima. 293. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1617 Secunda 301. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1618 Tertia 314. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1619 Specatum secretorum. 387.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1620 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1621 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1622 <pb file="add_6782_f073" o="73" n="145"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1623 <div xml:id="echoid-div42" type="page_commentary" level="2" n="42">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1624 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1625 <s xml:id="echoid-s195" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1626 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1627 <s xml:id="echoid-s195" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1628 The choice of numbers on this page suggests that it might have been written in the yeasr 1599?
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1629 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1630 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1631 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1632 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1633 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1634 <s xml:id="echoid-s197" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1635 The denary Arithmetick which is in common use <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1636 doth expresse nombers of figures in a continuall progression <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1637 of which a unit is the first; the second is ten & may <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1638 be termed as in a algebra a roote; the third is a hundred & <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1639 may be termed a square. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1640 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1641 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1642 <pb file="add_6782_f073v" o="73v" n="146"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1643 <pb file="add_6782_f074" o="74" n="147"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1644 <div xml:id="echoid-div43" type="page_commentary" level="2" n="43">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1645 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1646 <s xml:id="echoid-s198" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1647 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1648 <s xml:id="echoid-s198" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1649 At the beginning of this set of sheets Harriot has written: 'Waste papers of figurate nombers'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1650 They are waste only in the sense that they contain rough working. At the same time,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1651 they show Harriot attempting something highly original, namely,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1652 finding formulae for sequences of figurate numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1653 In modern terms, we would say he is fitting third-, fourth- or fifth-degree polynomials
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1654 to numerical sequences. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1655 At the top is the sequence 1, 5, 14, 30, 55, ... of sums of squares
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1656 (or of square-pyramidal numbers, see Add MS 6782, f. 155).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1657 Just below that, Harriot has written the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>9</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>1</mn><mi>a</mi><mo>+</mo><mn>2</mn><mi>a</mi></mstyle></math>, which, it seems,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1658 is his first attempt to find a formula for the numbers in the sequence multiplied by 24
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1659 (that is, 24, 120, 336, ...). Putting <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>1</mn></mstyle></math> gives <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>1</mn><mn>1</mn><mo>+</mo><mn>2</mn></mstyle></math>, as required.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1660 Putting <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>, however, gives <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mo>×</mo><mn>1</mn><mn>6</mn><mo>+</mo><mn>9</mn><mo>×</mo><mn>8</mn><mo>+</mo><mn>1</mn><mn>1</mn><mo>+</mo><mn>4</mn><mo>+</mo><mn>2</mn><mo>×</mo><mn>4</mn><mo>=</mo><mn>1</mn><mn>5</mn><mn>2</mn></mstyle></math>, which is too large.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1661 This calculation can be seen displayed vertically just below the formula.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1662 Harriot notes that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mo>×</mo><mn>2</mn><mn>4</mn><mo>=</mo><mn>1</mn><mn>4</mn><mn>4</mn></mstyle></math> falls short of this total by 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1663 Similar trial and error calculations appear on this and several pages that follow.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1664 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1665 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1666 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1667 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1668 <head xml:id="echoid-head18" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1669 Waste papers. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1670 of figurate <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1671 nombers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1672 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1673 <pb file="add_6782_f074v" o="74v" n="148"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1674 <div xml:id="echoid-div44" type="page_commentary" level="2" n="44">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1675 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1676 <s xml:id="echoid-s200" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1677 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1678 <s xml:id="echoid-s200" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1679 Trials similar to those on f. 74, but now for the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mi>a</mi><mo>+</mo><mn>1</mn><mn>1</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>6</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1680 represented by the coefficients 6, 11, 6, 1. This is evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1681 giving <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>6</mn><mn>0</mn><mo>=</mo><mn>2</mn><mn>4</mn><mo>×</mo><mn>1</mn><mn>5</mn></mstyle></math>;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1682 for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>5</mn></mstyle></math>, giving <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>6</mn><mn>8</mn><mn>0</mn><mo>=</mo><mn>2</mn><mn>4</mn><mo>×</mo><mn>7</mn><mn>0</mn></mstyle></math>; and (lower right) for for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1683 giving <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>2</mn><mn>0</mn><mo>=</mo><mn>2</mn><mn>4</mn><mo>×</mo><mn>5</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1684 It seems Harriot is still trying to fit the sequence 1, 5, 14, 30, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1685 which appears again alongside the coefficients 6, 11, 6, 1 on f. 76v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1686 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1687 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1688 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1689 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1690 <pb file="add_6782_f075" o="75" n="149"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1691 <pb file="add_6782_f075v" o="75v" n="150"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1692 <pb file="add_6782_f076" o="76" n="151"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1693 <pb file="add_6782_f076v" o="76v" n="152"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1694 <div xml:id="echoid-div45" type="page_commentary" level="2" n="45">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1695 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1696 <s xml:id="echoid-s202" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1697 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1698 <s xml:id="echoid-s202" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1699 Further calculations with the coefficients 6, 11, 6, 1 (see f. 74v), now for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>4</mn></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1700 giving <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>8</mn><mn>4</mn><mn>0</mn><mo>=</mo><mn>2</mn><mn>4</mn><mo>×</mo><mn>3</mn><mn>5</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1701 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1702 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1703 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1704 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1705 <pb file="add_6782_f077" o="77" n="153"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1706 <div xml:id="echoid-div46" type="page_commentary" level="2" n="46">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1707 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1708 <s xml:id="echoid-s204" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1709 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1710 <s xml:id="echoid-s204" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1711 On this folio Harriot appears to be searchng for a formula for the sequence 1, 6, 20, 50, ...
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1712 of sums of square-pyramidal numbers (see Add MS 6782, f. 155), or rather,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1713 for those numbers multiplied 24, that is, 24, 144, 480, ... . <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1714 Examples on the left hand side of the page test the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>8</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>2</mn><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1715 (note that 8 + 4 + 10 + 2 = 24). This is evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>, giving 144 (as required)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1716 and for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></math>, giving 492 (too large). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1717 Examples in the bottom left hand corner rearrange the same coefficients in different orders:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1718 (2, 10, 8, 4), (8, 10, 2, 4), (8, 2, 10, 4), etc. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1719 In examples further to the right, the fifth-degree polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>4</mn><mi>a</mi><mo>+</mo><mn>5</mn><mn>0</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>3</mn><mn>5</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1720 represented by the coefficients 24, 50, 35, 10, 1, is evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>, giving 640,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1721 and for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></math> giving 2520.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1722 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1723 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1724 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1725 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1726 <pb file="add_6782_f077v" o="77v" n="154"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1727 <div xml:id="echoid-div47" type="page_commentary" level="2" n="47">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1728 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1729 <s xml:id="echoid-s206" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1730 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1731 <s xml:id="echoid-s206" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1732 This page shows further attempts, as on f. 77, to find coefficients that deliver
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1733 24 (when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>1</mn></mstyle></math>), 144 (when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>), and 480 (when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1734 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1735 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1736 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1737 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1738 <pb file="add_6782_f078" o="78" n="155"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1739 <pb file="add_6782_f078v" o="78v" n="156"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1740 <pb file="add_6782_f079" o="79" n="157"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1741 <pb file="add_6782_f079v" o="79v" n="158"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1742 <pb file="add_6782_f080" o="80" n="159"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1743 <div xml:id="echoid-div48" type="page_commentary" level="2" n="48">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1744 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1745 <s xml:id="echoid-s208" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1746 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1747 <s xml:id="echoid-s208" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1748 On this folio Harriot is seraching for a formula for the sequence 1, 6, 15, 28, ... of hexagonal numbers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1749 (see Add MS 6782, f. 157), or rather, for those numbers multiplied by 24, that is, 24, 144, 360, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1750 Note that some of the coefficients on this page are negative.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1751 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1752 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1753 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1754 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1755 <pb file="add_6782_f080v" o="80v" n="160"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1756 <pb file="add_6782_f081" o="81" n="161"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1757 <div xml:id="echoid-div49" type="page_commentary" level="2" n="49">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1758 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1759 <s xml:id="echoid-s210" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1760 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1761 <s xml:id="echoid-s210" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1762 On this folio Harriot is searching for a formula for the sequence 1, 5, 12, 22, ... of pentagonal numbers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1763 (see f. Add MS 6782, 156), or rather, for those numbers multiplied by 24, that is, 24, 120, 288, ....
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1764 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1765 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1766 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1767 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1768 <pb file="add_6782_f081v" o="81v" n="162"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1769 <div xml:id="echoid-div50" type="page_commentary" level="2" n="50">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1770 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1771 <s xml:id="echoid-s212" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1772 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1773 <s xml:id="echoid-s212" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1774 This folio shows many examples of fifth-degree polynomials, as represented by their coefficients,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1775 evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>5</mn></mstyle></math>. At top left, for example,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1776 the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>0</mn><mi>a</mi><mo>+</mo><mn>2</mn><mn>3</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>5</mn><mn>2</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>3</mn><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> is evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>, giving 840.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1777 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1778 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1779 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1780 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1781 <pb file="add_6782_f082" o="82" n="163"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1782 <div xml:id="echoid-div51" type="page_commentary" level="2" n="51">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1783 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1784 <s xml:id="echoid-s214" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1785 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1786 <s xml:id="echoid-s214" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1787 Like f. 81v, this folio shows examples of fifth-degree polynomials, as represented by their coefficients,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1788 evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>5</mn></mstyle></math>. At top left, for example,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1789 the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>8</mn><mi>a</mi><mo>+</mo><mn>4</mn><mn>5</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>4</mn><mn>0</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>5</mn><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>2</mn><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> is evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></math>, giving 3240.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1790 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1791 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1792 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1793 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1794 <pb file="add_6782_f082v" o="82v" n="164"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1795 <pb file="add_6782_f083" o="83" n="165"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1796 <div xml:id="echoid-div52" type="page_commentary" level="2" n="52">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1797 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1798 <s xml:id="echoid-s216" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1799 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1800 <s xml:id="echoid-s216" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1801 On this folio Harriot appears to be searching a formula for the sequence 1, 7, 27, 77, ...
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1802 of sums of sums of square-pyramidal numbers (see Add MS 6782, f. 155), or rather,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1803 for those numbers multiplied by 120, that is, 120, 840, 3240, ....
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1804 For ths he needs polynmials of the fifth degree.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1805 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1806 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1807 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1808 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1809 <pb file="add_6782_f083v" o="83v" n="166"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1810 <pb file="add_6782_f084" o="84" n="167"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1811 <div xml:id="echoid-div53" type="page_commentary" level="2" n="53">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1812 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1813 <s xml:id="echoid-s218" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1814 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1815 <s xml:id="echoid-s218" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1816 The first reference in the heading is to Michael Stifel, <emph style="it">Arithmetica integra</emph> (1544),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1817 page 15.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1818 For Stifel, a diagonal number was obtained by multiplying the first two entries of a Pythagorean triple.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1819 The diagonal number corresponding to the triple (3, 4, 5), for example, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mo>×</mo><mn>4</mn><mo>=</mo><mn>1</mn><mn>2</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1820 Stifel also defined Pythagorean triples by the ratio of the two shorter sides, in this case <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1821 He was able to write out two lists, or orders, of triples,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1822 one with the shorter side odd (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>, and so on),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1823 the other with the shorter side even (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn><mn>5</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>3</mn><mn>5</mn></mrow><mrow><mn>1</mn><mn>2</mn></mrow></mfrac></mstyle></math>, and so on).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1824 Stifel claimed that all possible triples were included in these two orders. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1825 The second reference in the heading, possibly added a little later, is to Johannes Praetorius (Johann Richter),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1826 <emph style="it">Problema, quod iubet ex quatuor rectis lineis datis quadrilaterum fieri,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1827 quod sit in circulo</emph> (1598). On the final page,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1828 Praetorius discusses the problem of constructing cyclic quadrilaterals with rational sides. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1829 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1830 Harriot sets out to disprove Stifel's claim, by demonstrating the existence of new orders of triples. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1831 His first order (ordo. 1.) is the same as Stifel's first order.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1832 The triples are set out in three columns with differences calculated between rows.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1833 This allows Harriot to extrapolate forwards, but also backwards to a starting triple (1, 0, 1). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1834 The second order (ordo. 2.) is the same as Stifel's second order.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1835 Again the triples are set out in three columns with differences calculated between rows.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1836 As for the first order this allows Harriot to extrapolate backwards to a starting triple (4, 3, 5).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1837 This is the first triple of the first order with the first two entries interchanged.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1838 Perhaps this gave Harriot the idea of interchanging other pairs.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1839 Thus he begins a third and new order (ordo. 3. novus) with (12, 5, 8),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1840 which is the second triple from the first order with the first two entries interchanged.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1841 This order immediately contains (20, 21, 29), which was not included in either of Stifel's orders.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1842 The fourth order begins with (15, 8, 17),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1843 which is the first triple from the second order with the first two entries interchanged.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1844 And so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1845 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1846 By the end of the page, Harriot has six orders, with differences in the left column of 2, 4, 8, 6, 10, 12,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1847 respectively.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1848 This seems to suggest to him a more systematic method of displaying the orders,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1849 which he goes on to do on the next page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1850 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1851 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1852 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1853 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1854 <head xml:id="echoid-head19" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1855 Examinatur Stifelius <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1856 de numeris diagonalibus. pa. 15 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1857 et prætorius. pag. ult
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1858 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1859 An examination of Stifel on diagonal numbers, page 15, and Praetorius, last page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1860 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1861 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1862 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1863 <s xml:id="echoid-s220" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1864 ordo. 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1865 pythag.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1866 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1867 Order 1, Pythagorean
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1868 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1869 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1870 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1871 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1872 <s xml:id="echoid-s221" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1873 ord. 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1874 <reg norm="Platonic" type="abbr">platon</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1875 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1876 Order 2, Platonic.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1877 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1878 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1879 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1880 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1881 <s xml:id="echoid-s222" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1882 hoc est.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1883 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1884 that is:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1885 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1886 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1887 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1888 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1889 <s xml:id="echoid-s223" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1890 Dixit quod rationes omni <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1891 laterum sunt in istis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1892 duobus ordinibus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1893 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1894 He said that all the ratios of sides are in these two orders.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1895 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1896 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1897 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1898 <s xml:id="echoid-s224" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1899 Ego dico quod non.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1900 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1901 I say that is not so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1902 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1903 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1904 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1905 <s xml:id="echoid-s225" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1906 ordines sunt alij <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1907 infiniti.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1908 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1909 <s xml:id="echoid-s226" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1910 Ut per <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1911 sequentia patet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1912 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1913 There are infinitely many other orders. As is clear from what follows.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1914 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1915 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1916 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1917 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1918 <s xml:id="echoid-s227" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1919 ordo. 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1920 ordo. 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1921 ordo. 3. novus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1922 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1923 Order 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1924 Order 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1925 Order 3, new.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1926 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1927 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1928 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1929 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1930 <s xml:id="echoid-s228" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1931 Melior est dispositio ordinum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1932 in alijs chartis sequentibus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1933 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1934 The arrangement of orders is better in the other sheets following.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1935 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1936 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1937 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1938 <pb file="add_6782_f084v" o="84v" n="168"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1939 <div xml:id="echoid-div54" type="page_commentary" level="2" n="54">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1940 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1941 <s xml:id="echoid-s229" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1942 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1943 <s xml:id="echoid-s229" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1944 This folio gives a list of the hypotenuses that have been discovered on the previous page,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1945 with the differences between them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1946 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1947 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1948 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1949 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1950 <head xml:id="echoid-head20" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1951 Hypotenusorum progressio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1952 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1953 A progression of the hypotenuses
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1954 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1955 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1956 <pb file="add_6782_f085" o="85" n="169"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1957 <div xml:id="echoid-div55" type="page_commentary" level="2" n="55">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1958 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1959 <s xml:id="echoid-s231" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1960 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1961 <s xml:id="echoid-s231" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1962 On this folio the orders discovered on the previous sheet (f. 84) are listed systematically.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1963 Each new order begins with the second triple from the previous order,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1964 with the first two entries interchanged. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1965 At the bottom of the page, Harriot notes the starting differences for each order. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1966 He has also written the enigmatic note
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1967 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1968 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1969 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1970 Hic sunt omnes primi sed hic omnes non sunt primi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1971 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1972 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1973 <s xml:id="echoid-s232" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1974 which was greatly to confuse his friend Nathaniel Torporley when he came across it some years later. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1975 For discussion of this and the surrounding sheets see Tanner 1977.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1976 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1977 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1978 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1979 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1980 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1981 <s xml:id="echoid-s234" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1982 1.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1983 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1984 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1985 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1986 <s xml:id="echoid-s235" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1987 1) ordo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1988 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1989 order 1
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1990 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1991 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1992 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1993 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1994 <s xml:id="echoid-s236" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1995 Et sic in cæteribus in infinitum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1996 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1997 And so on for the rest indefinitely.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1998 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	1999 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2000 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2001 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2002 <s xml:id="echoid-s237" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2003 Hic sunt omnes primi <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2004 sed hic omnes non sunt primi.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2005 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2006 Here are all the primes but here not all are prime.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2007 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2008 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2009 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2010 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2011 <s xml:id="echoid-s238" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2012 Nota <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2013 prima Differentia ordinis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2014 primi. 2. 4. sub dupla. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2015 Secundi. 4. 12. tripla <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2016 Tertij. 6. 12. Dupla <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2017 Quarti. 8. 24. tripla <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2018 Quinti. 10. 20. Dupla <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2019 Sexti. 12. 36. tripla <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2020 Septimi. 14. 28. Dupla <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2021 Octavi. 16. 48. tripla <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2022 &c in infinitum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2023 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2024 Note<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2025 First differences of the order <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2026 First double <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2027 Second triple <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2028 Third double <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2029 Fourth triple <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2030 Fifth double <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2031 Sixth triple <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2032 Seventh double <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2033 Eighth triple <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2034 etc. indefinitely
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2035 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2036 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2037 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2038 <pb file="add_6782_f085v" o="85v" n="170"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2039 <pb file="add_6782_f086" o="86" n="171"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2040 <div xml:id="echoid-div56" type="page_commentary" level="2" n="56">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2041 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2042 <s xml:id="echoid-s239" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2043 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2044 <s xml:id="echoid-s239" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2045 Harriot continues his orders 1 to 4 of Pythagorean triples from f. 85.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2046 In each case the orders are continued as far as the hypotenuse closest to 1105.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2047 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2048 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2049 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2050 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2051 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2052 <s xml:id="echoid-s241" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2053 2.) continuationes
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2054 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2055 continuations
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2056 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2057 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2058 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2059 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2060 <s xml:id="echoid-s242" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2061 1) ordinis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2062 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2063 order 1
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2064 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2065 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2066 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2067 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2068 <s xml:id="echoid-s243" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2069 recte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2070 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2071 correct
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2072 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2073 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2074 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2075 <pb file="add_6782_f086v" o="86v" n="172"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2076 <pb file="add_6782_f087" o="87" n="173"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2077 <div xml:id="echoid-div57" type="page_commentary" level="2" n="57">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2078 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2079 <s xml:id="echoid-s244" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2080 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2081 <s xml:id="echoid-s244" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2082 Harriot continues his orders 5 to 7 of Pythagorean triples from f. 85, and adds order 8.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2083 In each case the orders are continued until the hypotenuse is equal to or greater 1105.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2084 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2085 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2086 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2087 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2088 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2089 <s xml:id="echoid-s246" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2090 3.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2091 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2092 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2093 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2094 <s xml:id="echoid-s247" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2095 5 ordo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2096 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2097 order 5
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2098 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2099 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2100 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2101 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2102 <s xml:id="echoid-s248" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2103 recte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2104 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2105 correct
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2106 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2107 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2108 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2109 <pb file="add_6782_f087v" o="87v" n="174"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2110 <pb file="add_6782_f088" o="88" n="175"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2111 <div xml:id="echoid-div58" type="page_commentary" level="2" n="58">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2112 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2113 <s xml:id="echoid-s249" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2114 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2115 <s xml:id="echoid-s249" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2116 Harriot lists his orders 9 to 12 of Pythagorean triples,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2117 continuing in each case until the hypotenuse is greater than 1105.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2118 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2119 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2120 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2121 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2122 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2123 <s xml:id="echoid-s251" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2124 4)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2125 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2126 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2127 <pb file="add_6782_f088v" o="88v" n="176"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2128 <pb file="add_6782_f089" o="89" n="177"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2129 <div xml:id="echoid-div59" type="page_commentary" level="2" n="59">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2130 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2131 <s xml:id="echoid-s252" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2132 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2133 <s xml:id="echoid-s252" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2134 Harriot lists his orders 13 to 22 of Pythagorean triples,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2135 continuing in each case until the hypotenuse is equal to or greater than 1105.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2136 Unfortunately an error in the last step of order 19 has led him to miss one of the triples ending in 1105:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2137 the final set of differences should have been 38, 84, 84,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2138 leading to the triple (817, 744, 1105).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2139 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2140 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2141 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2142 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2143 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2144 <s xml:id="echoid-s254" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2145 <emph style="super">5</emph>.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2146 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2147 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2148 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2149 <s xml:id="echoid-s255" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2150 &c. in infinitum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2151 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2152 etc. indefinitely.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2153 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2154 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2155 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2156 <pb file="add_6782_f089v" o="89v" n="178"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2157 <pb file="add_6782_f090" o="90" n="179"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2158 <div xml:id="echoid-div60" type="page_commentary" level="2" n="60">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2159 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2160 <s xml:id="echoid-s256" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2161 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2162 <s xml:id="echoid-s256" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2163 On this folio, Harriot demonstrates both geometrically and arithmetically that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2164 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mrow><mn>8</mn><mn>5</mn></mrow><mn>2</mn></msup></mrow><mo>=</mo><mrow><msup><mrow><mn>8</mn><mn>4</mn></mrow><mn>2</mn></msup></mrow><mo>+</mo><mrow><msup><mrow><mn>1</mn><mn>2</mn></mrow><mn>2</mn></msup></mrow><mo>+</mo><mrow><msup><mn>4</mn><mn>2</mn></msup></mrow><mo>+</mo><mrow><msup><mn>3</mn><mn>2</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2165 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2166 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2167 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2168 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2169 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2170 <s xml:id="echoid-s258" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2171 one square æquall to many. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2172 whence <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2173 To devide one square into <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2174 many
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2175 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2176 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2177 <pb file="add_6782_f090v" o="90v" n="180"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2178 <pb file="add_6782_f091" o="91" n="181"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2179 <div xml:id="echoid-div61" type="page_commentary" level="2" n="61">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2180 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2181 <s xml:id="echoid-s259" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2182 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2183 <s xml:id="echoid-s259" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2184 An investigation into Pythagorean triples with hypotenuse 1105.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2185 Harriot obtains several such triples by multiplication of triples already known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2186 Those marked 'supra +' or '+ supra' duplicate others earlier in the list. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2187 Three triples are identified by Harriot as prime, that is, with no common factors,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2188 that is, (47, 1104, 1105), (264, 1073, 1105), (576, 943, 1105).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2189 An error in his 19th order, on Add MS 6782, f. 89, has led him to miss a fourth, (817, 744, 1105).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2190 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2191 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2192 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2193 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2194 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2195 <s xml:id="echoid-s261" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2196 supra +
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2197 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2198 as above
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2199 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2200 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2201 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2202 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2203 <s xml:id="echoid-s262" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2204 primi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2205 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2206 prime
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2207 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2208 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2209 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2210 <pb file="add_6782_f091v" o="91v" n="182"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2211 <pb file="add_6782_f092" o="92" n="183"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2212 <pb file="add_6782_f092v" o="92v" n="184"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2213 <pb file="add_6782_f093" o="93" n="185"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2214 <pb file="add_6782_f093v" o="93v" n="186"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2215 <pb file="add_6782_f094" o="94" n="187"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2216 <pb file="add_6782_f094v" o="94v" n="188"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2217 <pb file="add_6782_f095" o="95" n="189"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2218 <pb file="add_6782_f095v" o="95v" n="190"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2219 <div xml:id="echoid-div62" type="page_commentary" level="2" n="62">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2220 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2221 <s xml:id="echoid-s263" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2222 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2223 <s xml:id="echoid-s263" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2224 Successive halving of 90 degrees.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2225 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2226 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2227 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2228 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2229 <pb file="add_6782_f096" o="96" n="191"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2230 <div xml:id="echoid-div63" type="page_commentary" level="2" n="63">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2231 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2232 <s xml:id="echoid-s265" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2233 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2234 <s xml:id="echoid-s265" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2235 Successive halving of 90 degrees, continued from the previous page (f. 95v).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2236 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2237 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2238 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2239 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2240 <pb file="add_6782_f096v" o="96v" n="192"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2241 <pb file="add_6782_f097" o="97" n="193"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2242 <pb file="add_6782_f097v" o="97v" n="194"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2243 <pb file="add_6782_f098" o="98" n="195"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2244 <pb file="add_6782_f098v" o="98v" n="196"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2245 <pb file="add_6782_f099" o="99" n="197"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2246 <pb file="add_6782_f099v" o="99v" n="198"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2247 <pb file="add_6782_f100" o="100" n="199"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2248 <pb file="add_6782_f100v" o="100v" n="200"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2249 <pb file="add_6782_f101" o="101" n="201"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2250 <pb file="add_6782_f101v" o="101v" n="202"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2251 <div xml:id="echoid-div64" type="page_commentary" level="2" n="64">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2252 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2253 <s xml:id="echoid-s267" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2254 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2255 <s xml:id="echoid-s267" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2256 A double-page calculation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>2</mn></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2257 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2258 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2259 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2260 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2261 <pb file="add_6782_f102" o="102" n="203"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2262 <pb file="add_6782_f102v" o="102v" n="204"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2263 <pb file="add_6782_f103" o="103" n="205"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2264 <pb file="add_6782_f103v" o="103v" n="206"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2265 <pb file="add_6782_f104" o="104" n="207"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2266 <pb file="add_6782_f104v" o="104v" n="208"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2267 <div xml:id="echoid-div65" type="page_commentary" level="2" n="65">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2268 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2269 <s xml:id="echoid-s269" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2270 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2271 <s xml:id="echoid-s269" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2272 A calculation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>2</mn></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2273 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2274 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2275 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2276 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2277 <pb file="add_6782_f105" o="105" n="209"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2278 <pb file="add_6782_f105v" o="105v" n="210"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2279 <pb file="add_6782_f106" o="106" n="211"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2280 <div xml:id="echoid-div66" type="page_commentary" level="2" n="66">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2281 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2282 <s xml:id="echoid-s271" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2283 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2284 <s xml:id="echoid-s271" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2285 64 digits of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>2</mn></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2286 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2287 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2288 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2289 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2290 <pb file="add_6782_f106v" o="106v" n="212"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2291 <div xml:id="echoid-div67" type="page_commentary" level="2" n="67">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2292 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2293 <s xml:id="echoid-s273" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2294 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2295 <s xml:id="echoid-s273" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2296 A check on the first few digits of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>2</mn></mrow></msqrt></mstyle></math> by multiplication.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2297 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2298 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2299 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2300 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2301 <pb file="add_6782_f107" o="107" n="213"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2302 <div xml:id="echoid-div68" type="page_commentary" level="2" n="68">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2303 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2304 <s xml:id="echoid-s275" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2305 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2306 <s xml:id="echoid-s275" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2307 A half sheet, very worn, and darker in colour than the pages that follow,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2308 with a title and Harriot's initials. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2309 For a detailed account of the history and the mathematics of the treatise that follows,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2310 see Janet Beery and Jacqueline Stedall,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2311 <emph style="it">Thomas Harriot 19s doctrine of triangular numbers: the 'Magisteria magna'</emph> (2009).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2312 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2313 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2314 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2315 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2316 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2317 <s xml:id="echoid-s277" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2318 De Numeris Triangularibus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2319 et inde <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2320 De progressionibus Arithmeticis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2321 Magisteria magna <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2322 T. H.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2323 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2324 On triangular numbers and thence artihmetic progressions <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2325 The great doctrine of Thomas Harriot.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2326 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2327 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2328 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2329 <pb file="add_6782_f107v" o="107v" n="214"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2330 <pb file="add_6782_f108" o="108" n="215"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2331 <div xml:id="echoid-div69" type="page_commentary" level="2" n="69">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2332 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2333 <s xml:id="echoid-s278" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2334 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2335 <s xml:id="echoid-s278" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2336 Throughout the treatise that follows, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> is to be read as a positive integer. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2337 The table at the top of the page is an array of general triangular numbers:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2338 the first row and first column contain units, the second row and second column contain lengths,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2339 the third row and third column contain triangular numbers, the fourth row and fourth column contain pyramidal numbers,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2340 and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2341 Between the numbers are signs that combine 'plus' and 'equals',
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2342 illustrating the additive property of the table. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2343 The numerators and denominators of the fractions are to be read as products.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2344 Thus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>7</mn><mn>8</mn><mn>9</mn><mo>,</mo><mn>1</mn><mn>0</mn><mo>,</mo><mn>1</mn><mn>1</mn></mrow><mrow><mn>1</mn><mn>2</mn><mn>3</mn><mn>4</mn><mn>5</mn></mrow></mfrac></mstyle></math> in the bottom right-hand corner, for example, is to be read as
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2345 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>7</mn><mo>×</mo><mn>8</mn><mo>×</mo><mn>9</mn><mo>×</mo><mn>1</mn><mn>0</mn><mo>×</mo><mn>1</mn><mn>1</mn></mrow><mrow><mn>1</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>4</mn><mo>×</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mn>9</mn><mn>2</mn><mn>4</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2346 Below the tables Harriot has written general formulae for the numbers in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th row.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2347 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2348 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2349 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2350 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2351 <head xml:id="echoid-head21" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2352 1.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2353 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2354 <pb file="add_6782_f108v" o="108v" n="216"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2355 <pb file="add_6782_f109" o="109" n="217"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2356 <div xml:id="echoid-div70" type="page_commentary" level="2" n="70">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2357 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2358 <s xml:id="echoid-s280" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2359 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2360 <s xml:id="echoid-s280" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2361 The formulae from page 1 (Add MS 6782, f. 108) are expanded by long multiplication,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2362 with each formula used as a starting point for the next.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2363 The formula in the second box, for example, is obtained from the formula in the first box,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2364 by multiplying by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo maxsize="1">)</mo></mstyle></math> and dividing by 3 (as also instructed by Cardano, see Add MS 6782, f. 44).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2365 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2366 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2367 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2368 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2369 <head xml:id="echoid-head22" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2370 2.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2371 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2372 <pb file="add_6782_f109v" o="109v" n="218"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2373 <pb file="add_6782_f110" o="110" n="219"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2374 <div xml:id="echoid-div71" type="page_commentary" level="2" n="71">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2375 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2376 <s xml:id="echoid-s282" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2377 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2378 <s xml:id="echoid-s282" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2379 In the table at the top of the page, the triangular numbers from page 1 (Add MS 6782, f. 108)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2380 are rearranged into a triangular pattern, with the sum of each row on the right. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2381 In the next table, each entry from the top table is written as a fraction, as on page 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2382 Below the table are general formulae for the entries in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo maxsize="1">)</mo></mstyle></math>th row.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2383 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2384 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2385 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2386 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2387 <head xml:id="echoid-head23" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2388 3.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2389 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2390 <pb file="add_6782_f110v" o="110v" n="220"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2391 <pb file="add_6782_f111" o="111" n="221"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2392 <div xml:id="echoid-div72" type="page_commentary" level="2" n="72">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2393 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2394 <s xml:id="echoid-s284" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2395 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2396 <s xml:id="echoid-s284" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2397 The formulae from the bottom of page 3 (Add MS 6782, f. 110), expanded by long multiplication.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2398 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2399 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2400 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2401 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2402 <head xml:id="echoid-head24" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2403 4.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2404 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2405 <pb file="add_6782_f111v" o="111v" n="222"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2406 <pb file="add_6782_f112" o="112" n="223"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2407 <div xml:id="echoid-div73" type="page_commentary" level="2" n="73">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2408 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2409 <s xml:id="echoid-s286" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2410 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2411 <s xml:id="echoid-s286" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2412 At the top of the page are two differences tables.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2413 In each case column headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> may be taken as the starting column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2414 Column <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> contains successive differences between entries in column <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2415 As elsewhere, a triangle broadening downwards thus, Δ, indicates an increasing column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2416 A small square is used to indicate columns of equal entries. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2417 The central table shows a difference table generated from a constant differenc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2418 Now the lower case letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> represent the first entry of each column
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2419 (the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, which for Harriot represented an un unknown quantity, is omitted).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2420 Harriot has drawn a diagonal line under the table generated from a single entry
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2421 in the constant difference column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2422 Two small inset charts to the right of the main table show
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2423 the pattern of increasing and decreasing rows (here they are all increasing)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2424 and the pattern of signs in each column (here they are all <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>+</mo></mstyle></math>). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2425 The lower table contains general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo maxsize="1">)</mo></mstyle></math>th entry
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2426 in each column of the difference table,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2427 using the triangular number coefficients established on page 3 (Add MS 6782, f. 110).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2428 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2429 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2430 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2431 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2432 <head xml:id="echoid-head25" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2433 5.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2434 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2435 <pb file="add_6782_f112v" o="112v" n="224"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2436 <pb file="add_6782_f113" o="113" n="225"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2437 <div xml:id="echoid-div74" type="page_commentary" level="2" n="74">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2438 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2439 <s xml:id="echoid-s288" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2440 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2441 <s xml:id="echoid-s288" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2442 As on page 5 (Add MS 6782, f. 112), this page begins with two difference tables,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2443 but now the columns headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> are decreasing, indicated by a triangle narrowing downwards. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2444 As on page 5, the central table contains formulae for the individual entries.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2445 The two small inset charts to the right of the main table show
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2446 the pattern of increasing and decreasing rows (here they are alternately increasing and decreasing)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2447 and the pattern of signs in each column. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2448 The lower table contains general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo maxsize="1">)</mo></mstyle></math>th entry
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2449 in each column of the difference table,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2450 using the triangular number coefficients established on page 3 (Add MS 6782, f. 110).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2451 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2452 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2453 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2454 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2455 <head xml:id="echoid-head26" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2456 6.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2457 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2458 <pb file="add_6782_f113v" o="113v" n="226"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2459 <pb file="add_6782_f114" o="114" n="227"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2460 <div xml:id="echoid-div75" type="page_commentary" level="2" n="75">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2461 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2462 <s xml:id="echoid-s290" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2463 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2464 <s xml:id="echoid-s290" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2465 Page 7 is similar to page 6 (Add MS 6782, f. 113),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2466 except for a change in the pattern of increasing and decreasing columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2467 The difference table at the top right contains a rare error: the last entry of column <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2468 should be 1031 not 1030.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2469 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2470 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2471 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2472 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2473 <head xml:id="echoid-head27" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2474 7.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2475 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2476 <pb file="add_6782_f114v" o="114v" n="228"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2477 <pb file="add_6782_f115" o="115" n="229"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2478 <div xml:id="echoid-div76" type="page_commentary" level="2" n="76">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2479 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2480 <s xml:id="echoid-s292" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2481 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2482 <s xml:id="echoid-s292" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2483 Here Harriot has listed all possible patterns of increasing (c) and decreasing (d) columns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2484 for difference tables of up to six columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2485 In the lower half of the page, Harriot has produced 32 charts, like those on pages 5 to 7
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2486 (Add MS 6782, f. 111 to f. 113), showing the sign patterns in the column entries,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2487 for each pattern of increasing and decreasing columns, for up to six columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2488 The symbols above charts 1 and 32, which look rather like <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2489 are Harriot's symbols for tangents and secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2490 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> above tables 11 and 22 is his symbol for sines. In each case,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2491 the patterns of c and d columns are those required for the corresponding trigonometric tables.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2492 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2493 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2494 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2495 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2496 <head xml:id="echoid-head28" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2497 8.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2498 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2499 <pb file="add_6782_f115v" o="115v" n="230"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2500 <pb file="add_6782_f116" o="116" n="231"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2501 <div xml:id="echoid-div77" type="page_commentary" level="2" n="77">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2502 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2503 <s xml:id="echoid-s294" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2504 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2505 <s xml:id="echoid-s294" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2506 This page shows general entries in a difference table with six columns,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2507 generated from 24 entries in the constant difference column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2508 As on page 5 (Add MS 6782, f. 112), a diagonal line has been drawn below the entries
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2509 generated from just one entry in the constant difference column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2510 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2511 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2512 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2513 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2514 <head xml:id="echoid-head29" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2515 9.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2516 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2517 <pb file="add_6782_f116v" o="116v" n="232"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2518 <pb file="add_6782_f117" o="117" n="233"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2519 <div xml:id="echoid-div78" type="page_commentary" level="2" n="78">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2520 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2521 <s xml:id="echoid-s296" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2522 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2523 <s xml:id="echoid-s296" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2524 The left hand side of the page contains a difference table with increasing columns,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2525 generated from a constant difference 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2526 In the first table on the right, the column headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2527 contains every third entry (denoted by the note <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>=</mo><mn>3</mn></mstyle></math>) from the column headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2528 In the second table on the right, the column headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2529 contains every second entry (denoted by the note <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>=</mo><mn>2</mn></mstyle></math>) from the column headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2530 The other three tables on the right are constructed in a similar way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2531 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2532 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2533 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2534 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2535 <head xml:id="echoid-head30" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2536 10.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2537 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2538 <pb file="add_6782_f117v" o="117v" n="234"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2539 <pb file="add_6782_f118" o="118" n="235"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2540 <div xml:id="echoid-div79" type="page_commentary" level="2" n="79">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2541 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2542 <s xml:id="echoid-s298" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2543 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2544 <s xml:id="echoid-s298" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2545 This folio is very similar to the previous one (Add MS 6782, f. 117).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2546 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2547 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2548 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2549 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2550 <head xml:id="echoid-head31" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2551 11.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2552 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2553 <pb file="add_6782_f118v" o="118v" n="236"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2554 <pb file="add_6782_f119" o="119" n="237"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2555 <div xml:id="echoid-div80" type="page_commentary" level="2" n="80">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2556 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2557 <s xml:id="echoid-s300" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2558 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2559 <s xml:id="echoid-s300" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2560 This folio is similar to the previous two (Add MS 6782, f. 117 and f. 118)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2561 except for a different pattern of increasing and decreasing columns.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2562 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2563 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2564 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2565 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2566 <head xml:id="echoid-head32" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2567 12.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2568 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2569 <pb file="add_6782_f119v" o="119v" n="238"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2570 <pb file="add_6782_f120" o="120" n="239"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2571 <div xml:id="echoid-div81" type="page_commentary" level="2" n="81">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2572 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2573 <s xml:id="echoid-s302" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2574 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2575 <s xml:id="echoid-s302" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2576 This folio is similar to the previous one (Add MS 6782, f. 119)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2577 except for the opposite pattern of increasing and decreasing columns.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2578 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2579 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2580 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2581 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2582 <head xml:id="echoid-head33" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2583 13.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2584 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2585 <pb file="add_6782_f120v" o="120v" n="240"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2586 <pb file="add_6782_f121" o="121" n="241"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2587 <div xml:id="echoid-div82" type="page_commentary" level="2" n="82">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2588 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2589 <s xml:id="echoid-s304" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2590 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2591 <s xml:id="echoid-s304" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2592 On the right hand side of the page are three partial difference tables from earlier pages;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2593 the first and third tables are from page 10 (Add MS 6782, f. 117) while the second is from page 11 (f. 121).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2594 In each case, Harriot has also listed the first entries of the columns of the original difference table,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2595 denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2596 On the left hand side are algebraic versions of the same partial difference tables.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2597 The first table gives formulae for successive second entries
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2598 of the column beginning with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, together with successive differences. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2599 The second table gives formulae for successive third entries
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2600 of the column beginning with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, together with successive differences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2601 The third table gives formulae for succesive <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2602 of the column beginning with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2603 The final table shows the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th-entry formulae multiplied out,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2604 with differences calculated between them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2605 This demonstrates that the constant difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2606 in a table constructed from every <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entry of the original table, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>n</mi><mi>n</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2607 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2608 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2609 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2610 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2611 <head xml:id="echoid-head34" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2612 14.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2613 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2614 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2615 <s xml:id="echoid-s306" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2616 hoc est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2617 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2618 that is:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2619 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2620 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2621 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2622 <pb file="add_6782_f121v" o="121v" n="242"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2623 <pb file="add_6782_f122" o="122" n="243"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2624 <div xml:id="echoid-div83" type="page_commentary" level="2" n="83">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2625 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2626 <s xml:id="echoid-s307" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2627 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2628 <s xml:id="echoid-s307" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2629 Following from the calculations in the previous folio (Add MS 6782, f. 121)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2630 for the column beginning with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2631 this folio gives the formulae for successive <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2632 from the columns beginning with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> and with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2633 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2634 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2635 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2636 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2637 <head xml:id="echoid-head35" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2638 15.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2639 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2640 <pb file="add_6782_f122v" o="122v" n="244"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2641 <pb file="add_6782_f123" o="123" n="245"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2642 <head xml:id="echoid-head36" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2643 16.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2644 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2645 <div xml:id="echoid-div84" type="page_commentary" level="2" n="84">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2646 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2647 <s xml:id="echoid-s309" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2648 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2649 <s xml:id="echoid-s309" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2650 Following from the calculations in the previous folios (Add MS 6782, f. 122)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2651 for the columns beginning with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2652 this folio gives the formulae for successive <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2653 from the columns beginning with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2654 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2655 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2656 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2657 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2658 <pb file="add_6782_f123v" o="123v" n="246"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2659 <pb file="add_6782_f124" o="124" n="247"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2660 <div xml:id="echoid-div85" type="page_commentary" level="2" n="85">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2661 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2662 <s xml:id="echoid-s311" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2663 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2664 <s xml:id="echoid-s311" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2665 This folio shows the formulae from page 15 (Add MS 6782, f. 122) for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> column,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2666 multiplied out in full and with differences calculated bewteen all entries.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2667 The table is too wide to fit on the page,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2668 so the differences appear in the boxes below the main entries.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2669 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2670 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2671 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2672 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2673 <head xml:id="echoid-head37" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2674 17.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2675 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2676 <pb file="add_6782_f124v" o="124v" n="248"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2677 <pb file="add_6782_f125" o="125" n="249"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2678 <div xml:id="echoid-div86" type="page_commentary" level="2" n="86">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2679 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2680 <s xml:id="echoid-s313" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2681 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2682 <s xml:id="echoid-s313" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2683 This folio shows the formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> columns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2684 from pages 15 and 16 (Add MS 6782, f. 122 and f. 123)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2685 multiplied out in full and with differences calculated between all entries.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2686 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2687 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2688 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2689 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2690 <head xml:id="echoid-head38" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2691 18.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2692 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2693 <pb file="add_6782_f125v" o="125v" n="250"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2694 <pb file="add_6782_f126" o="126" n="251"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2695 <div xml:id="echoid-div87" type="page_commentary" level="2" n="87">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2696 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2697 <s xml:id="echoid-s315" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2698 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2699 <s xml:id="echoid-s315" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2700 On this folio and the next (Add MS 6782, f. 126 and f. 127),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2701 Harriot has used the formulae from page 17 (Add MS 6782, f. 124)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2702 to write equations for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2703 in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2704 He has solved first for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2705 then for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2706 then for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2707 He has ended each calculation with 'RE', indicating 'recto' or 'correct'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2708 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2709 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2710 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2711 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2712 <head xml:id="echoid-head39" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2713 19.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2714 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2715 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2716 <s xml:id="echoid-s317" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2717 1. Canon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2718 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2719 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2720 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2721 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2722 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2723 <pb file="add_6782_f126v" o="126v" n="252"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2724 <pb file="add_6782_f127" o="127" n="253"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2725 <div xml:id="echoid-div88" type="page_commentary" level="2" n="88">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2726 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2727 <s xml:id="echoid-s318" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2728 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2729 <s xml:id="echoid-s318" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2730 This folios is the continuation of page 19 (Add MS 6782, f. 126).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2731 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2732 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2733 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2734 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2735 <head xml:id="echoid-head40" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2736 20.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2737 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2738 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2739 <s xml:id="echoid-s320" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2740 Residuum : 1. canonis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2741 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2742 Remainder of the canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2743 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2744 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2745 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2746 <pb file="add_6782_f127v" o="127v" n="254"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2747 <pb file="add_6782_f128" o="128" n="255"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2748 <div xml:id="echoid-div89" type="page_commentary" level="2" n="89">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2749 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2750 <s xml:id="echoid-s321" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2751 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2752 <s xml:id="echoid-s321" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2753 On this folio Harriot has carried out calculations similar to those on pages 19 and 20
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2754 (Add MS 6782, f. 126 and f. 127),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2755 this time to find equations for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2756 in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2757 Note that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>8</mn><mi>n</mi><mi>n</mi></mstyle></math> in line 7 should be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>8</mn><mi>n</mi><mi>n</mi><mi>n</mi></mstyle></math>; the error is corrected in the next line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2758 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2759 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2760 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2761 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2762 <head xml:id="echoid-head41" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2763 21.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2764 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2765 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2766 <s xml:id="echoid-s323" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2767 1. Canon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2768 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2769 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2770 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2771 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2772 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2773 <pb file="add_6782_f128v" o="128v" n="256"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2774 <pb file="add_6782_f129" o="129" n="257"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2775 <div xml:id="echoid-div90" type="page_commentary" level="2" n="90">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2776 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2777 <s xml:id="echoid-s324" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2778 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2779 <s xml:id="echoid-s324" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2780 On this folio Harriot has carried out calculations similar to those on pages 19, 20, and 21
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2781 (Add MS 6782, f. 126, f. 127, and f. 128),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2782 this time to find equations for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2783 in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2784 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2785 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2786 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2787 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2788 <head xml:id="echoid-head42" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2789 22.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2790 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2791 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2792 <s xml:id="echoid-s326" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2793 1. Canon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2794 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2795 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2796 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2797 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2798 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2799 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2800 <s xml:id="echoid-s327" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2801 1. Canon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2802 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2803 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2804 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2805 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2806 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2807 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2808 <s xml:id="echoid-s328" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2809 1. Canon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2810 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2811 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2812 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2813 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2814 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2815 <pb file="add_6782_f129v" o="129v" n="258"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2816 <pb file="add_6782_f130" o="130" n="259"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2817 <div xml:id="echoid-div91" type="page_commentary" level="2" n="91">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2818 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2819 <s xml:id="echoid-s329" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2820 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2821 <s xml:id="echoid-s329" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2822 On this folio, Harriot has summarized his results from pages 19 and 20 (Add MS 6782, f. 126 and f. 127)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2823 and has extended them to other patterns of increasing and decreasing columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2824 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> in the upper tables indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2825 may be used to interpolate values in tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2826 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> in the lower tables indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2827 may be used to interpolate tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2828 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2829 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2830 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2831 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2832 <head xml:id="echoid-head43" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2833 23.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2834 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2835 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2836 <s xml:id="echoid-s331" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2837 Canones, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2838 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2839 Canons for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2840 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2841 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2842 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2843 <pb file="add_6782_f130v" o="130v" n="260"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2844 <pb file="add_6782_f131" o="131" n="261"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2845 <div xml:id="echoid-div92" type="page_commentary" level="2" n="92">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2846 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2847 <s xml:id="echoid-s332" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2848 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2849 <s xml:id="echoid-s332" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2850 On this folio, Harriot has summarized his results from page 21 (Add MS 6782, f. 128)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2851 and has extended them to other patterns of increasing and decreasing columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2852 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> in the upper tables indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2853 may be used to interpolate values in tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2854 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> in the lower tables indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2855 may be used to interpolate tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2856 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2857 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2858 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2859 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2860 <head xml:id="echoid-head44" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2861 24.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2862 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2863 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2864 <s xml:id="echoid-s334" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2865 Canones, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2866 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2867 Canons for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2868 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2869 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2870 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2871 <pb file="add_6782_f131v" o="131v" n="262"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2872 <pb file="add_6782_f132" o="132" n="263"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2873 <div xml:id="echoid-div93" type="page_commentary" level="2" n="93">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2874 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2875 <s xml:id="echoid-s335" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2876 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2877 <s xml:id="echoid-s335" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2878 On this folio, Harriot has summarized his results from page 22 (Add MS 6782, f. 129)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2879 and has extended them to other patterns of increasing and decreasing columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2880 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> in the upper tables indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2881 may be used to interpolate tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2882 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> in the lower tables indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2883 may be used to interpolate tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2884 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2885 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2886 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2887 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2888 <head xml:id="echoid-head45" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2889 25.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2890 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2891 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2892 <s xml:id="echoid-s337" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2893 Canones, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2894 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2895 Canons for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2896 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2897 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2898 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2899 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2900 <s xml:id="echoid-s338" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2901 Canones, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2902 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2903 Canons for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2904 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2905 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2906 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2907 <pb file="add_6782_f132v" o="132v" n="264"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2908 <pb file="add_6782_f133" o="133" n="265"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2909 <div xml:id="echoid-div94" type="page_commentary" level="2" n="94">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2910 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2911 <s xml:id="echoid-s339" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2912 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2913 <s xml:id="echoid-s339" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2914 This folio contains a set of formulae for interpolating <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo maxsize="1">)</mo></mstyle></math> new terms between each pair of entries
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2915 in the fourth column of a difference table (the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> column).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2916 For reasons of space, Harriot has written the entries for the fourth column below those
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2917 for the first, second, and third columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2918 At the bottom of the page, he has written a single general formula for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>th interpolated term
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2919 in the fourth column. This he calls the 'magisterium', which may here be translated as 'rule'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2920 Since this formula is expressed entirely in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2921 he longer needs to compute <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2922 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2923 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2924 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2925 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2926 <head xml:id="echoid-head46" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2927 26.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2928 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2929 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2930 <s xml:id="echoid-s341" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2931 Pro Magisterio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2932 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2933 For the rule for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2934 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2935 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2936 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2937 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2938 <s xml:id="echoid-s342" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2939 Magisterium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2940 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2941 Rule
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2942 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2943 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2944 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2945 <pb file="add_6782_f133v" o="133v" n="266"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2946 <pb file="add_6782_f134" o="134" n="267"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2947 <div xml:id="echoid-div95" type="page_commentary" level="2" n="95">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2948 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2949 <s xml:id="echoid-s343" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2950 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2951 <s xml:id="echoid-s343" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2952 This page shows formulae analogous to the 'magisterium' on page 26 (Add MS 6782, f. 133)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2953 for the interpolation of difference tables of up to six columns, with all columns increasing. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2954 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2955 may be used to interpolate tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2956 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> in this context is not a fraction,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2957 but indicates that the expression to the left of it
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2958 is the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>th entry of a table interpolated to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> times its original length.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2959 The sign )=( may therefore be read as 'indexed by'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2960 On BL Add MS 6787, f. 352, Harriot experiments with various alternatives for the symbol )=(.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2961 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2962 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2963 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2964 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2965 <head xml:id="echoid-head47" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2966 27.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2967 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2968 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2969 <s xml:id="echoid-s345" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2970 Magisteria
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2971 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2972 Rules
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2973 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2974 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2975 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2976 <pb file="add_6782_f134v" o="134v" n="268"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2977 <pb file="add_6782_f135" o="135" n="269"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2978 <head xml:id="echoid-head48" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2979 28.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2980 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2981 <div xml:id="echoid-div96" type="page_commentary" level="2" n="96">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2982 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2983 <s xml:id="echoid-s346" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2984 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2985 <s xml:id="echoid-s346" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2986 Interpolation formulae as on page 27 (Add MS 6782, f. 134) but now with all columns decreasing. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2987 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> indicate that these formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2988 may be used to interpolate tables of tangents and secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2989 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2990 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2991 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2992 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2993 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2994 <s xml:id="echoid-s348" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2995 Magisteria
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2996 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2997 Rules
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2998 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	2999 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3000 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3001 <pb file="add_6782_f135v" o="135v" n="270"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3002 <pb file="add_6782_f136" o="136" n="271"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3003 <div xml:id="echoid-div97" type="page_commentary" level="2" n="97">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3004 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3005 <s xml:id="echoid-s349" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3006 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3007 <s xml:id="echoid-s349" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3008 Interpolation formulae as on page 27 (Add MS 6782, f. 134) but now
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3009 for columns that are alternately increasing and decreasing. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3010 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> indicates that these formulae may be used to interpolate tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3011 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3012 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3013 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3014 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3015 <head xml:id="echoid-head49" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3016 29.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3017 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3018 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3019 <s xml:id="echoid-s351" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3020 Magisteria
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3021 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3022 Rules
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3023 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3024 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3025 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3026 <pb file="add_6782_f136v" o="136v" n="272"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3027 <pb file="add_6782_f137" o="137" n="273"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3028 <div xml:id="echoid-div98" type="page_commentary" level="2" n="98">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3029 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3030 <s xml:id="echoid-s352" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3031 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3032 <s xml:id="echoid-s352" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3033 Interpolation formulae as on page 29 (Add MS 6782, f. 136) but now
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3034 for columns that are alternately decreasing and increasing. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3035 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> indicates that these formulae may be used to interpolate tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3036 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3037 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3038 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3039 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3040 <head xml:id="echoid-head50" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3041 30.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3042 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3043 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3044 <s xml:id="echoid-s354" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3045 Magisteria
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3046 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3047 Rules
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3048 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3049 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3050 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3051 <pb file="add_6782_f137v" o="137v" n="274"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3052 <pb file="add_6782_f138" o="138" n="275"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3053 <div xml:id="echoid-div99" type="page_commentary" level="2" n="99">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3054 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3055 <s xml:id="echoid-s355" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3056 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3057 <s xml:id="echoid-s355" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3058 The numbers 4, 3, 2, and 1 in the upper righthand corners of pages 31, 32, 33, and 34,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3059 (Add MS 6782, f. 138 to f. 141) indicate that these four folios are closely related
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3060 and could be read in either direction. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3061 This folio brings together the formulae from pages 27 to 30 (Add MS 6782, f. 134 to f. 137). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3062 The coefficients of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3063 are now written as descending rather than ascending powers of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3064 This means that the signs of the coefficients now follow the patterns given in the sign charts
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3065 for all increasing, or all decreasing, or alternately increasing and decreasing columns.<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3066 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> below the upper table indicate that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3067 are required for interpolating tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3068 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> below the lower table indicates that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3069 are required for interpolating tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3070 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3071 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3072 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3073 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3074 <head xml:id="echoid-head51" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3075 31.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3076 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3077 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3078 <s xml:id="echoid-s357" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3079 (4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3080 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3081 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3082 <pb file="add_6782_f138v" o="138v" n="276"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3083 <pb file="add_6782_f139" o="139" n="277"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3084 <div xml:id="echoid-div100" type="page_commentary" level="2" n="100">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3085 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3086 <s xml:id="echoid-s358" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3087 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3088 <s xml:id="echoid-s358" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3089 This folio contains the same interpolation formulae as on page 31,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3090 but now the coefficients of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> have been factorized. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3091 The inclusion of columns headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> in the inset charts, on this and the two following pages
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3092 (Add MS 6782, f. 140 and f. 141), emphasizes that the formulae may be generalized
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3093 to any number of columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3094 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> below the lower left table indicate that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3095 are required for interpolating tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3096 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> below the lower right table indicates that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3097 are required for interpolating tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3098 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3099 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3100 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3101 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3102 <head xml:id="echoid-head52" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3103 32.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3104 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3105 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3106 <s xml:id="echoid-s360" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3107 (3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3108 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3109 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3110 <pb file="add_6782_f139v" o="139v" n="278"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3111 <pb file="add_6782_f140" o="140" n="279"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3112 <div xml:id="echoid-div101" type="page_commentary" level="2" n="101">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3113 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3114 <s xml:id="echoid-s361" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3115 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3116 <s xml:id="echoid-s361" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3117 This folio contains another version of the interpolation formulae on pages 31 and 32
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3118 (Add MS 6782, f. 138 and f. 139),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3119 but now each coefficient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> has its own denominator.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3120 This appears to be Harriot's preferred form. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3121 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> below the lower left table indicate that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3122 are required for interpolating tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3123 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> below the lower right table indicates that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3124 are required for interpolating tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3125 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3126 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3127 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3128 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3129 <head xml:id="echoid-head53" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3130 33.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3131 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3132 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3133 <s xml:id="echoid-s363" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3134 (2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3135 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3136 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3137 <pb file="add_6782_f140v" o="140v" n="280"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3138 <pb file="add_6782_f141" o="141" n="281"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3139 <div xml:id="echoid-div102" type="page_commentary" level="2" n="102">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3140 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3141 <s xml:id="echoid-s364" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3142 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3143 <s xml:id="echoid-s364" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3144 This folio contains the same formulae as page 33 (Add MS 6782, f. 140)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3145 but with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> now replaced by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3146 That is, there is no interpolation. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3147 This page is numbered 1 in its upper righthand corner,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3148 making it the first in the subsequence of pages 34, 33, 32, and 31 (Add MS f. 141 to f. 138).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3149 Harriot explained on the next page (Add MS 6782, f. 142), which is a second version of this one,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3150 also numbered 1 in its upper righthand corner,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3151 that one may begin with the formulae on page 34 (Add MS 6782, 141),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3152 then derive the formulae on page 33 (Add MS 6782, f. 140) by replacing <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3153 That is, one can reverse the sequence of pages 31 to 34. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3154 As on pages 32 and 33 (Add MS 6782, f. 139 and f. 140)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3155 the sign charts show how to adapt the formulae to different patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3156 of increasing and decreasing columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3157 The symbols <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>σ</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math> below the lower left table indicate that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3158 are required for interpolating tables of tangents and secants. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3159 The symbol <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>υ</mi></mstyle></math> below the lower right table indicates that these patterns
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3160 are required for interpolating tables of sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3161 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3162 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3163 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3164 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3165 <head xml:id="echoid-head54" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3166 34.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3167 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3168 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3169 <s xml:id="echoid-s366" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3170 (1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3171 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3172 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3173 <pb file="add_6782_f141v" o="141v" n="282"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3174 <pb file="add_6782_f142" o="142" n="283"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3175 <div xml:id="echoid-div103" type="page_commentary" level="2" n="103">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3176 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3177 <s xml:id="echoid-s367" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3178 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3179 <s xml:id="echoid-s367" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3180 On this folio, Harriot explains the relationship between the formulae on pages 33 and 34
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3181 (Add MS 6782, f. 140 and f. 141), and their common origin in those that appeared earlier,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3182 on page 5 (Add MS 6782, f. 112). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3183 In the lower half of the page, just below the dividing line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3184 Harriot replaces <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> in formula 3) from page 34,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3185 arriving at formula 3) from page 33.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3186 In this case, he is using <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> to denote an ordinary fraction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3187 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3188 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3189 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3190 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3191 <head xml:id="echoid-head55" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3192 34.) 2<emph style="super">o</emph>.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3193 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3194 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3195 <s xml:id="echoid-s369" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3196 1.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3197 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3198 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3199 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3200 <s xml:id="echoid-s370" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3201 Etsi species quæ habentur (pag: 34.1.) ortum ducunt ex (pag: 33.2.) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3202 Attamen primam originem videre licet pag. 5. ubi illæ omnes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3203 appareat notatæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3204 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3205 Although the cases we have on page 34.1 arise from those on page 33.2,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3206 nevertheless one may see their origins on page 5 where all of them appear in notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3207 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3208 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3209 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3210 <s xml:id="echoid-s371" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3211 Utile etiam ac incundum est, considerare harum reductionum (vide versa) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3212 ad species in pag: 33.2. quæ huius operis sunt magisteria maxima.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3213 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3214 It is useful and also pleasing to consider (conversely) the reduction to the cases on page 33.2,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3215 which are the most important rules of this work.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3216 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3217 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3218 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3219 <s xml:id="echoid-s372" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3220 Examplum unum sufficiet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3221 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3222 One example will suffice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3223 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3224 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3225 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3226 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3227 <s xml:id="echoid-s373" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3228 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mo>=</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3229 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3230 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mo>=</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3231 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3232 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3233 <s xml:id="echoid-s374" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3234 Et species reducta erit: (ut pag: 33.2.) et ut sequitur:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3235 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3236 And the cases will be reduced (as on page 33.2) and as follows:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3237 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3238 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3239 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3240 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3241 <s xml:id="echoid-s375" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3242 Fit ita: Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mo>=</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3243 erit:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3244 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3245 Let it be done thus: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3246 then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3247 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3248 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3249 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3250 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3251 <s xml:id="echoid-s376" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3252 Et sic de alijs speciebus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3253 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3254 And so on for other cases.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3255 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3256 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3257 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3258 <pb file="add_6782_f142v" o="142v" n="284"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3259 <pb file="add_6782_f143" o="143" n="285"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3260 <div xml:id="echoid-div104" type="page_commentary" level="2" n="104">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3261 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3262 <s xml:id="echoid-s377" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3263 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3264 <s xml:id="echoid-s377" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3265 On this and the following folio (Add MS 6782, f. 144),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3266 Harriot gives numerical examples of his interpolation method. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3267 At the top of the page are formulae for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> and for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3268 for difference tables with two columns.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3269 Below that are four examples of tables with two columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3270 The table on the left, with columns headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, is interpolated
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3271 first to six, then four, then five times the number of original entries;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3272 that is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> takes the values 6, then 4, then 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3273 The symbol * next to the interpolated tables marks entries from the original lefthand table. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3274 Below the tables, the first column of working uses the formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> from the top of the page,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3275 to obtain the entries 17, 77, and 149 in the difference table on the left. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3276 The second column of working uses the formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> from the top of the page,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3277 to obtain one entry in each of the three remaining difference tables. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3278 The third column of working presents the converse problem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3279 showing how to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> ),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3280 given values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> and an entry <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3281 Where the solution is not an integer, Harriot replaces <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3282 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3283 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3284 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3285 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3286 <head xml:id="echoid-head56" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3287 35.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3288 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3289 <pb file="add_6782_f143v" o="143v" n="286"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3290 <pb file="add_6782_f144" o="144" n="287"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3291 <div xml:id="echoid-div105" type="page_commentary" level="2" n="105">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3292 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3293 <s xml:id="echoid-s379" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3294 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3295 <s xml:id="echoid-s379" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3296 This folio gives further numerical examples of interpolation for tables with three columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3297 As on page 35 (Add MS 6782, f. 143), Harriot gives the appropriate <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> formulae
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3298 at the top of the page. The formula in the first line is from page 33 (Add MS 6782, f. 140),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3299 while the formulae on the second line are from page 32 (Add MS 6782, f. 139). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3300 The difference table on the left (headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>) is interpolated
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3301 to five times, and then twice, the number of original entries;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3302 that is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> takes the values 5 and 2, respectively. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3303 The working in the first column illustrates the use of the formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3304 to calculate values in the left hand table. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3305 The working in the second column illustrates the use of the formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3306 to calculate the first new value in the second table (indexed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3307 and the third new value in the third table (indexed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3308 The working in the third column shows, as on page 35 (Add MS 6782, f. 143), how to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3309 given values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>, and an entry <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3310 In this case the working leads to a quadratic equation for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3311 which Harriot solves by completing the square.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3312 As on page 35, the solution is not an integer, and so Harriot replaces <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3313 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3314 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3315 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3316 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3317 <head xml:id="echoid-head57" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3318 36.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3319 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3320 <pb file="add_6782_f144v" o="144v" n="288"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3321 <pb file="add_6782_f145" o="145" n="289"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3322 <div xml:id="echoid-div106" type="page_commentary" level="2" n="106">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3323 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3324 <s xml:id="echoid-s381" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3325 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3326 <s xml:id="echoid-s381" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3327 This folios contains an interpolation formula from the 'Magisteria'
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3328 but instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, ...
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3329 we now have <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>p</mi><mn>1</mn></msup></mrow></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>p</mi><mn>2</mn></msup></mrow></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>p</mi><mn>3</mn></msup></mrow></mstyle></math>, ... (these are superscripts, not powers). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3330 The notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>P</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>D</mi><mn>1</mn></msup></mrow></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>D</mi><mn>2</mn></msup></mrow></mstyle></math>, ... at the top of the page is unusual;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3331 the formula is otherwise identical to formula 5) from page 33.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3332 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3333 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3334 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3335 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3336 <pb file="add_6782_f145v" o="145v" n="290"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3337 <pb file="add_6782_f146" o="146" n="291"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3338 <div xml:id="echoid-div107" type="page_commentary" level="2" n="107">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3339 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3340 <s xml:id="echoid-s383" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3341 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3342 <s xml:id="echoid-s383" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3343 Interpolated tables, see page 35 of the 'Magisteria' (Add MS 6782, f. 143).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3344 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3345 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3346 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3347 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3348 <pb file="add_6782_f146v" o="146v" n="292"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3349 <div xml:id="echoid-div108" type="page_commentary" level="2" n="108">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3350 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3351 <s xml:id="echoid-s385" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3352 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3353 <s xml:id="echoid-s385" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3354 This folio contains interpolation formulae similar to those on page 32 (Add MS 6782, f. 139). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3355 It also contains a title similar, but not identical, to that at the beginning of the 'Magisteria'
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3356 (Add MS 6782, f. 107).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3357 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3358 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3359 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3360 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3361 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3362 <s xml:id="echoid-s387" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3363 THOMÆ HARIOTI <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3364 Magisteria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3365 Numerorum Trangularium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3366 et inde <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3367 Progressionum Arithmeticarum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3368 (veteribus et recentioribus ignota) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3369 incognita)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3370 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3371 THOMAS HARRIOT'S doctrine of triangular numbers and thence arithmetic progressions <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3372 (unkonwn and unrecognized by ancient and more recent authors)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3373 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3374 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3375 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3376 <pb file="add_6782_f147" o="147" n="293"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3377 <div xml:id="echoid-div109" type="page_commentary" level="2" n="109">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3378 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3379 <s xml:id="echoid-s388" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3380 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3381 <s xml:id="echoid-s388" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3382 The two lines at the end of the page have nothing to do with the mathematics above them,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3383 and are not apparently connected with each other.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3384 <foreign xml:lang="lat">'Porcus per taurum sequitur vestigia ferri'</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3385 is the first line of an epitaph engraved on the tombstone of Edmund Bunny,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3386 rector of Bolton Percy and canon of York,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3387 who died in February 1617/8 and was interred in York Minster:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3388 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3389 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3390 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3391 Porcus per taurum sequitur vestigia ferri Â <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3392 Anser ovem maculat, cui potum vacca ministrat. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3393 Expone et redde sensum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3394 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3395 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3396 <s xml:id="echoid-s389" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3397 This is an illustration of synecdoche, in which a part is referred to as the whole;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3398 thus the pig (lard, here as used to lubricate cobbler's thread) follows the footprints of the iron (needle)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3399 through the bull (leather); the goose (quill), to whom the cow (inkhorn) provides drink (ink), stains the sheep (skin).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3400 (The standard version has
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3401 <foreign xml:lang="lat">variat</foreign> instead of <foreign xml:lang="lat">maculat</foreign>.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3402 <foreign xml:lang="lat">Expone et redde sensum</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3403 is an instruction to the student: 'explain and translate'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3404 It ispossible that <foreign xml:lang="lat">porcus</foreign> is a play on Percy.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3405 If the York epitaph was Harriot's source, it gives us a possible date of 1618 for this folio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3406 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3407 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3408 <s xml:id="echoid-s390" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3409 'Bombardagladiofunhastiflammiloquentes'
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3410 (Breathing bombs, swords, death, spears, and flames)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3411 is from a Latin translation by the 16th-century German humanist Martin Crucius of a Greek verse
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3412 (perhaps also by Crucius) consisting of compound words.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3413 The verse appears in the preface to the <emph style="it">Opera omnnia theologica</emph> (1583) of Lambert Daneau
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3414 and in the third edition of his <emph style="it">Elenchi hæreticorum</emph> (1592).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3415 The same line appears also in Add MS 6788, f. 50.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3416 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3417 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3418 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3419 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3420 <head xml:id="echoid-head58" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3421 A.1. Ad numeros triangulos <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3422 quadratos <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3423 pentagonos &c. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3424 et illorum progenies
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3425 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3426 On triangular, square, pentagonal numbers, and their progeny
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3427 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3428 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3429 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3430 <s xml:id="echoid-s392" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3431 Generaliter
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3432 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3433 Generally
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3434 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3435 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3436 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3437 <s xml:id="echoid-s393" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3438 Ad progressiones arithmeticas <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3439 incipientes ab unitate vel quovis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3440 numero; quolibet etiam excessu <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3441 progredientes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3442 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3443 For arithmetic porgressions starting from one or any number; proceeding with whatever excess.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3444 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3445 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3446 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3447 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3448 <s xml:id="echoid-s394" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3449 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. primus numerus in progressione. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3450 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. excessus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3451 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>. numerus loci in progressione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3452 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3453 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. the first number in the progression <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3454 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. the excess <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3455 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>. the number of places in the progression
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3456 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3457 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3458 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3459 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3460 <s xml:id="echoid-s395" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3461 Quomodo istæ æqautiones <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3462 continuentur ad infinitum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3463 apparet in altera charta.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3464 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3465 By what meanst these equations may be continued indefinitely appears in another sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3466 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3467 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3468 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3469 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3470 <s xml:id="echoid-s396" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3471 porcus per taurum sequitur vestigia ferri. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3472 Bombardagladiofunhastiflammiloquentes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3473 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3474 The pig follows the footsteps of the iron through the bull. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3475 Breathing bombs, swords, death, spears, and flames.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3476 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3477 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3478 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3479 <pb file="add_6782_f147v" o="147v" n="294"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3480 <pb file="add_6782_f148" o="148" n="295"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3481 <div xml:id="echoid-div110" type="page_commentary" level="2" n="110">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3482 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3483 <s xml:id="echoid-s397" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3484 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3485 <s xml:id="echoid-s397" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3486 Rules for the numbers in six successive columns,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3487 generated from a constant difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math> in column 0.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3488 The first entry in each column is also <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3489 The expression in the first box, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mi>n</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3490 gives the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entry in the first column (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mi>p</mi></mstyle></math>, and so on). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3491 The expression in the second box, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mi>n</mi><mi>n</mi><mo>+</mo><mn>1</mn><mi>p</mi><mi>n</mi></mstyle></math>, divided by 2,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3492 gives the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entry in the second column (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>0</mn><mi>p</mi></mstyle></math>, and so on). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3493 The expression in the third box, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mi>n</mi><mi>n</mi><mi>n</mi><mo>+</mo><mn>3</mn><mi>p</mi><mi>n</mi><mi>n</mi><mo>+</mo><mn>2</mn><mi>p</mi><mi>n</mi></mstyle></math>, divided by 6,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3494 gives the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entry in the third column (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>0</mn><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>0</mn><mi>p</mi></mstyle></math>, and so on). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3495 The layout shows how the general term in row <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mo>+</mo><mn>1</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3496 is generated from the general term in row <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3497 by multiplying by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>+</mo><mi>k</mi></mstyle></math> and dividing by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mo>+</mo><mn>1</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3498 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3499 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3500 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3501 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3502 <head xml:id="echoid-head59" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3503 A.1.) Ad numeros triangulos et illorum progenies.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3504 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3505 On triangular numbers and their progeny
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3506 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3507 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3508 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3509 <s xml:id="echoid-s399" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3510 In Via Generali.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3511 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3512 In a general way
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3513 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3514 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3515 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3516 <pb file="add_6782_f148v" o="148v" n="296"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3517 <pb file="add_6782_f149" o="149" n="297"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3518 <div xml:id="echoid-div111" type="page_commentary" level="2" n="111">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3519 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3520 <s xml:id="echoid-s400" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3521 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3522 <s xml:id="echoid-s400" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3523 This folio shows how to generate the coeffcients from the previous page, f. 148.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3524 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3525 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3526 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3527 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3528 <head xml:id="echoid-head60" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3529 A.2. Ad æquationes numerorum figuratorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3530 ut continuentur ad libitum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3531 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3532 On equations of figurate numbers so that they may be continued at will
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3533 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3534 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3535 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3536 <s xml:id="echoid-s402" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3537 In genere.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3538 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3539 In general
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3540 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3541 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3542 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3543 <pb file="add_6782_f149v" o="149v" n="298"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3544 <pb file="add_6782_f150" o="150" n="299"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3545 <div xml:id="echoid-div112" type="page_commentary" level="2" n="112">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3546 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3547 <s xml:id="echoid-s403" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3548 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3549 <s xml:id="echoid-s403" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3550 This folio shows calculations similar to those on f. 148, but now <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>+</mo><mi>k</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3551 has been replaced by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mo>+</mo><mi>k</mi><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3552 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3553 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3554 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3555 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3556 <head xml:id="echoid-head61" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3557 A.3. Ad æquationes numerorum figuratorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3558 ut continuentur ad libitum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3559 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3560 On equations of figurate numbers so that they may be continued at will
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3561 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3562 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3563 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3564 <s xml:id="echoid-s405" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3565 in Genere.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3566 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3567 in general
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3568 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3569 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3570 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3571 <pb file="add_6782_f150v" o="150v" n="300"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3572 <pb file="add_6782_f151" o="151" n="301"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3573 <pb file="add_6782_f151v" o="151v" n="302"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3574 <pb file="add_6782_f152" o="152" n="303"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3575 <pb file="add_6782_f152v" o="152v" n="304"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3576 <pb file="add_6782_f153" o="153" n="305"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3577 <div xml:id="echoid-div113" type="page_commentary" level="2" n="113">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3578 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3579 <s xml:id="echoid-s406" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3580 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3581 <s xml:id="echoid-s406">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3582 In the upper left table, the key column is the one beneath the sketch of a triangular prism.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3583 The numbers beneath the sketch are those needed to construct triangular prisms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3584 with length equal to one side of the base: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>=</mo><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mo>=</mo><mn>2</mn><mo>×</mo><mn>3</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>8</mn><mo>=</mo><mn>3</mn><mo>×</mo><mn>6</mn></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3585 and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3586 These are also the pentagonal-pyramidal numbers 1, 6, 18, ... as calculated in f. 156. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3587 Successive sums of these numbers are shown in the column to the left headed S (for sum). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3588 Successive differences are shown in the columns to the right.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3589 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3590 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3591 <s xml:id="echoid-s407">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3592 In the upper right table, the key column is the one beneath the sketch of a cube.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3593 The numbers beneath the sketch are the cube numbers, which can also be thought of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3594 (in keeping with the previous table) as the numbers needed to construct square prisms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3595 with height equal to one side of the base: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>=</mo><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>8</mn><mo>=</mo><mn>2</mn><mo>×</mo><mn>4</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>7</mn><mo>=</mo><mn>3</mn><mo>×</mo><mn>9</mn></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3596 and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3597 Successive sums are shown in the column to the left headed S (for sum). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3598 Successive differences are shown in the columns to the right. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3599 The column beginning 1, 7, 19, 37, ... is marked 'hexagonae equianguli 19 (equiangled hexagons);
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3600 it is possible that at first glance Harriot mistook this column for
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3601 the the hexagonal-pyramidal numbers 1, 7, 22, 50, ....
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3602 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3603 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3604 <s xml:id="echoid-s408">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3605 In the lower left table, the key column is the one beneath the sketch of a pentagonal prism.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3606 The numbers beneath the sketch are the numbers needed to construct pentagonal prisms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3607 with length equal to one side of the base: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>=</mo><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>0</mn><mo>=</mo><mn>2</mn><mo>×</mo><mn>5</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>6</mn><mo>=</mo><mn>3</mn><mo>×</mo><mn>1</mn><mn>2</mn></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3608 and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3609 Successive sums are shown in the column to the left headed S (for sum). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3610 Successive differences are shown in the columns to the right.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3611 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3612 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3613 <s xml:id="echoid-s409">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3614 In the lower right table, the key column is the one beneath the sketch of a hexagonal prism.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3615 The numbers beneath the sketch are the numbers needed to construct hexagonal prisms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3616 with length equal to one side of the base: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>=</mo><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>2</mn><mo>=</mo><mn>2</mn><mo>×</mo><mn>6</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mn>5</mn><mo>=</mo><mn>3</mn><mo>×</mo><mn>1</mn><mn>5</mn></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3617 and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3618 Successive sums are shown in the column headed to the left headed S (for sum). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3619 Successive differences are shown in the columns to the right.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3620 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3621 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3622 <s xml:id="echoid-s410" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3623 The formulae at the bottom of the page are for sums of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3624 triangular, square, pentagonal, and hexagonal prisms.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3625 Thus the sum of the first two triangular prisms is shown in the upper left table as 1 + 6 = 7.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3626 The same number may be calculated from the formula <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>3</mn><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>9</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>2</mn><mi>a</mi></mrow><mrow><mn>2</mn><mn>4</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3627 by putting <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3628 For clues as to how Harriot found and tested these formulae,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3629 see ARITHMETIC/Figurate numbers/Fitting polynomials to sequences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3630 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3631 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3632 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3633 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3634 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3635 <s xml:id="echoid-s412" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3636 columnæ [triangulari]æ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3637 quæ sint pyramides [pentagones].
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3638 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3639 Triangular prism numbers, which are also pentagonal pyramidals
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3640 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3641 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3642 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3643 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3644 <s xml:id="echoid-s413" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3645 columnæ tetragonæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3646 seu cubi.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3647 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3648 Four-sided prism numbers, or cubes
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3649 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3650 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3651 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3652 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3653 <s xml:id="echoid-s414" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3654 Hexagones æquianguli.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3655 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3656 Equiangular hexagonals
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3657 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3658 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3659 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3660 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3661 <s xml:id="echoid-s415" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3662 columnæ [pentagon]æ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3663 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3664 Pentagonal prisms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3665 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3666 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3667 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3668 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3669 <s xml:id="echoid-s416" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3670 columnæ <reg norm="hexagonae" type="abbr">Hexag</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3671 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3672 hexagonal prisms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3673 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3674 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3675 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3676 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3677 <s xml:id="echoid-s417" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3678 per Reductionem
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3679 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3680 by reduction
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3681 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3682 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3683 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3684 <pb file="add_6782_f153v" o="153v" n="306"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3685 <pb file="add_6782_f154" o="154" n="307"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3686 <div xml:id="echoid-div114" type="page_commentary" level="2" n="114">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3687 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3688 <s xml:id="echoid-s418" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3689 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3690 <s xml:id="echoid-s418" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3691 The numerical tables on the right list, from right to left:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3692 units, lengths, triangular numbers, triangular-pyramidal naumbers, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3693 The expressions on the left are general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>th entry in each column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3694 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3695 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3696 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3697 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3698 <head xml:id="echoid-head62" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3699 De numeris triangulis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3700 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3701 On triangular numbers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3702 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3703 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3704 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3705 <s xml:id="echoid-s420" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3706 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>) est numerus locorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3707 seu radix.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3708 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3709 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>) is the number of places, or the root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3710 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3711 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3712 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3713 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3714 <s xml:id="echoid-s421" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3715 Quomodo istæ æquationes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3716 continuentur ad libitum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3717 apparet in Chartis. A.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3718 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3719 How these equations may be continued at will is shown in sheet A.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3720 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3721 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3722 Sheet A is probably Add MS 6782, f. 237.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3723 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3724 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3725 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3726 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3727 <s xml:id="echoid-s422" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3728 The difference of difference of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3729 squares is 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3730 The <reg norm="difference" type="abbr">diff</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3731 of <reg norm="difference" type="abbr">diff</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3732 of <reg norm="difference" type="abbr">diff</reg>: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3733 of cubes is 6 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3734 of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>: is 24. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3735 of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> is 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3736 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3737 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3738 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3739 <s xml:id="echoid-s423" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3740 Of progressions the same <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3741 make <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3742 Triangular <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3743 Square <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3744 Pentagonall <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3745 nombers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3746 &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3747 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3748 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3749 <pb file="add_6782_f154v" o="154v" n="308"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3750 <pb file="add_6782_f155" o="155" n="309"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3751 <div xml:id="echoid-div115" type="page_commentary" level="2" n="115">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3752 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3753 <s xml:id="echoid-s424" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3754 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3755 <s xml:id="echoid-s424" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3756 The numerical table at the top of the page lists, from right to left:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3757 odd numbers, square numbers, square-pyramidal numbers, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3758 The column on the far right is headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> for root, that is,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3759 the length of the side of each figure. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3760 An intercalated column shows a constant difference 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3761 The column under the short line (the side) gives the sequence 1, 3, 5, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3762 in which the differences are 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3763 The column under the square gives the square numbers 1, 4, 9, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3764 whose differences are 1, 3, 5, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3765 The column under the square-pyramid gives the square-pyramidal numbers 1, 5, 14, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3766 whose differences are 1, 4, 9, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3767 And so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3768 The expressions below the table are general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>th entry in each column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3769 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3770 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3771 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3772 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3773 <pb file="add_6782_f155v" o="155v" n="310"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3774 <pb file="add_6782_f156" o="156" n="311"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3775 <div xml:id="echoid-div116" type="page_commentary" level="2" n="116">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3776 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3777 <s xml:id="echoid-s426" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3778 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3779 <s xml:id="echoid-s426" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3780 The numerical table at the top of the page lists
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3781 pentagonal numbers, pentagonal-pyramidal numbers, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3782 The column on the far right is headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> for root, that is,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3783 the length of the side of each figure. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3784 An intercalated column shows a constant difference 3. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3785 The column under the short line (the side) gives the sequence 1, 4, 7, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3786 in which the differences are 3. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3787 The column under the pentagon gives the pentagonal numbers 1, 5, 12, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3788 whose differences are 1, 4, 7, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3789 The column under the pentagonal-pyramid gives the pentagonal-pyramidal numbers 1, 6, 18, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3790 whose differences are 1, 5, 12, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3791 And so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3792 The expressions below the table are general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>th entry in each column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3793 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3794 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3795 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3796 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3797 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3798 <s xml:id="echoid-s428" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3799 Of the rootes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3800 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3801 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3802 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3803 <s xml:id="echoid-s429" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3804 A unit is the first [first pentagonal number].
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3805 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3806 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3807 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3808 <s xml:id="echoid-s430" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3809 Omitte the first & the summe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3810 of the next two, is 5. [the second pentagonal number]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3811 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3812 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3813 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3814 <s xml:id="echoid-s431" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3815 Omitte two rootes, & the summe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3816 of the next 3, is 12. [the third pentagonal number]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3817 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3818 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3819 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3820 <s xml:id="echoid-s432" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3821 Omitte 3 rootes, & the summe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3822 of the next 4, is 22. [the fourth pentagonal number] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3823 &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3824 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3825 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3826 <pb file="add_6782_f156v" o="156v" n="312"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3827 <pb file="add_6782_f157" o="157" n="313"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3828 <div xml:id="echoid-div117" type="page_commentary" level="2" n="117">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3829 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3830 <s xml:id="echoid-s433" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3831 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3832 <s xml:id="echoid-s433" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3833 The numerical table at the top of the page lists
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3834 hexagonal numbers, hexagonal-pyramidal numbers, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3835 The column on the far right is headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> for root, that is,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3836 the length of the side of each figure. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3837 An intercalated column shows a constant difference 4. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3838 The column under the short line (the side) gives the sequence 1, 5, 9, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3839 in which the differences are 4. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3840 The column under the hexagon gives the hexagonal numbers 1, 6, 15, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3841 whose differences are 1, 5, 9, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3842 The column under the hexagonal-pyramid gives the hexagonal-pyramidal numbers 1, 7, 22, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3843 whose differences are 1, 6, 15, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3844 And so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3845 The expressions below the table are general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>th entry in each column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3846 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3847 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3848 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3849 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3850 <pb file="add_6782_f157v" o="157v" n="314"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3851 <pb file="add_6782_f158" o="158" n="315"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3852 <div xml:id="echoid-div118" type="page_commentary" level="2" n="118">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3853 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3854 <s xml:id="echoid-s435" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3855 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3856 <s xml:id="echoid-s435" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3857 The numerical table at the top of the page lists
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3858 heptagonal numbers, heptagonal-pyramidal numbers, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3859 The column on the far right is headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> for root, that is,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3860 the length of the side of each figure. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3861 An intercalated column shows a constant difference 5. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3862 The column under the short line (the side) gives the sequence 1, 6, 11, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3863 in which the differences are 5. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3864 The column under the heptagon gives the heptagonal numbers 1, 7, 18, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3865 whose differences are 1, 6, 11, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3866 The column under the heptagonal-pyramid gives the heptagonal-pyramidal numbers 1, 8, 26, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3867 whose differences are 1, 7, 18, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3868 And so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3869 The expressions below the table are general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>th entry in each column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3870 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3871 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3872 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3873 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3874 <pb file="add_6782_f158v" o="158v" n="316"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3875 <pb file="add_6782_f159" o="159" n="317"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3876 <div xml:id="echoid-div119" type="page_commentary" level="2" n="119">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3877 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3878 <s xml:id="echoid-s437" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3879 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3880 <s xml:id="echoid-s437" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3881 The numerical table at the top of the page lists
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3882 octagonal numbers, octagonal-pyramidal numbers, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3883 The column on the far right is headed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> for root, that is,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3884 the length of the side of each figure. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3885 An intercalated column shows a constant difference 6. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3886 The column under the short line (the side) gives the sequence 1, 7, 13, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3887 in which the differences are 6. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3888 The column under the octagon gives the octagonal numbers 1, 8, 21, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3889 whose differences are 1, 7, 13, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3890 The column under the octagonal-pyramid gives the octagonal-pyramidal numbers 1, 9, 30, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3891 whose differences are 1, 8, 21, .... <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3892 And so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3893 The expressions below the table are general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>th entry in each column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3894 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3895 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3896 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3897 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3898 <pb file="add_6782_f159v" o="159v" n="318"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3899 <pb file="add_6782_f160" o="160" n="319"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3900 <pb file="add_6782_f160v" o="160v" n="320"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3901 <pb file="add_6782_f161" o="161" n="321"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3902 <pb file="add_6782_f161v" o="161v" n="322"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3903 <pb file="add_6782_f162" o="162" n="323"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3904 <pb file="add_6782_f162v" o="162v" n="324"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3905 <pb file="add_6782_f163" o="163" n="325"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3906 <div xml:id="echoid-div120" type="page_commentary" level="2" n="120">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3907 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3908 <s xml:id="echoid-s439" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3909 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3910 <s xml:id="echoid-s439" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3911 Here as on Add MS 6782, f. 330, Harriot is using <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi></mstyle></math> notation, with superscripts 0, 1, 2, 3, ...
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3912 for successive entries in a general row of the table.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3913 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3914 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3915 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3916 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3917 <head xml:id="echoid-head63" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3918 Elementa triangularium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3919 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3920 The elements of triangular numbers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3921 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3922 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3923 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3924 <s xml:id="echoid-s441" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3925 Rationes compositas: et <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3926 componentes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3927 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3928 Ratios compounded, and their components.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3929 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3930 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3931 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3932 <pb file="add_6782_f163v" o="163v" n="326"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3933 <pb file="add_6782_f164" o="164" n="327"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3934 <div xml:id="echoid-div121" type="page_commentary" level="2" n="121">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3935 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3936 <s xml:id="echoid-s442" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3937 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3938 <s xml:id="echoid-s442" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3939 A table that appears to have been produced from the various rules set out on f. 163.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3940 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3941 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3942 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3943 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3944 <pb file="add_6782_f164v" o="164v" n="328"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3945 <pb file="add_6782_f165" o="165" n="329"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3946 <div xml:id="echoid-div122" type="page_commentary" level="2" n="122">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3947 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3948 <s xml:id="echoid-s444" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3949 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3950 <s xml:id="echoid-s444" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3951 Some experiments with Pascal's triangle. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3952 On the left, and again at the bottom of the page, the tables have been extended upwards,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3953 giving rise to negative triangular numbers. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3954 On the right, the table has been multiplied throughout by 3; see also Add MS 6785, f. 83. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3955 Note Harriot's use of superscript notation (not powers): <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>p</mi><mn>2</mn></msup></mrow></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>p</mi><mn>3</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3956 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3957 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3958 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3959 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3960 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3961 <s xml:id="echoid-s446" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3962 Male
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3963 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3964 badly done
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3965 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3966 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3967 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3968 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3969 <s xml:id="echoid-s447" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3970 Bene
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3971 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3972 better
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3973 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3974 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3975 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3976 <pb file="add_6782_f165v" o="165v" n="330"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3977 <pb file="add_6782_f166" o="166" n="331"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3978 <pb file="add_6782_f166v" o="166v" n="332"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3979 <pb file="add_6782_f167" o="167" n="333"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3980 <pb file="add_6782_f167v" o="167v" n="334"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3981 <pb file="add_6782_f168" o="168" n="335"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3982 <pb file="add_6782_f168v" o="168v" n="336"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3983 <pb file="add_6782_f169" o="169" n="337"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3984 <div xml:id="echoid-div123" type="page_commentary" level="2" n="123">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3985 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3986 <s xml:id="echoid-s448" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3987 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3988 <s xml:id="echoid-s448" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3989 These three tables show the formulae for the entries in each column of a table generated
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3990 from a constant difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, with different patterns ofincreasing and decreasing columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3991 Increasing columns are indicated by a triangle that broadens at the bottom, thus, Δ;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3992 decreasing columns are indicated by a trinagle that narrows at the bottom. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3993 Entries in the first column (after <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>) are denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>v</mi><mn>1</mn></msup></mrow></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3994 (where 1 is a superscript, not a power). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3995 Entries in the second column are denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>v</mi><mn>2</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3996 Entries in the third column are denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>v</mi><mn>3</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3997 Entries in the fourth column are denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>v</mi><mn>4</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3998 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	3999 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4000 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4001 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4002 <head xml:id="echoid-head64" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4003 Ad progressiones, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4004 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4005 On progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4006 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4007 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4008 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4009 <s xml:id="echoid-s450" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4010 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4011 Differences in tables of sines follow the alternately increasing and decreasing pattern given here.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4012 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4013 ad calculum sinuum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4014 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4015 for the calculation of sines
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4016 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4017 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4018 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4019 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4020 <s xml:id="echoid-s451" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4021 omnes <reg norm="examinantur" type="abbr">exam</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4022 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4023 all examined
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4024 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4025 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4026 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4027 <head xml:id="echoid-head65" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4028 Ad progressiones,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4029 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4030 On progressioins
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4031 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4032 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4033 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4034 <s xml:id="echoid-s452" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4035 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4036 Differences in tables of sines follow the alternately increasing and decreasing pattern given here.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4037 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4038 ad calculum sinuum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4039 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4040 for the calculation of sines
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4041 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4042 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4043 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4044 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4045 <s xml:id="echoid-s453" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4046 omnes <reg norm="examinantur" type="abbr">exam</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4047 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4048 all examined
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4049 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4050 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4051 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4052 <head xml:id="echoid-head66" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4053 Ad progressiones,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4054 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4055 On progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4056 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4057 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4058 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4059 <s xml:id="echoid-s454" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4060 omnes <reg norm="examinantur" type="abbr">exam</reg>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4061 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4062 all examined
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4063 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4064 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4065 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4066 <pb file="add_6782_f169v" o="169v" n="338"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4067 <pb file="add_6782_f170" o="170" n="339"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4068 <div xml:id="echoid-div124" type="page_commentary" level="2" n="124">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4069 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4070 <s xml:id="echoid-s455" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4071 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4072 <s xml:id="echoid-s455" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4073 At the top right is a numerical table in which every column is decreasing.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4074 The working below the table demonstrates in detail how the entries are calculated. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4075 The table below the first double line gives formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in each column. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4076 The table below the second double line gives the same information in a rearranged form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4077 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4078 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4079 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4080 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4081 <head xml:id="echoid-head67" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4082 Ad progressiones.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4083 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4084 On progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4085 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4086 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4087 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4088 <s xml:id="echoid-s457" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4089 omnes <reg norm="examinantur" type="abbr">exam</reg>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4090 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4091 all examined
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4092 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4093 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4094 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4095 <pb file="add_6782_f170v" o="170v" n="340"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4096 <pb file="add_6782_f171" o="171" n="341"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4097 <div xml:id="echoid-div125" type="page_commentary" level="2" n="125">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4098 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4099 <s xml:id="echoid-s458" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4100 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4101 <s xml:id="echoid-s458" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4102 At the top right is a numerical example in which the columns alternately increase and decrease.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4103 The working below the table demonstrates in detail how the entries are calculated. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4104 The first table below the double line gives formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in each column. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4105 The second table gives the same information but with the fractions rearranged over common denominators.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4106 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4107 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4108 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4109 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4110 <head xml:id="echoid-head68" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4111 Ad progressiones.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4112 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4113 On progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4114 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4115 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4116 <pb file="add_6782_f171v" o="171v" n="342"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4117 <pb file="add_6782_f172" o="172" n="343"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4118 <div xml:id="echoid-div126" type="page_commentary" level="2" n="126">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4119 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4120 <s xml:id="echoid-s460" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4121 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4122 <s xml:id="echoid-s460" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4123 At the top of the page is a numerical example in which the columns alternately decrease and increase.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4124 The working demonstrates in detail how the entries are calculated. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4125 The small table halfway down on the right contains negative entries in three of its columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4126 The table at the bottom of the page gives formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in each column.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4127 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4128 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4129 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4130 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4131 <head xml:id="echoid-head69" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4132 Ad progressiones.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4133 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4134 On progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4135 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4136 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4137 <pb file="add_6782_f172v" o="172v" n="344"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4138 <pb file="add_6782_f173" o="173" n="345"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4139 <div xml:id="echoid-div127" type="page_commentary" level="2" n="127">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4140 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4141 <s xml:id="echoid-s462" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4142 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4143 <s xml:id="echoid-s462" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4144 Rules for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in the third and fourth columns of a table
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4145 generated from a constant difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4146 for various patterns of increasing and decreasing columns.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4147 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4148 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4149 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4150 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4151 <pb file="add_6782_f173v" o="173v" n="346"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4152 <pb file="add_6782_f174" o="174" n="347"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4153 <div xml:id="echoid-div128" type="page_commentary" level="2" n="128">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4154 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4155 <s xml:id="echoid-s464" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4156 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4157 <s xml:id="echoid-s464" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4158 Rules for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in the third and fourth columns of a table
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4159 generated from a constant difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4160 for various patterns of increasing and decreasing columns.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4161 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4162 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4163 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4164 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4165 <pb file="add_6782_f174v" o="174v" n="348"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4166 <pb file="add_6782_f175" o="175" n="349"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4167 <div xml:id="echoid-div129" type="page_commentary" level="2" n="129">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4168 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4169 <s xml:id="echoid-s466" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4170 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4171 <s xml:id="echoid-s466" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4172 At the top right is a numerical example in which the first three columns increase but the fourth decreases.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4173 The working below the table demonstrates in detail how the entries are calculated. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4174 The rule for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entry in the fourth column is given in full, in two different versions. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4175 Below the double line, similar rules are given for a table in which the first and second columns increase
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4176 but the third and fourth columns decrease.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4177 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4178 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4179 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4180 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4181 <pb file="add_6782_f175v" o="175v" n="350"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4182 <pb file="add_6782_f176" o="176" n="351"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4183 <div xml:id="echoid-div130" type="page_commentary" level="2" n="130">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4184 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4185 <s xml:id="echoid-s468" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4186 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4187 <s xml:id="echoid-s468" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4188 General rules for the entries in the third and fourth columns of a table
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4189 generated from a constant difference. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4190 Instructions for the correct signs are given in a separate note at the end of the page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4191 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4192 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4193 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4194 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4195 <head xml:id="echoid-head70" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4196 Ad <emph style="st">finales</emph> æquationes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4197 generalis methodus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4198 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4199 On equations, general method
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4200 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4201 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4202 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4203 <s xml:id="echoid-s470" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4204 In <emph style="st">Descendibus</emph> <emph style="super">Decrescentibus</emph>: adde et subtrahe.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4205 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4206 In decreasing progressions: add and subtract.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4207 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4208 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4209 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4210 <s xml:id="echoid-s471" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4211 In Crescentibus: subtrahe et adde.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4212 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4213 In increasing progressions: subtract and add.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4214 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4215 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4216 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4217 <pb file="add_6782_f176v" o="176v" n="352"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4218 <pb file="add_6782_f177" o="177" n="353"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4219 <div xml:id="echoid-div131" type="page_commentary" level="2" n="131">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4220 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4221 <s xml:id="echoid-s472" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4222 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4223 <s xml:id="echoid-s472" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4224 Rules for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in the fifth and sixth columns of a table
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4225 generated from a constant difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4226 for various patterns of increasing and decreasing columns.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4227 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4228 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4229 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4230 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4231 <pb file="add_6782_f177v" o="177v" n="354"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4232 <pb file="add_6782_f178" o="178" n="355"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4233 <div xml:id="echoid-div132" type="page_commentary" level="2" n="132">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4234 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4235 <s xml:id="echoid-s474" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4236 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4237 <s xml:id="echoid-s474" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4238 General rules for the entries in the fifth and sixth columns of a table
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4239 generated from a constant difference. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4240 Instructions for the correct signs are given in a separate note at the end of the page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4241 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4242 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4243 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4244 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4245 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4246 <s xml:id="echoid-s476" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4247 In crescentibus. subtrahe et adde.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4248 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4249 In increasing porgressions, subtract and add.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4250 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4251 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4252 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4253 <s xml:id="echoid-s477" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4254 In decrescentibus. adde et subtrahe.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4255 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4256 In decreasing progressions, add and subtract.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4257 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4258 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4259 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4260 <pb file="add_6782_f178v" o="178v" n="356"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4261 <div xml:id="echoid-div133" type="page_commentary" level="2" n="133">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4262 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4263 <s xml:id="echoid-s478" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4264 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4265 <s xml:id="echoid-s478" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4266 The leftmost column is marked at the top as increasing (by the triangle widening downwards. Δ),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4267 but after a while it begins to decrease again.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4268 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4269 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4270 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4271 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4272 <head xml:id="echoid-head71" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4273 Nota.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4274 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4275 Note.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4276 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4277 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4278 <pb file="add_6782_f179" o="179" n="357"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4279 <pb file="add_6782_f179v" o="179v" n="358"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4280 <pb file="add_6782_f180" o="180" n="359"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4281 <div xml:id="echoid-div134" type="page_commentary" level="2" n="134">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4282 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4283 <s xml:id="echoid-s480" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4284 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4285 <s xml:id="echoid-s480" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4286 This folio shows all combinations of 0, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4287 including in each case the null combination consisting only of 0. As on Add MS 6782, f. 35,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4288 each set of combinations is constructed from the previous one
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4289 by adding the new letter to the end of each existing combination.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4290 This shows clearly why the number of combinations doubles with each new letter.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4291 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4292 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4293 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4294 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4295 <pb file="add_6782_f180v" o="180v" n="360"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4296 <pb file="add_6782_f181" o="181" n="361"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4297 <div xml:id="echoid-div135" type="page_commentary" level="2" n="135">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4298 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4299 <s xml:id="echoid-s482" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4300 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4301 <s xml:id="echoid-s482" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4302 Combinations of two or more quantities, generated by multiplication. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4303 The letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>, stand for
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4304 <foreign xml:lang="lat">pondus</foreign> (weight),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4305 <foreign xml:lang="lat">magnitudo</foreign> (magnitude),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4306 <foreign xml:lang="lat">figura</foreign> (area),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4307 <foreign xml:lang="lat">situs</foreign> (place)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4308 (see Add MS 6786, f. 291).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4309 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4310 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4311 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4312 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4313 <pb file="add_6782_f181v" o="181v" n="362"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4314 <pb file="add_6782_f182" o="182" n="363"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4315 <div xml:id="echoid-div136" type="page_commentary" level="2" n="136">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4316 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4317 <s xml:id="echoid-s484" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4318 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4319 <s xml:id="echoid-s484" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4320 This folio lists all the permutations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>,<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4321 and begins lists for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4322 The totals are written as factorials, that is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mo>=</mo><mn>1</mn><mo>×</mo><mn>2</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mo>=</mo><mn>1</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>3</mn></mstyle></math>, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4323 This enables Harriot to calculate the number of permutations of 4 or 5 letters as 120 or 720, respectively,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4324 without writing out the entire list. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4325 The calculations at the bottom of the page show how each total is obtained from the previous one;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4326 for example, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>4</mn><mo>=</mo><mn>4</mn><mo>×</mo><mn>6</mn></mstyle></math>, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4327 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4328 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4329 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4330 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4331 <pb file="add_6782_f182v" o="182v" n="364"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4332 <pb file="add_6782_f183" o="183" n="365"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4333 <div xml:id="echoid-div137" type="page_commentary" level="2" n="137">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4334 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4335 <s xml:id="echoid-s486" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4336 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4337 <s xml:id="echoid-s486" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4338 The square, cube, and fourth power of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, possibly in connection with combinations,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4339 which is the predominant subject in the surrounding pages.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4340 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4341 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4342 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4343 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4344 <pb file="add_6782_f183v" o="183v" n="366"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4345 <pb file="add_6782_f184" o="184" n="367"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4346 <div xml:id="echoid-div138" type="page_commentary" level="2" n="138">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4347 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4348 <s xml:id="echoid-s488" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4349 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4350 <s xml:id="echoid-s488" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4351 Tables showing all possible throws of 1, 2, or 3 dice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4352 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4353 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4354 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4355 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4356 <pb file="add_6782_f184v" o="184v" n="368"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4357 <pb file="add_6782_f185" o="185" n="369"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4358 <div xml:id="echoid-div139" type="page_commentary" level="2" n="139">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4359 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4360 <s xml:id="echoid-s490" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4361 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4362 <s xml:id="echoid-s490" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4363 This folio is a summary of Harriot's calculations on dice. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4364 The tables on the left, after the page has been turned sideways,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4365 are frequency tables for the possible sums that can be obtained by throwing 1, 2, 3, 4, 5, or 6 dice
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4366 (see Add MS 6782, f. 41 and f. 40v).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4367 The totals in each case are the appropriate powers of 6. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4368 The tables on the right are summaries of the tables that appear on Add MS 6782, f. 50,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4369 and indicate the number of ways repetitions can occur. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4370 Amongst the calculations at the bottom right are: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4371 (i) a table that appears to convert hours to £, at £30 per hour. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4372 (ii) a conversion of 46,656 shillings (one for each possibility for throws of six dice) into £ and shillings. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4373 Table (i) is based on £30 or 600 shillings per hour;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4374 converting shillings to throws of the dice, as suggested by table (ii),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4375 gives 600 throws per hour, or 10 throws per minute. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4376 (iii) the ratio of throws with repetitions to throws with no repetition, for six dice,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4377 namely (see the table above), <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mn>5</mn><mo>,</mo><mn>9</mn><mn>3</mn><mn>6</mn><mo>:</mo><mn>7</mn><mn>2</mn><mn>0</mn><mo>=</mo><mn>6</mn><mn>3</mn><mfrac><mrow><mn>5</mn><mn>7</mn><mn>6</mn></mrow><mrow><mn>7</mn><mn>2</mn><mn>0</mn></mrow></mfrac><mo>:</mo><mn>1</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4378 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4379 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4380 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4381 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4382 <pb file="add_6782_f185v" o="185v" n="370"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4383 <pb file="add_6782_f186" o="186" n="371"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4384 <pb file="add_6782_f186v" o="186v" n="372"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4385 <pb file="add_6782_f187" o="187" n="373"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4386 <pb file="add_6782_f187v" o="187v" n="374"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4387 <pb file="add_6782_f188" o="188" n="375"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4388 <pb file="add_6782_f188v" o="188v" n="376"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4389 <pb file="add_6782_f189" o="189" n="377"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4390 <pb file="add_6782_f189v" o="189v" n="378"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4391 <pb file="add_6782_f190" o="190" n="379"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4392 <pb file="add_6782_f190v" o="190v" n="380"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4393 <pb file="add_6782_f191" o="191" n="381"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4394 <pb file="add_6782_f191v" o="191v" n="382"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4395 <pb file="add_6782_f192" o="192" n="383"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4396 <pb file="add_6782_f192v" o="192v" n="384"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4397 <pb file="add_6782_f193" o="193" n="385"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4398 <div xml:id="echoid-div140" type="page_commentary" level="2" n="140">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4399 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4400 <s xml:id="echoid-s492" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4401 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4402 <s xml:id="echoid-s492" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4403 A partial draft of page 33 of the 'Magisteria' (Add MS 6782, f. 140).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4404 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4405 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4406 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4407 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4408 <pb file="add_6782_f193v" o="193v" n="386"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4409 <div xml:id="echoid-div141" type="page_commentary" level="2" n="141">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4410 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4411 <s xml:id="echoid-s494" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4412 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4413 <s xml:id="echoid-s494" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4414 Examples from pages 35 and 36 of the 'Magisteria' (Add MS 6782, f. 142 and f. 143).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4415 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4416 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4417 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4418 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4419 <pb file="add_6782_f194" o="194" n="387"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4420 <pb file="add_6782_f194v" o="194v" n="388"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4421 <pb file="add_6782_f195" o="195" n="389"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4422 <div xml:id="echoid-div142" type="page_commentary" level="2" n="142">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4423 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4424 <s xml:id="echoid-s496" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4425 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4426 <s xml:id="echoid-s496" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4427 A draft of page 31 of the 'Magisteria' (Add MS 6782, f. 138).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4428 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4429 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4430 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4431 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4432 <head xml:id="echoid-head72" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4433 Magisteria.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4434 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4435 Rules
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4436 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4437 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4438 <pb file="add_6782_f195v" o="195v" n="390"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4439 <pb file="add_6782_f196" o="196" n="391"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4440 <div xml:id="echoid-div143" type="page_commentary" level="2" n="143">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4441 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4442 <s xml:id="echoid-s498" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4443 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4444 <s xml:id="echoid-s498" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4445 A draft of page 26 of the 'Magisteria' (Add MS 6782, f. 133).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4446 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4447 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4448 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4449 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4450 <head xml:id="echoid-head73" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4451 Pro Magisterio. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4452 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4453 For rules for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4454 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4455 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4456 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4457 <s xml:id="echoid-s500" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4458 Magisterium. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4459 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4460 Rule for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4461 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4462 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4463 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4464 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4465 <s xml:id="echoid-s501" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4466 Hinc apparet quod <emph style="super">hoc</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4467 magisterium fit ex primo numero progressionis et prima <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4468 differentia, in primo canone, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, scribendo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mi>N</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mi>N</mi><mi>N</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4469 <emph style="st">[???]</emph> grad<emph style="super">at</emph>im <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4470 ut in exemplo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4471 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4472 Here it is clear that this rule stems from the first number of the progression and the first difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4473 in the first canon, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, writing <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mi>N</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mi>N</mi><mi>N</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4474 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4475 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4476 <s xml:id="echoid-s502" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4477 Idem observandum ex <emph style="st">cæteris</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4478 alijs canonibus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, pro <emph style="st">alijs</emph> cæteris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4479 magisterijs.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4480 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4481 The same is to be observed from other canons for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, for the remaining rules.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4482 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4483 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4484 <s xml:id="echoid-s503" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4485 Similiter agendum pro alijs omnibus Magisterijs <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4486 cæterarum progressionum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4487 <emph style="st">mutandis</emph> <emph style="super">notandis</emph>affectionibus secundum speciem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4488 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4489 Similarly it may be done for all other rules for the remaining progressions,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4490 noting the sign of the second case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4491 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4492 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4493 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4494 <pb file="add_6782_f196v" o="196v" n="392"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4495 <head xml:id="echoid-head74" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4496 Variation of ye needle <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4497 offered <emph style="super">by</emph> Schouten in his navigation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4498 about ye world.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4499 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4500 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4501 <s xml:id="echoid-s504" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4502 To the southeward of the east mouth of the strayts <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4503 of Magellan in the sight of 57.88 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4504 variatio. 12.0. to the NE.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4505 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4506 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4507 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4508 <s xml:id="echoid-s505" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4509 To the southward of the westmost <emph style="super">of Magellane</emph> & 20 legues more <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4510 westward in 55.43 lat <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4511 variatio 11.0 (NE).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4512 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4513 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4514 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4515 <s xml:id="echoid-s506" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4516 To the southern altitude 17 & 20 degrees westward <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4517 from the middest of Magel: straytes, in the common plot <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4518 of æquall degrees. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4519 variatio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> poynt or 6. NW.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4520 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4521 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4522 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4523 <s xml:id="echoid-s507" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4524 20. degrees more westward. lat: [???]: 14.12
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4525 variatio. nulla.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4526 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4527 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4528 <pb file="add_6782_f197" o="197" n="393"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4529 <div xml:id="echoid-div144" type="page_commentary" level="2" n="144">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4530 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4531 <s xml:id="echoid-s508" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4532 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4533 <s xml:id="echoid-s508" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4534 A partial draft of page 32 of the 'Magisteria' (Add MS 6782, f. 139).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4535 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4536 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4537 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4538 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4539 <pb file="add_6782_f197v" o="197v" n="394"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4540 <pb file="add_6782_f198" o="198" n="395"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4541 <div xml:id="echoid-div145" type="page_commentary" level="2" n="145">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4542 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4543 <s xml:id="echoid-s510" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4544 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4545 <s xml:id="echoid-s510" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4546 Rules for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in four columns of a table generated from a constant difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4547 as on Add MS 6782, f 169–176, but here using the notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> (for sum) instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4548 to indicate that the entries may be thought of as sums (of lower numbered columns)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4549 rather than differences (of higher numbered columns).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4550 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4551 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4552 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4553 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4554 <head xml:id="echoid-head75" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4555 Ad aggregata seu summas progressionum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4556 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4557 On the gathering together or sum of progressions.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4558 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4559 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4560 <pb file="add_6782_f198v" o="198v" n="396"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4561 <pb file="add_6782_f199" o="199" n="397"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4562 <div xml:id="echoid-div146" type="page_commentary" level="2" n="146">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4563 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4564 <s xml:id="echoid-s512" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4565 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4566 <s xml:id="echoid-s512" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4567 A partial draft of page 32 of the 'Magisteria' (Add MS 6782, f. 139).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4568 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4569 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4570 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4571 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4572 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4573 <s xml:id="echoid-s514" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4574 & In Infinitum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4575 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4576 etc. Indefinitely.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4577 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4578 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4579 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4580 <pb file="add_6782_f199v" o="199v" n="398"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4581 <pb file="add_6782_f200" o="200" n="399"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4582 <div xml:id="echoid-div147" type="page_commentary" level="2" n="147">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4583 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4584 <s xml:id="echoid-s515" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4585 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4586 <s xml:id="echoid-s515" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4587 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>, see page 23 of the 'Magisteria' (Add MS 6782, f. 130).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4588 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4589 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4590 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4591 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4592 <pb file="add_6782_f200v" o="200v" n="400"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4593 <pb file="add_6782_f201" o="201" n="401"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4594 <div xml:id="echoid-div148" type="page_commentary" level="2" n="148">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4595 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4596 <s xml:id="echoid-s517" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4597 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4598 <s xml:id="echoid-s517" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4599 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, see page 22 of the 'Magisteria' (Add MS 6782, f. 129).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4600 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4601 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4602 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4603 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4604 <head xml:id="echoid-head76" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4605 Canon <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4606 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4607 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4608 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4609 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4610 <pb file="add_6782_f201v" o="201v" n="402"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4611 <pb file="add_6782_f202" o="202" n="403"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4612 <div xml:id="echoid-div149" type="page_commentary" level="2" n="149">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4613 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4614 <s xml:id="echoid-s519" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4615 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4616 <s xml:id="echoid-s519" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4617 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, see page 25 of the 'Magisteria' (Add MS 6782, f. 132).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4618 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4619 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4620 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4621 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4622 <head xml:id="echoid-head77" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4623 Canon <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4624 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4625 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4626 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4627 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4628 <pb file="add_6782_f202v" o="202v" n="404"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4629 <pb file="add_6782_f203" o="203" n="405"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4630 <div xml:id="echoid-div150" type="page_commentary" level="2" n="150">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4631 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4632 <s xml:id="echoid-s521" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4633 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4634 <s xml:id="echoid-s521" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4635 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, see pages 22 and 25 of the 'Magisteria' (Add MS 6782, f. 129 and f. 132).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4636 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4637 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4638 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4639 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4640 <head xml:id="echoid-head78" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4641 De canone pro <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4642 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4643 On the canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4644 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4645 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4646 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4647 <s xml:id="echoid-s523" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4648 Videlicet: pro 4<emph style="super">ta</emph> progressione,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4649 3<emph style="super">m</emph> differentiarum gradualium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4650 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4651 Clearly set out: for the fourth progression, three grades of differences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4652 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4653 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4654 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4655 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4656 <s xml:id="echoid-s524" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4657 Cuius <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4658 species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4659 hic
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4660 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4661 For these cases here
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4662 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4663 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4664 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4665 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4666 <s xml:id="echoid-s525" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4667 Et affectio-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4668 nes speciem <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4669 ita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4670 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4671 And for these cases of sign thus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4672 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4673 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4674 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4675 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4676 <s xml:id="echoid-s526" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4677 Sed si species progressiones <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4678 sit:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4679 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4680 But if the cases of progressions are:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4681 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4682 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4683 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4684 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4685 <s xml:id="echoid-s527" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4686 Affectiones erunt.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4687 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4688 The signs will be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4689 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4690 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4691 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4692 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4693 <s xml:id="echoid-s528" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4694 Etiam, si species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4695 sit:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4696 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4697 Also, if the cases are:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4698 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4699 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4700 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4701 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4702 <s xml:id="echoid-s529" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4703 Affectiones erunt.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4704 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4705 The signs will be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4706 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4707 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4708 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4709 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4710 <s xml:id="echoid-s530" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4711 Et similiter de alijs
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4712 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4713 And similarly for others.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4714 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4715 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4716 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4717 <pb file="add_6782_f203v" o="203v" n="406"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4718 <pb file="add_6782_f204" o="204" n="407"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4719 <head xml:id="echoid-head79" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4720 Canon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4721 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4722 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4723 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4724 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4725 <pb file="add_6782_f204v" o="204v" n="408"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4726 <pb file="add_6782_f205" o="205" n="409"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4727 <div xml:id="echoid-div151" type="page_commentary" level="2" n="151">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4728 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4729 <s xml:id="echoid-s531" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4730 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4731 <s xml:id="echoid-s531" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4732 Canons 3 and 4 for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, with columns alternately increasing and decreasing;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4733 see page 24 of the 'Magisteria' (Add MS 6782, f. 131).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4734 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4735 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4736 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4737 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4738 <head xml:id="echoid-head80" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4739 3. Canon <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4740 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4741 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4742 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4743 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4744 <head xml:id="echoid-head81" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4745 4. Canon <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4746 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4747 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4748 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4749 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4750 <pb file="add_6782_f205v" o="205v" n="410"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4751 <pb file="add_6782_f206" o="206" n="411"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4752 <div xml:id="echoid-div152" type="page_commentary" level="2" n="152">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4753 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4754 <s xml:id="echoid-s533" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4755 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4756 <s xml:id="echoid-s533" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4757 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, see page 21 of the 'Magisteria' (Add MS 6782, f. 128).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4758 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4759 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4760 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4761 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4762 <head xml:id="echoid-head82" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4763 De canone ad dividendam progressionum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4764 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4765 On the canon for dividing the progression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4766 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4767 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4768 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4769 <s xml:id="echoid-s535" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4770 Videlicet; 5<emph style="super">tam</emph> progressionem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4771 4<emph style="super">or</emph> differentiarum gradualium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4772 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4773 Clearly set out: the fifth progression, four grades of differences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4774 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4775 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4776 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4777 <pb file="add_6782_f206v" o="206v" n="412"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4778 <pb file="add_6782_f207" o="207" n="413"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4779 <div xml:id="echoid-div153" type="page_commentary" level="2" n="153">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4780 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4781 <s xml:id="echoid-s536" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4782 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4783 <s xml:id="echoid-s536" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4784 Canon 1 for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, with all rows increasing;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4785 see page 24 of the 'Magisteria' (Add MS 6782, f. 131).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4786 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4787 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4788 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4789 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4790 <head xml:id="echoid-head83" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4791 1. Canon <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4792 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4793 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4794 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4795 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4796 <pb file="add_6782_f207v" o="207v" n="414"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4797 <pb file="add_6782_f208" o="208" n="415"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4798 <div xml:id="echoid-div154" type="page_commentary" level="2" n="154">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4799 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4800 <s xml:id="echoid-s538" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4801 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4802 <s xml:id="echoid-s538" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4803 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, see page 21 of the 'Magisteria' (Add MS 6782, f. 128).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4804 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4805 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4806 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4807 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4808 <head xml:id="echoid-head84" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4809 Canon <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4810 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4811 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4812 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4813 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4814 <pb file="add_6782_f208v" o="208v" n="416"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4815 <pb file="add_6782_f209" o="209" n="417"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4816 <div xml:id="echoid-div155" type="page_commentary" level="2" n="155">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4817 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4818 <s xml:id="echoid-s540" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4819 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4820 <s xml:id="echoid-s540" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4821 Canon 2 for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, with all rows decreasing;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4822 see page 24 of the 'Magisteria' (Add MS 6782, f. 131).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4823 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4824 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4825 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4826 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4827 <head xml:id="echoid-head85" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4828 2. Canon <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4829 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4830 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4831 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4832 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4833 <pb file="add_6782_f209v" o="209v" n="418"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4834 <pb file="add_6782_f210" o="210" n="419"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4835 <div xml:id="echoid-div156" type="page_commentary" level="2" n="156">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4836 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4837 <s xml:id="echoid-s542" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4838 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4839 <s xml:id="echoid-s542" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4840 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>, see pages 19–20 of the 'Magisteria' (Add MS 6782, f. 126 and f. 127).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4841 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4842 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4843 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4844 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4845 <head xml:id="echoid-head86" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4846 1. Canon. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4847 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4848 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4849 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4850 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4851 <pb file="add_6782_f210v" o="210v" n="420"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4852 <div xml:id="echoid-div157" type="page_commentary" level="2" n="157">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4853 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4854 <s xml:id="echoid-s544" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4855 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4856 <s xml:id="echoid-s544" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4857 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>, see pages 19–20 of the 'Magisteria' (Add MS 6782, f. 126 and f. 127).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4858 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4859 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4860 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4861 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4862 <pb file="add_6782_f211" o="211" n="421"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4863 <div xml:id="echoid-div158" type="page_commentary" level="2" n="158">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4864 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4865 <s xml:id="echoid-s546" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4866 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4867 <s xml:id="echoid-s546" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4868 Canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>, see pages 19-20 of the 'Magisteria' (Add MS 6782, f. 126 and f. 127).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4869 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4870 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4871 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4872 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4873 <head xml:id="echoid-head87" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4874 De canone ad dividendam progressionum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4875 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4876 On the canon for dividing the progression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4877 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4878 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4879 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4880 <s xml:id="echoid-s548" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4881 Videlicet; sextam progressionem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4882 quinque differentiarum gradualium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4883 gradatarum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4884 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4885 Clearly set out: the sixth progression, five grades of differences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4886 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4887 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4888 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4889 <pb file="add_6782_f211v" o="211v" n="422"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4890 <div xml:id="echoid-div159" type="page_commentary" level="2" n="159">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4891 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4892 <s xml:id="echoid-s549" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4893 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4894 <s xml:id="echoid-s549" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4895 Sign patterns for columns of difference tables. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4896 For further examples see page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4897 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4898 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4899 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4900 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4901 <pb file="add_6782_f212" o="212" n="423"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4902 <div xml:id="echoid-div160" type="page_commentary" level="2" n="160">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4903 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4904 <s xml:id="echoid-s551" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4905 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4906 <s xml:id="echoid-s551" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4907 Difference tables showing some possible variations of increasing (c) and decreasing (d) columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4908 The charts on the right hand side show sign patterns for each column. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4909 For further examples see page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4910 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4911 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4912 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4913 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4914 <pb file="add_6782_f212v" o="212v" n="424"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4915 <pb file="add_6782_f213" o="213" n="425"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4916 <div xml:id="echoid-div161" type="page_commentary" level="2" n="161">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4917 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4918 <s xml:id="echoid-s553" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4919 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4920 <s xml:id="echoid-s553" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4921 Difference tables showing some possible variations of increasing (c) and decreasing (d) columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4922 The charts on the right hand side show the sign patterns for each column. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4923 For further examples see page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4924 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4925 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4926 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4927 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4928 <pb file="add_6782_f213v" o="213v" n="426"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4929 <pb file="add_6782_f214" o="214" n="427"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4930 <div xml:id="echoid-div162" type="page_commentary" level="2" n="162">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4931 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4932 <s xml:id="echoid-s555" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4933 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4934 <s xml:id="echoid-s555" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4935 Difference tables showing some possible variations of increasing (c) and decreasing (d) columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4936 The charts on the right hand side show the sign patterns for each column. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4937 For further examples see page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4938 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4939 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4940 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4941 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4942 <pb file="add_6782_f214v" o="214v" n="428"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4943 <pb file="add_6782_f215" o="215" n="429"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4944 <div xml:id="echoid-div163" type="page_commentary" level="2" n="163">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4945 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4946 <s xml:id="echoid-s557" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4947 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4948 <s xml:id="echoid-s557" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4949 Lists of all possible variations of increasing (c) and decreasing (d) columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4950 See page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4951 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4952 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4953 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4954 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4955 <pb file="add_6782_f215v" o="215v" n="430"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4956 <div xml:id="echoid-div164" type="page_commentary" level="2" n="164">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4957 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4958 <s xml:id="echoid-s559" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4959 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4960 <s xml:id="echoid-s559" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4961 Lists of all possible variations of increasing (c) and decreasing (d) columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4962 The charts on the right hand side show sign patterns for individual columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4963 For a full array of such charts see page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4964 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4965 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4966 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4967 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4968 <pb file="add_6782_f216" o="216" n="431"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4969 <div xml:id="echoid-div165" type="page_commentary" level="2" n="165">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4970 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4971 <s xml:id="echoid-s561" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4972 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4973 <s xml:id="echoid-s561" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4974 Difference tables showing some possible variations of increasing (c) and decreasing (d) columns. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4975 The charts on the right hand side show the sign patterns for each column. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4976 For further examples see page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4977 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4978 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4979 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4980 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4981 <pb file="add_6782_f216v" o="216v" n="432"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4982 <div xml:id="echoid-div166" type="page_commentary" level="2" n="166">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4983 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4984 <s xml:id="echoid-s563" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4985 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4986 <s xml:id="echoid-s563" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4987 Sign patterns for columns of difference tables. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4988 For further examples see page 8 of the 'Magisteria' (Add MS 6782, f. 115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4989 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4990 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4991 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4992 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4993 <pb file="add_6782_f217" o="217" n="433"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4994 <div xml:id="echoid-div167" type="page_commentary" level="2" n="167">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4995 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4996 <s xml:id="echoid-s565" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4997 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4998 <s xml:id="echoid-s565" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	4999 See pages 5 to 7 of the 'Magisteria' (Add MS 6782, f. 110 to f. 112), which contain similar numerical tables.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5000 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5001 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5002 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5003 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5004 <pb file="add_6782_f217v" o="217v" n="434"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5005 <pb file="add_6782_f218" o="218" n="435"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5006 <div xml:id="echoid-div168" type="page_commentary" level="2" n="168">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5007 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5008 <s xml:id="echoid-s567" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5009 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5010 <s xml:id="echoid-s567" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5011 A draft for page 2 of the 'Magisteria' (Add MS 6782, f. 109). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5012 At the end of the page, Harriot suggestes the notation: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>,</mo><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mo>,</mo><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mo>,</mo><mi>n</mi></mstyle></math>, ... inside small boxes,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5013 or better: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>,</mo><mn>7</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>,</mo><mn>6</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>,</mo><mn>5</mn></mstyle></math>, ... inside small boxes,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5014 for what we now write as: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>n</mi><mn>7</mn></msup></mrow></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>n</mi><mn>6</mn></msup></mrow></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>n</mi><mn>5</mn></msup></mrow></mstyle></math>, ....
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5015 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5016 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5017 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5018 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5019 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5020 <s xml:id="echoid-s569" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5021 Magis placet. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5022 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5023 More pleasing.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5024 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5025 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5026 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5027 <pb file="add_6782_f218v" o="218v" n="436"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5028 <pb file="add_6782_f219" o="219" n="437"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5029 <div xml:id="echoid-div169" type="page_commentary" level="2" n="169">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5030 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5031 <s xml:id="echoid-s570" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5032 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5033 <s xml:id="echoid-s570" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5034 The calculations of the previous page (Add MS 6782, f. 218) demonstrated numerically.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5035 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5036 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5037 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5038 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5039 <pb file="add_6782_f219v" o="219v" n="438"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5040 <pb file="add_6782_f220" o="220" n="439"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5041 <div xml:id="echoid-div170" type="page_commentary" level="2" n="170">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5042 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5043 <s xml:id="echoid-s572" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5044 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5045 <s xml:id="echoid-s572" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5046 Canons for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, see page 22 of the 'Magisteria' (Add MS 6782, f. 129).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5047 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5048 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5049 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5050 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5051 <head xml:id="echoid-head88" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5052 De Canone. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. De Canone. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5053 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5054 On the canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. On the canon for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5055 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5056 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5057 <pb file="add_6782_f220v" o="220v" n="440"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5058 <pb file="add_6782_f221" o="221" n="441"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5059 <pb file="add_6782_f221v" o="221v" n="442"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5060 <pb file="add_6782_f222" o="222" n="443"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5061 <pb file="add_6782_f222v" o="222v" n="444"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5062 <pb file="add_6782_f223" o="223" n="445"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5063 <pb file="add_6782_f223v" o="223v" n="446"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5064 <pb file="add_6782_f224" o="224" n="447"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5065 <pb file="add_6782_f224v" o="224v" n="448"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5066 <pb file="add_6782_f225" o="225" n="449"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5067 <pb file="add_6782_f225v" o="225v" n="450"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5068 <pb file="add_6782_f226" o="226" n="451"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5069 <pb file="add_6782_f226v" o="226v" n="452"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5070 <pb file="add_6782_f227" o="227" n="453"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5071 <pb file="add_6782_f227v" o="227v" n="454"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5072 <pb file="add_6782_f228" o="228" n="455"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5073 <div xml:id="echoid-div171" type="page_commentary" level="2" n="171">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5074 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5075 <s xml:id="echoid-s574" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5076 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5077 <s xml:id="echoid-s574" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5078 A numerical example of the rule for square root of a sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5079 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5080 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5081 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5082 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5083 <pb file="add_6782_f228v" o="228v" n="456"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5084 <pb file="add_6782_f229" o="229" n="457"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5085 <div xml:id="echoid-div172" type="page_commentary" level="2" n="172">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5086 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5087 <s xml:id="echoid-s576" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5088 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5089 <s xml:id="echoid-s576" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5090 The references on this page are to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5091 <emph style="it">Supplementum geometriæ</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5092 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5093 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5094 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5095 Propositio III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5096 Si duae lineae rectae Ã puncto extra circulum eductae ipsum secent,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5097 pars autem exterior primae fit proportionalis inter partem exteriorem secundae & partem interiorem ejusdem:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5098 erit quoque pars exterior secundae proportionalis inter partem exteriorem primae & partem interiorem ejusdem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5099 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5100 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5101 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5102 If two straight lines drawn from a point outside a circle cut it in such a way that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5103 the external part of the first is a proportional between the external and internal parts of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5104 the external part of the second will be a proportional between the external and internal parts of the first.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5105 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5106 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5107 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5108 Propositio IV. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5109 Si duae lineae rectae Ã puncto extra circulum eductae ipsum secent
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5110 quod autem fit sub partibus exterioribus eductarum, aequale fit ei quod fit sub intertioribus:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5111 exteriores partes permutatim sumptae, erunt continue proportionales inter partes interiors.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5112 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5113 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5114 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5115 If two straight lines drawn from a point outside a circle cut it,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5116 and moreover the product of the external parts is equal to that of the internal parts,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5117 the external parts taken in turn will be continued proportionals between the internal parts.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5118 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5119 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5120 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5121 Propositio V. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5122 Datis duabus lineis rectis, invenire inter easdem duas medias continue, proportionales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5123 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5124 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5125 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5126 Given two straight lines, to find two mean proportionals between them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5127 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5128 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5129 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5130 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5131 <head xml:id="echoid-head89" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5132 Vieta. supl.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5133 pag. 14. b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5134 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5135 Viète, Supplementum, page 14v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5136 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5137 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5138 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5139 <s xml:id="echoid-s578" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5140 prop. 5.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5141 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5142 Proposition 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5143 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5144 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5145 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5146 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5147 <s xml:id="echoid-s579" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5148 prop 3.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5149 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5150 Proposition 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5151 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5152 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5153 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5154 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5155 <s xml:id="echoid-s580" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5156 prop: 4.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5157 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5158 Proposition 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5159 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5160 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5161 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5162 <pb file="add_6782_f229v" o="229v" n="458"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5163 <pb file="add_6782_f230" o="230" n="459"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5164 <pb file="add_6782_f230v" o="230v" n="460"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5165 <pb file="add_6782_f231" o="231" n="461"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5166 <div xml:id="echoid-div173" type="page_commentary" level="2" n="173">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5167 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5168 <s xml:id="echoid-s581" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5169 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5170 <s xml:id="echoid-s581" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5171 This sheet refers to Stevin's <emph style="it">L'arithmétique ... aussi l'algebre</emph> (1585), page 215,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5172 where there is a section entitled 'De l'addition des racines de multinomies radicaux'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5173 Stevin gave numerical examples, whereas Harrot has worked in letters.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5174 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5175 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5176 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5177 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5178 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5179 <s xml:id="echoid-s583" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5180 vide: Stevin. 215.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5181 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5182 See Stevin, page 215.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5183 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5184 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5185 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5186 <pb file="add_6782_f231v" o="231v" n="462"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5187 <pb file="add_6782_f232" o="232" n="463"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5188 <div xml:id="echoid-div174" type="page_commentary" level="2" n="174">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5189 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5190 <s xml:id="echoid-s584" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5191 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5192 <s xml:id="echoid-s584" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5193 Proofs of the inequalities <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>></mo><mn>2</mn><mi>b</mi><mi>c</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>b</mi><mo>+</mo><mi>c</mi><mi>c</mi><mi>c</mi><mo>></mo><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5194 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5195 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5196 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5197 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5198 <pb file="add_6782_f232v" o="232v" n="464"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5199 <pb file="add_6782_f233" o="233" n="465"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5200 <pb file="add_6782_f233v" o="233v" n="466"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5201 <pb file="add_6782_f234" o="234" n="467"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5202 <div xml:id="echoid-div175" type="page_commentary" level="2" n="175">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5203 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5204 <s xml:id="echoid-s586" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5205 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5206 <s xml:id="echoid-s586" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5207 The table at the top gives formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entry in each column of a table generated
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5208 from a constant difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, with every column increasing. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5209 Entries in column 0 are constant (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5210 Entries in column 1 are denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>v</mi><mn>1</mn></msup></mrow></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5211 Entries in column 2 are denoted by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>v</mi><mn>2</mn></msup></mrow></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5212 and so on; the small numbers are superscripts, not powers. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5213 The lower half of the page lists the possible combinations of increreasing columns (c) and decreasing columns (d),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5214 for up to four columns.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5215 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5216 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5217 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5218 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5219 <head xml:id="echoid-head90" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5220 Ad progressiones.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5221 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5222 On progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5223 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5224 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5225 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5226 <s xml:id="echoid-s588" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5227 Casus differentiarum progressionum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5228 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5229 Cases of progressions of differences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5230 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5231 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5232 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5233 <s xml:id="echoid-s589" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5234 c. designat crescentes progressiones:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5235 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5236 c. denotes increasing progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5237 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5238 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5239 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5240 <s xml:id="echoid-s590" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5241 d. decrescentes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5242 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5243 d. decreasing
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5244 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5245 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5246 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5247 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5248 <s xml:id="echoid-s591" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5249 æquationis secundi omnes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5250 hoc casus habentur in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5251 alijs chartis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5252 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5253 all cases of the second equation here are to be found in other sheets.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5254 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5255 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5256 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5257 <pb file="add_6782_f234v" o="234v" n="468"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5258 <pb file="add_6782_f235" o="235" n="469"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5259 <div xml:id="echoid-div176" type="page_commentary" level="2" n="176">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5260 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5261 <s xml:id="echoid-s592" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5262 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5263 <s xml:id="echoid-s592" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5264 Rules for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in six columns of a table generated from a constant difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5265 as on Add MS 6782, f 177–178, but here using the notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> (for sum) instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5266 to indicate that the entries may be thought of as sums (of lower numbered columns)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5267 rather than differences (of higher numbered columns).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5268 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5269 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5270 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5271 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5272 <pb file="add_6782_f235v" o="235v" n="470"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5273 <pb file="add_6782_f236" o="236" n="471"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5274 <div xml:id="echoid-div177" type="page_commentary" level="2" n="177">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5275 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5276 <s xml:id="echoid-s594" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5277 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5278 <s xml:id="echoid-s594" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5279 Rules for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries in six columns of a table generated from a constant difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5280 as on Add MS 6782, f 177–178, but here using the notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> (for sum) instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5281 to indicate that the entries may be thought of as sums (of lower numbered columns)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5282 rather than differences (of higher numbered columns).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5283 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5284 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5285 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5286 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5287 <pb file="add_6782_f236v" o="236v" n="472"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5288 <pb file="add_6782_f237" o="237" n="473"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5289 <div xml:id="echoid-div178" type="page_commentary" level="2" n="178">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5290 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5291 <s xml:id="echoid-s596" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5292 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5293 <s xml:id="echoid-s596" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5294 Calculations similar to those set out on Add MS 6782, f. 148.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5295 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5296 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5297 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5298 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5299 <head xml:id="echoid-head91" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5300 A.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5301 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5302 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5303 <s xml:id="echoid-s598" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5304 Ad numeros triangulos et illorum progenies.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5305 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5306 On triangular numbers and their progeny.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5307 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5308 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5309 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5310 <pb file="add_6782_f237v" o="237v" n="474"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5311 <pb file="add_6782_f238" o="238" n="475"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5312 <pb file="add_6782_f238v" o="238v" n="476"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5313 <pb file="add_6782_f239" o="239" n="477"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5314 <div xml:id="echoid-div179" type="page_commentary" level="2" n="179">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5315 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5316 <s xml:id="echoid-s599" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5317 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5318 <s xml:id="echoid-s599" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5319 At the top of the page is a numerical table in which the leftmost column contains sums of fourth powers
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5320 (1 + 16 + 81 + ...). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5321 Below that is a smaller numerical table in which the leftmost column contains sums of squares. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5322 Further down on the right is a numerical table in which the leftmost column contains sums of cubes. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5323 Each table lists successive differences until a final (constant) difference is reached.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5324 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5325 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5326 <s xml:id="echoid-s600" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5327 The reference to Maurolico is to his <emph style="it">Arithmeticorum libri duo</emph> (1575).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5328 Pages 52, 63, and 67 contain tables of several kinds of figurate numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5329 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5330 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5331 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5332 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5333 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5334 <s xml:id="echoid-s602" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5335 Ad summam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi><mi>Z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5336 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5337 For the sum of squares of squares
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5338 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5339 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5340 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5341 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5342 <s xml:id="echoid-s603" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5343 Vide Maurolicum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5344 in Arithmeticis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5345 pag. 52. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5346 63. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5347 67.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5348 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5349 See Maurolico, in his Arithmetic, pages 52, 63, 67.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5350 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5351 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5352 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5353 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5354 <s xml:id="echoid-s604" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5355 Ad summam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5356 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5357 For the sum of cubes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5358 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5359 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5360 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5361 <pb file="add_6782_f239v" o="239v" n="478"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5362 <pb file="add_6782_f240" o="240" n="479"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5363 <div xml:id="echoid-div180" type="page_commentary" level="2" n="180">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5364 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5365 <s xml:id="echoid-s605" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5366 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5367 <s xml:id="echoid-s605" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5368 The top of the page shows the working out of the formula for the sum of square-squares.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5369 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5370 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5371 <s xml:id="echoid-s606" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5372 The proposition quoted from Maurolico is from his
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5373 <emph style="it">Arithmeticorum libri duo</emph> (1575),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5374 Proposition 58 (page 25):
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5375 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5376 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5377 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5378 Omnis trianguli quadratus, aequalis est aggregato cuborum ab unitate
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5379 usque ad cubum triangulo collateralem inclusiue sumptorum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5380 </quote>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5382 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5383 The square of every triangular number is equal to the sum of cubes from one,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5384 to the cube of the side of the triangular number, all taken together.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5385 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5386 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5387 <s xml:id="echoid-s607" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5388 Maurolico gives as an example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>2</mn><mn>5</mn><mo>=</mo><mn>1</mn><mo>+</mo><mn>8</mn><mo>+</mo><mn>2</mn><mn>7</mn><mo>+</mo><mn>6</mn><mn>4</mn><mo>+</mo><mn>1</mn><mn>2</mn><mn>5</mn></mstyle></math>.
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5392 At the bottom of the page are formulae for sums of units, lines, squares, cubes, and square-squares.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5393 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5394 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5395 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5396 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5397 <head xml:id="echoid-head92" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5398 Ad aggregata Z. C. ZZ. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5399 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5400 Towards the sums of squares, cubes, square-squares, etc.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5401 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5402 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5403 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5404 <s xml:id="echoid-s610" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5405 least
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5406 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5407 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5408 <p xml:lang="lat">
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5410 <reg norm="Maurolico" type="abbr">Maurol</reg>. pag. 25
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5411 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5412 Maurolico page 25
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5414 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5415 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5416 <s xml:id="echoid-s612" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5417 omnis triangula quadratus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5418 æqualis est aggregato cuborum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5419 ab unitate usque ad cubum triangulo <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5420 collateralem incipio sumptae.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5421 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5422 the square of every triangluar number is equal to the sum of cubes from one,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5423 to the cube of the corresponding triangular number taken from the beginning.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5424 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5425 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5426 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5427 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5428 <s xml:id="echoid-s613" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5429 lines æquall.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5430 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5431 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5432 <s xml:id="echoid-s614" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5433 lines æqually [???]
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5435 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5436 <s xml:id="echoid-s615" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5437 squares æqually [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5438 in their rootes. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5439 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5440 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5441 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5442 <s xml:id="echoid-s616" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5443 Vel: per reductionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5444 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5445 Or: by reduction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5446 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5447 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5448 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5449 <pb file="add_6782_f240v" o="240v" n="480"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5450 <pb file="add_6782_f241" o="241" n="481"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5451 <pb file="add_6782_f241v" o="241v" n="482"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5452 <pb file="add_6782_f242" o="242" n="483"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5453 <pb file="add_6782_f242v" o="242v" n="484"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5454 <pb file="add_6782_f243" o="243" n="485"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5455 <pb file="add_6782_f243v" o="243v" n="486"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5456 <div xml:id="echoid-div181" type="page_commentary" level="2" n="181">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5457 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5458 <s xml:id="echoid-s617" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5459 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5460 <s xml:id="echoid-s617" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5461 A generalized table of triangular numbers,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5462 in which each entry is the sum of the entry above it and the entry to the left of it.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5463 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5464 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5465 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5466 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5467 <pb file="add_6782_f244" o="244" n="487"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5468 <pb file="add_6782_f244v" o="244v" n="488"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5469 <div xml:id="echoid-div182" type="page_commentary" level="2" n="182">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5470 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5471 <s xml:id="echoid-s619" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5472 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5473 <s xml:id="echoid-s619" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5474 A 28-row difference table with constant third difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5475 The third, second, and first columns begin with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>y</mi></mstyle></math>, repsectively.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5476 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5477 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5478 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5479 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5480 <head xml:id="echoid-head93" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5481 Ad Differentias differentiarum. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5482 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5483 On differences of differences etc.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5484 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5485 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5486 <pb file="add_6782_f245" o="245" n="489"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5487 <pb file="add_6782_f245v" o="245v" n="490"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5488 <pb file="add_6782_f246" o="246" n="491"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5489 <div xml:id="echoid-div183" type="page_commentary" level="2" n="183">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5490 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5491 <s xml:id="echoid-s621" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5492 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5493 <s xml:id="echoid-s621" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5494 The table at the top of the page shows the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>C</mi><mo>+</mo><mn>1</mn><mi>r</mi></mstyle></math> (in modern notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>+</mo><mi>x</mi></mstyle></math>)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5495 evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>.</mo></mstyle></math> To the right are columns of successive differences
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5496 as far as the constant difference 6. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5497 Below that are two further tables, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>C</mi><mo>+</mo><mn>2</mn><mi>r</mi></mstyle></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>+</mo><mi>x</mi></mstyle></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>C</mi><mo>+</mo><mn>3</mn><mi>r</mi></mstyle></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>+</mo><mi>x</mi></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5498 The last one is extrapolated upwards to include values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5499 At the bottom of the page are formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th entries columns 0 to 4 of a table generated from
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5500 a constant difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> in column 0.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5501 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5502 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5503 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5504 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5505 <pb file="add_6782_f246v" o="246v" n="492"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5506 <pb file="add_6782_f247" o="247" n="493"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5507 <div xml:id="echoid-div184" type="page_commentary" level="2" n="184">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5508 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5509 <s xml:id="echoid-s623" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5510 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5511 <s xml:id="echoid-s623" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5512 The lower part of this page contains some jottings on binary arithmetic:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5513 addition of 10000 and 10010, multiplication of 101 by 111, and numbers from 1 to 16 in binary
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5514 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5515 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5516 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5517 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5518 <pb file="add_6782_f247v" o="247v" n="494"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5519 <pb file="add_6782_f248" o="248" n="495"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5520 <head xml:id="echoid-head94" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5521 A. Data media trium proportionalium et differentia extremorum invenire extremas.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5522 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5523 Given the mean of three proportionals and the difference of the extremes, find the extremes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5524 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5525 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5526 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5527 <s xml:id="echoid-s625" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5528 Zet. 2,3:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5529 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5530 Zetetic II.3
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5531 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5532 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5533 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5534 <s xml:id="echoid-s626" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5535 z. 1,1:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5536 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5537 Zetetic I.1
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5538 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5539 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5540 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5541 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5542 <s xml:id="echoid-s627" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5543 Zet. 2,3: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math> aggregatum extremarum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5544 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5545 Zetetic II.3: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math> sum of the extrmes
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5546 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5547 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5548 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5549 <s xml:id="echoid-s628" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5550 z. 1,1: Tum:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5551 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5552 Zetetic I.1: then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5553 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5554 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5555 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5556 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5557 <s xml:id="echoid-s629" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5558 Zet. 2,3: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math> aggregatum extremarum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5559 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5560 Zetetic II.3: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math> sum of the extremes
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5561 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5562 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5563 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5564 <s xml:id="echoid-s630" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5565 zet. 1,1. tum:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5566 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5567 Zetetic I.1, then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5568 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5569 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5570 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5571 <head xml:id="echoid-head95" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5572 A. Data media trium proportionalium et summa extremorum invenire extremas.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5573 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5574 Given the mean of three proportionals and the sum of the extremes, find the extremes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5575 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5576 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5577 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5578 <s xml:id="echoid-s631" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5579 Tum est <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5580 supra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5581 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5582 Then is the above
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5583 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5584 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5585 <s xml:id="echoid-s632" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5586 Ergo: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5587 Zet. 2,4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5588 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5589 Therefore, Zetetic II.3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5590 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5591 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5592 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5593 <s xml:id="echoid-s633" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5594 Zet. 1,1. tum:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5595 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5596 Zetetic I.1, then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5597 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5598 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5599 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5600 <pb file="add_6782_f248v" o="248v" n="496"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5601 <pb file="add_6782_f249" o="249" n="497"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5602 <pb file="add_6782_f249v" o="249v" n="498"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5603 <div xml:id="echoid-div185" type="page_commentary" level="2" n="185">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5604 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5605 <s xml:id="echoid-s634" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5606 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5607 <s xml:id="echoid-s634" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5608 On this page Harriot solves <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mo>=</mo><mn>1</mn><mn>0</mn></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mo>=</mo><mn>8</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5609 The latter has real roots 4 and 2, but the roots of the former are complex, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mo>±</mo><msqrt><mrow><mo>-</mo><mn>1</mn></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5610 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5611 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5612 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5613 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5614 <pb file="add_6782_f250" o="250" n="499"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5615 <div xml:id="echoid-div186" type="page_commentary" level="2" n="186">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5616 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5617 <s xml:id="echoid-s636" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5618 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5619 <s xml:id="echoid-s636" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5620 At the bottom of this page Harriot solves <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>d</mi><mi>d</mi><mo>=</mo><mn>2</mn><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5621 giving the solutions <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>d</mi><mo>±</mo><msqrt><mrow><mo>-</mo><mi>d</mi><mi>d</mi></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5622 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5623 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5624 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5625 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5626 <pb file="add_6782_f250v" o="250v" n="500"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5627 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5628 <s xml:id="echoid-s638" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5629 Bombell
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5630 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5631 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5632 <pb file="add_6782_f251" o="251" n="501"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5633 <pb file="add_6782_f251v" o="251v" n="502"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5634 <pb file="add_6782_f252" o="252" n="503"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5635 <pb file="add_6782_f252v" o="252v" n="504"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5636 <pb file="add_6782_f253" o="253" n="505"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5637 <pb file="add_6782_f253v" o="253v" n="506"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5638 <pb file="add_6782_f254" o="254" n="507"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5639 <div xml:id="echoid-div187" type="page_commentary" level="2" n="187">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5640 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5641 <s xml:id="echoid-s639" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5642 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5643 <s xml:id="echoid-s639" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5644 The table at the top of the page shows the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>C</mi><mo>+</mo><mn>1</mn><mi>z</mi><mo>+</mo><mn>1</mn><mi>r</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5645 (in modern notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>+</mo><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mi>x</mi></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5646 evaluated for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></mstyle></math>. To the right are columns of successive differences
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5647 as far as the constant difference 6. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5648 Below that are three further tables for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>C</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>+</mo><mn>3</mn><mi>r</mi></mstyle></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>+</mo><mn>2</mn><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mn>3</mn><mi>x</mi></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5649 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>C</mi><mo>+</mo><mn>3</mn><mi>z</mi><mo>+</mo><mn>2</mn><mi>r</mi></mstyle></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>+</mo><mn>3</mn><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mn>2</mn><mi>x</mi></mstyle></math>), and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mi>C</mi><mo>+</mo><mn>4</mn><mi>z</mi><mo>+</mo><mn>5</mn><mi>r</mi></mstyle></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>+</mo><mn>4</mn><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mn>5</mn><mi>x</mi></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5650 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5651 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5652 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5653 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5654 <pb file="add_6782_f254v" o="254v" n="508"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5655 <pb file="add_6782_f255" o="255" n="509"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5656 <pb file="add_6782_f255v" o="255v" n="510"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5657 <pb file="add_6782_f256" o="256" n="511"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5658 <div xml:id="echoid-div188" type="page_commentary" level="2" n="188">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5659 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5660 <s xml:id="echoid-s641" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5661 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5662 <s xml:id="echoid-s641" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5663 The reference on this page is to Proposition 16 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5664 <emph style="it">Supplementum geometriæ</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5665 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5666 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5667 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5668 Proposition XVI. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5669 Si duo triangula fuerint aequicrura singula, & ipsa alterum alteri cruribus aequalia,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5670 angulus autem qui est ad basin secundi sit triplus anguli qui est ad basin primi:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5671 cubus ex base primi, minus triplo solido sub base primi & cruris communis quadrato,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5672 aequalis est solido sub base secundi & ejusdem cruris quadrato.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5673 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5674 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5675 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5676 If two triangles are each isosceles, the legs of one equal to the legs of the other,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5677 and moreover the angle at the base of the second is three times the angle at the base of the first,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5678 then the cube of the first base, minus three times the product of the base of the first and the square of the common side,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5679 is equal to the product of the second base and the square of the same side.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5680 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5681 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5682 <s xml:id="echoid-s642" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5683 For Harriot's statement of Proposition 16, and a geometric version of the proof, see Add MS 6784, f. 351.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5684 Here he works the proposition algebraically.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5685 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5686 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5687 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5688 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5689 <head xml:id="echoid-head96" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5690 prop. 16. Supplementi.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5691 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5692 Proposition 16 from the Supplement
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5693 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5694 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5695 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5696 <s xml:id="echoid-s644" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5697 duplicature <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5698 cubus <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5699 the cube is doubled.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5700 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5701 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5702 </p>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5705 <pb file="add_6782_f257v" o="257v" n="514"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5706 <pb file="add_6782_f258" o="258" n="515"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5707 <pb file="add_6782_f258v" o="258v" n="516"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5708 <pb file="add_6782_f259" o="259" n="517"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5709 <pb file="add_6782_f259v" o="259v" n="518"/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5712 <pb file="add_6782_f261" o="261" n="521"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5713 <pb file="add_6782_f261v" o="261v" n="522"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5714 <pb file="add_6782_f262" o="262" n="523"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5715 <head xml:id="echoid-head97" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5716 1.) Apotome ex linea secta in extrema et media <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5717 ratione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5718 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5719 An apotome from cutting a line in extreme and mean ratio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5720 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5721 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5722 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5723 <s xml:id="echoid-s645" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5724 Apotome 5<emph style="super">ta</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5725 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5726 A fifth apotome.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5727 </emph>]<lb/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5729 </p>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5732 Apotome 1<emph style="super">a</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5733 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5734 A first apotome.
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5740 Apotome 1<emph style="super">a</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5741 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5742 A first apotome.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5743 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5744 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5745 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5746 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5747 <s xml:id="echoid-s648" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5748 Apot: 5<emph style="super">a</emph>. Apot: 1<emph style="super">a</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5749 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5750 A fifth apotome. A first apotome.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5751 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5752 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5753 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5754 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5755 <s xml:id="echoid-s649" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5756 Bin: 5. Apot: 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5757 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5758 A fifth binome. A fifth apotome.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5759 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5760 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5761 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5762 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5763 <s xml:id="echoid-s650" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5764 Bin: 1<emph style="super">a</emph>. Bin: 5<emph style="super">a</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5765 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5766 A first binome. A fifth apotome.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5767 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5768 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5769 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5770 <pb file="add_6782_f262v" o="262v" n="524"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5771 <pb file="add_6782_f263" o="263" n="525"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5772 <div xml:id="echoid-div189" type="page_commentary" level="2" n="189">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5773 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5774 <s xml:id="echoid-s651" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5775 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5776 <s xml:id="echoid-s651" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5777 Continued from Add MS 6782, f. 262.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5778 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5779 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5780 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5781 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5782 <head xml:id="echoid-head98" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5783 2.) De linea secta extrema e media ratione
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5784 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5785 On a line cut in extreme and mean ratio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5786 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5787 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5788 <pb file="add_6782_f263v" o="263v" n="526"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5789 <pb file="add_6782_f264" o="264" n="527"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5790 <div xml:id="echoid-div190" type="page_commentary" level="2" n="190">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5791 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5792 <s xml:id="echoid-s653" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5793 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5794 <s xml:id="echoid-s653" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5795 This page contains an analysis of Proposition 1 from Book XIII of Euclid's <emph style="it">Elements</emph>:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5796 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5797 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5798 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5799 XIII.1 If a straight line is cut in extreme and mean ratio,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5800 then the square on the greater segment added to the half of the whole is five times the square on the half.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5801 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5802 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5803 <s xml:id="echoid-s654" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5804 The left hand column gives the 'analysis' or 'resolution' of the problem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5805 beginning from the final statement and working backwards to discover what conditions must hold. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5806 The right hand column gives the 'synthesis' or 'composition',
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5807 beginning from the given conditions and working forward to the proof of the proposition.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5808 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5809 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5810 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5811 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5812 <head xml:id="echoid-head99" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5813 Euclid: lib: 13
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5814 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5815 Euclid Book XIII
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5816 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5817 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5818 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5819 <s xml:id="echoid-s656" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5820 prop. 1. analysis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5821 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5822 Proposition 1, analysis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5823 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5824 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5825 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5826 <s xml:id="echoid-s657" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5827 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> secta extra: & med. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5828 in puncto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5829 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5830 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> be cut in extrme and mean ratio in point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5831 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5832 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5833 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5834 <s xml:id="echoid-s658" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5835 dico quod
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5836 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5837 I say that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5838 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5839 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5840 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5841 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5842 <s xml:id="echoid-s659" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5843 Resolutio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5844 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5845 Resolution
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5846 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5847 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5848 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5849 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5850 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5851 <s xml:id="echoid-s660" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5852 Est igitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5853 est enim:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5854 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5855 Therefore it is so; for it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5856 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5857 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5858 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5859 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5860 <s xml:id="echoid-s661" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5861 Compositio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5862 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5863 Composition
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5864 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5865 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5866 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5867 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5868 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5869 <s xml:id="echoid-s662" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5870 Quod demonstrare <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5871 oportuit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5872 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5873 Which was to be demonstrated.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5874 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5875 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5876 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5877 <pb file="add_6782_f264v" o="264v" n="528"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5878 <pb file="add_6782_f265" o="265" n="529"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5879 <div xml:id="echoid-div191" type="page_commentary" level="2" n="191">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5880 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5881 <s xml:id="echoid-s663" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5882 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5883 <s xml:id="echoid-s663" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5884 The irrationals defined by Euclid in Book X of the <emph style="it">Elements</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5885 are binomes, bimedials, and so on. For their definitions and properties see Add MS 6783, f. 356v to f. 343v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5886 Here Harriot defines some further irrational quantities, all of them involving fourth roots,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5887 which do not fall into any of Euclid's categories. See also Add MS 6782, f. 266.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5888 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5889 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5890 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5891 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5892 <head xml:id="echoid-head100" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5893 De speciebus irrationalium ab Euclide omissis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5894 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5895 On types of irrationals missed by Eculid
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5896 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5897 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5898 <pb file="add_6782_f265v" o="265v" n="530"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5899 <pb file="add_6782_f266" o="266" n="531"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5900 <div xml:id="echoid-div192" type="page_commentary" level="2" n="192">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5901 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5902 <s xml:id="echoid-s665" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5903 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5904 <s xml:id="echoid-s665" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5905 The irrationals defined by Euclid in Book X of the <emph style="it">Elements</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5906 are binomes, bimedials, and so on. For their definitions and properties see Add MS 6783, f. 356v to f. 343v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5907 Here Harriot defines some further irrational quantities, all of them involving fourth roots,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5908 which do not fall into any of Euclid's categories. See also Add MS 6782, f. 265.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5909 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5910 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5911 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5912 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5913 <head xml:id="echoid-head101" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5914 De speciebus irrationalium ab Euclide omissis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5915 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5916 On types of irrationals missed by Eculid
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5917 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5918 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5919 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5920 <s xml:id="echoid-s667" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5921 Nota
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5922 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5923 Note
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5924 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5925 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5926 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5927 <s xml:id="echoid-s668" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5928 Animadvertendum quod quælibet harum <emph style="st">specier</emph> <emph style="super">irrationalium</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5929 producit quadratum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5930 trinomium compositum ex binomio et mediali.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5931 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5932 <s xml:id="echoid-s669" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5933 Et quodlibet bino-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5934 mium huius<emph style="super">modi</emph> speciei <emph style="super">logisticæ</emph> continet in se
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5935 implicite duas subspecies.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5936 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5937 <s xml:id="echoid-s670" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5938 Quod <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5939 si <emph style="super">in singulis</emph> distincte explica<emph style="super">tur</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5940 ex istis 5 irrationalibus fient 10.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5941 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5942 <s xml:id="echoid-s671" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5943 Ut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5944 alijs chartis sequentibus apparebit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5945 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5946 It is to be noted that any of these irrationals squared produces a trinomial composed of a binome and a medial.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5947 And any binome of this form in letters contains in itself two subforms.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5948 Which if in each case are set out, from these five irrationals there arise 10.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5949 As will appear in the following sheets.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5950 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5951 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5952 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5953 <pb file="add_6782_f266v" o="266v" n="532"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5954 <pb file="add_6782_f267" o="267" n="533"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5955 <div xml:id="echoid-div193" type="page_commentary" level="2" n="193">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5956 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5957 <s xml:id="echoid-s672" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5958 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5959 <s xml:id="echoid-s672" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5960 In modern notation, binomes are numbers of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5961 where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> are integers. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5962 In Book X, Definitions II, Euclid defined six kinds of binomes,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5963 according to various relationships of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5964 which for Euclid were geometric lengths (see Heath, III, 5–6 and 101–115).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5965 In modern notation, the six binomes may be defined as follows. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5966 Binome 1: a binome of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>+</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>></mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5967 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>m</mi><mn>2</mn></msup></mrow><mo>=</mo><mi>n</mi><mo>+</mo><mi>k</mi></mstyle></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>m</mi></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac></mstyle></math> is rational; for example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>+</mo><msqrt><mrow><mn>4</mn><mn>8</mn></mrow></msqrt></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5968 Binome 2: a binome of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>+</mo><mi>n</mi></mstyle></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>></mo><mi>n</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5969 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>=</mo><mrow><msup><mi>n</mi><mn>2</mn></msup></mrow><mo>+</mo><mi>k</mi></mstyle></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><msqrt><mrow><mi>m</mi></mrow></msqrt></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac></mstyle></math> is rational; for example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>1</mn><mn>2</mn></mrow></msqrt><mo>+</mo><mn>3</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5970 Binome 3: a binome of the form<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>></mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5971 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>=</mo><mi>n</mi><mo>+</mo><mi>k</mi></mstyle></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><msqrt><mrow><mi>m</mi></mrow></msqrt></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac></mstyle></math> is rational; for example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>8</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>6</mn></mrow></msqrt></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5972 Binome 4: a binome of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>+</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>></mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5973 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>m</mi><mn>2</mn></msup></mrow><mo>=</mo><mi>n</mi><mo>+</mo><mi>k</mi></mstyle></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>m</mi></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac></mstyle></math> is non-rational; for example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mo>+</mo><msqrt><mrow><mn>2</mn></mrow></msqrt></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5974 Binome 5: a binome of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>+</mo><mi>n</mi></mstyle></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>></mo><mi>n</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5975 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>=</mo><mrow><msup><mi>n</mi><mn>2</mn></msup></mrow><mo>+</mo><mi>k</mi></mstyle></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><msqrt><mrow><mi>m</mi></mrow></msqrt></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac></mstyle></math> is non-rational; for example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>+</mo><mn>1</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5976 Binome 6: a binome of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>></mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5977 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>=</mo><mi>n</mi><mo>+</mo><mi>k</mi></mstyle></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><msqrt><mrow><mi>m</mi></mrow></msqrt></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac></mstyle></math> is non-rational; for example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>2</mn></mrow></msqrt></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5978 Harriot made two further distinctions for binomes of the fifth and sixth kind according to whether
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5979 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi></mstyle></math> is itself a square (type i) or not (type (ii). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5980 In this and the following folio, Add MS 6782, f. 268,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5981 Harriot shows that the square of any binome is always a binome of the first kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5982 This folio shows his working for first, second, and third binomes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5983 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5984 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5985 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5986 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5987 <head xml:id="echoid-head102" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5988 Binomiorum quadrata, sunt binomia prima.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5989 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5990 Squares of binomes are binomes of the first kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5991 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5992 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5993 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5994 <s xml:id="echoid-s674" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5995 1. bin)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5996 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5997 A binomial of the first kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5998 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	5999 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6000 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6001 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6002 <s xml:id="echoid-s675" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6003 2.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6004 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6005 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6006 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6007 <s xml:id="echoid-s676" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6008 3.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6009 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6010 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6011 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6012 <s xml:id="echoid-s677" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6013 ut supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6014 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6015 as above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6016 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6017 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6018 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6019 <pb file="add_6782_f267v" o="267v" n="534"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6020 <pb file="add_6782_f268" o="268" n="535"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6021 <div xml:id="echoid-div194" type="page_commentary" level="2" n="194">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6022 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6023 <s xml:id="echoid-s678" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6024 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6025 <s xml:id="echoid-s678" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6026 This folio is the continuation of Add MS 6782, f. 267.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6027 Here Harriot checks that the squares of fourth, fifth, and sixth binomes,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6028 are always binomes of the first kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6029 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6030 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6031 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6032 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6033 <head xml:id="echoid-head103" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6034 Binomiorum quadrata, sunt binomia prima.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6035 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6036 Squares of binomes are binomes of the first kind.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6037 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6038 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6039 <pb file="add_6782_f268v" o="268v" n="536"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6040 <pb file="add_6782_f269" o="269" n="537"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6041 <pb file="add_6782_f269v" o="269v" n="538"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6042 <pb file="add_6782_f270" o="270" n="539"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6043 <pb file="add_6782_f270v" o="270v" n="540"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6044 <pb file="add_6782_f271" o="271" n="541"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6045 <pb file="add_6782_f271v" o="271v" n="542"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6046 <pb file="add_6782_f272" o="272" n="543"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6047 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6048 <s xml:id="echoid-s680" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6049 Data secundum trium proportionalium: invenire primam et tertiam, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6050 ut illarum differentia sit æqualis bis secundæ datæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6051 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6052 Given the second of three proportionals:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6053 find the first and third so that their difference is equal to twice the given second.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6054 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6055 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6056 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6057 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6058 <s xml:id="echoid-s681" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6059 Sit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> prima, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, secunda. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6060 ut illarum differentia sit æqualis bis secundæ datæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6061 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6062 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the first, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> the second, such that their difference is equal to twice the given second.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6063 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6064 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6065 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6066 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6067 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6068 <s xml:id="echoid-s682" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6069 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>a</mi><mi>t</mi><mo>=</mo><mi>a</mi><mi>c</mi></mstyle></math>. Rationalis potentia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6070 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6071 Rational in square.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6072 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6073 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6074 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6075 <s xml:id="echoid-s683" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6076 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>c</mi></mstyle></math> Apotome 5<emph style="super">ta</emph>, 1<emph style="super">o</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6077 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6078 A fifth apotome
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6079 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6080 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6081 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6082 <s xml:id="echoid-s684" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6083 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>b</mi></mstyle></math> Rationalis posita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6084 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6085 The supposed rational
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6086 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6087 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6088 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6089 <s xml:id="echoid-s685" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6090 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>f</mi></mstyle></math> Binomia 5<emph style="super">a</emph>, 1<emph style="super">o</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6091 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6092 A fifth binome
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6093 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6094 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6095 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6096 <s xml:id="echoid-s686" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6097 Erit etiam <lb/>[...]<lb/> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math>. Binomia 4<emph style="super">a</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6098 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6099 There will also be <lb/>[...]<lb/> a fourth binome
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6100 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6101 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6102 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6103 <s xml:id="echoid-s687" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6104 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>b</mi></mstyle></math>. Apotome 4<emph style="super">a</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6105 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6106 a fourth apotome
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6107 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6108 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6109 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6110 <s xml:id="echoid-s688" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6111 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>e</mi></mstyle></math>. cum rationalium medium totum efficiens 1<emph style="super">o</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6112 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6113 with the rational, making the mean of all
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6114 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6115 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6116 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6117 <s xml:id="echoid-s689" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6118 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi></mstyle></math>. Minor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6119 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6120 Lesser
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6121 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6122 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6123 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6124 <s xml:id="echoid-s690" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6125 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>e</mi></mstyle></math>. Media.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6126 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6127 Mean
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6128 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6129 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6130 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6131 <s xml:id="echoid-s691" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6132 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi></mstyle></math>. Rationale et medium potens. 1<emph style="super">o</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6133 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6134 A power of the rational and the mean
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6135 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6136 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6137 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6138 <pb file="add_6782_f272v" o="272v" n="544"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6139 <pb file="add_6782_f273" o="273" n="545"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6140 <pb file="add_6782_f273v-274" o="273v-274" n="546"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6141 <pb file="add_6782_f273v" o="273v" n="547"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6142 <pb file="add_6782_f274" o="274" n="548"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6143 <pb file="add_6782_f274v" o="274v" n="549"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6144 <pb file="add_6782_f275" o="275" n="550"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6145 <pb file="add_6782_f275v" o="275v" n="551"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6146 <pb file="add_6782_f276" o="276" n="552"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6147 <div xml:id="echoid-div195" type="page_commentary" level="2" n="195">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6148 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6149 <s xml:id="echoid-s692" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6150 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6151 <s xml:id="echoid-s692" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6152 Powers of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo></mstyle></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mrow><msup><mo maxsize="1">)</mo><mn>5</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6153 Each power is calculated from the previous one by multiplication. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6154 Note the use of cossist notation:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6155 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> for a first power, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi></mstyle></math> for a square, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> for a cube, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>z</mi></mstyle></math> for a square-suare or fourth power,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6156 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>ß</mo></mstyle></math> for a sursolid or fifth power. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6157 Below the main table is a list of the final sums, including the sixth power (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>c</mi></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6158 which has not been calculated on this page
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6159 but which can be deduced from the pattern for the previous cases. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6160 For a similar table see Add MS 6786, f. 457.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6161 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6162 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6163 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6164 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6165 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6166 <s xml:id="echoid-s694" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6167 Forma <emph style="st">generationis continue</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6168 <emph style="super">generandi figurata</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6169 <emph style="st">proportionalium ab unitate</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6170 <emph style="super">in binomia radice</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6171 per logisticen speciosam: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6172 <emph style="st">ad demonstrandum pro parte alium</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6173 <emph style="st">in numeris analysin.</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6174 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6175 A method of generating figurate numbers from binomial roots in letters:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6176 </emph>]<lb/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6178 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6179 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6180 <s xml:id="echoid-s695" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6181 Nota: pro porismo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6182 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6183 Note: for the proof.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6184 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6185 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6186 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6187 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6188 <s xml:id="echoid-s696" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6189 Species partium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6190 unius cuisque potentiæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6191 sunt continue proportionales <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6192 ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6193 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6194 The case of a single part where the powers are in continued proportion as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6195 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6196 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6197 <s xml:id="echoid-s697" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6198 Et in numeris, sunt <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6199 termini minimi si <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> sunt primi &c. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6200 et non in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6201 ratione <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6202 multiplicant.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6203 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6204 And in numbers, these are the lowest terms, if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> are the first, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6205 and they are not multiplied by some ratio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6206 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6207 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6208 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6209 <pb file="add_6782_f276v" o="276v" n="553"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6210 <pb file="add_6782_f277" o="277" n="554"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6211 <div xml:id="echoid-div196" type="page_commentary" level="2" n="196">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6212 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6213 <s xml:id="echoid-s698" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6214 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6215 <s xml:id="echoid-s698" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6216 This page shows notation used for first, second, third, ...., ninth powers in the following authors: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6217 Diophantus in <emph style="it">Diophanti Alexandrini rerum arithmeticarum libri sex</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6218 edited by Wilhelm Xylander (1575); <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6219 François Viète in, for example, <emph style="it">In artem analyticen isagoge</emph> (1591); <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6220 Bernard Salignac in <emph style="it">Arithmeticae libri duo et algebrae totidem</emph> (1580, 1593); <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6221 Michael Stifel in <emph style="it">Arithmetica integra</emph> (1544); <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6222 Christoph Clavius in <emph style="it">Algebra</emph> (1608); <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6223 Simon Stevin in <emph style="it">L'arithmétique ... aussi l'algèbre</emph> (1585). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6224 The inclusion of Clavius in this list is particularly significant since it dates the page to 1608 or later.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6225 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6226 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6227 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6228 <lb/><lb/></s></p></div>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6230 <s xml:id="echoid-s700" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6231 & indices gradarum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6232 <t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6233 ec. indices of the degrees
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6235 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6236 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6237 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6238 <s xml:id="echoid-s701" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6239 ut Diophantus et Vieta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6240 <t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6241 as in Diophantus and Viète
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6242 </t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6243 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6244 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6245 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6246 <s xml:id="echoid-s702" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6247 ut Salignacus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6248 <t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6249 as in Salignacus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6250 </t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6251 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6252 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6253 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6254 <s xml:id="echoid-s703" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6255 ut Stifelius, Clavius et alij
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6256 <t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6257 as in Stifel, Clavius and others
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6258 </t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6259 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6260 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6261 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6262 <s xml:id="echoid-s704" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6263 ut Stevinus et alij
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6264 <t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6265 as in Stevin and others
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6266 </t>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6267 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6268 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6269 <pb file="add_6782_f277v" o="277v" n="555"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6270 <pb file="add_6782_f278" o="278" n="556"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6271 <div xml:id="echoid-div197" type="page_commentary" level="2" n="197">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6272 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6273 <s xml:id="echoid-s705" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6274 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6275 <s xml:id="echoid-s705" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6276 Powers of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>6</mn><mn>0</mn><mo>+</mo><mn>7</mn><mo maxsize="1">)</mo></mstyle></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>6</mn><mn>0</mn><mo>+</mo><mn>7</mn><mrow><msup><mo maxsize="1">)</mo><mn>5</mn></msup></mrow></mstyle></math> following the pattern laid out in f. 276. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6277 A calculation below each box gives the sum of the figures contained in it.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6278 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6279 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6280 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6281 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6282 <pb file="add_6782_f278v" o="278v" n="557"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6283 <pb file="add_6782_f279" o="279" n="558"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6284 <div xml:id="echoid-div198" type="page_commentary" level="2" n="198">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6285 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6286 <s xml:id="echoid-s707" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6287 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6288 <s xml:id="echoid-s707" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6289 The example <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>6</mn><mn>0</mn><mo>+</mo><mn>7</mn><mrow><msup><mo maxsize="1">)</mo><mn>3</mn></msup></mrow></mstyle></math> from f. 278 set out to show how the binomial coefficients are used.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6290 Thus, in calculating the cube, for wich the coefficients are 1,3, 3, 1,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6291 the cube of 6 (the relevant digit of 60) is used once,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6292 the square is taken 3 times and multiplied by 7,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6293 while 6 is also taken 3 times and multiplied by the square of 7;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6294 finally the cube of 7 is added once.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6295 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6296 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6297 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6298 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6299 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6300 <s xml:id="echoid-s709" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6301 Numerorum dispositio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6302 ad figuratorum genesin et <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6303 analysin demonstrandam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6304 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6305 The disposition of the numbers for the generation of figurate numbers and for demonstrating the analysis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6306 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6307 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6308 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6309 <pb file="add_6782_f279v" o="279v" n="559"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6310 <pb file="add_6782_f280" o="280" n="560"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6311 <div xml:id="echoid-div199" type="page_commentary" level="2" n="199">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6312 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6313 <s xml:id="echoid-s710" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6314 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6315 <s xml:id="echoid-s710" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6316 The upper third of the page contains calculations of powers of 24, up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mn>2</mn><mn>4</mn><mrow><msup><mo maxsize="1">)</mo><mn>5</mn></msup></mrow></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6317 The lower third of the page contain calculations of powers of 67 (see also f. 278). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6318 In the middle of the page, the binomial coefficients are listed in three different layouts.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6319 The table on the left shows how each row may be calculated by adding two copies of the previous row.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6320 A similar table appears again in the lower right of the page.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6321 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6322 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6323 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6324 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6325 <pb file="add_6782_f280v" o="280v" n="561"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6326 <div xml:id="echoid-div200" type="page_commentary" level="2" n="200">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6327 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6328 <s xml:id="echoid-s712" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6329 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6330 <s xml:id="echoid-s712" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6331 The first units mentioned are bushels, a measure of grain, equivalent to 4 pecks or 8 gallons. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6332 The page contains a conversion of 6553600000 bushels per square mile to 10485760 bushels per acre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6333 (1 square mile = 640 acres),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6334 and a conversion of 262144 acres to 409 square miles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6335 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6336 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6337 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6338 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6339 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6340 <s xml:id="echoid-s714" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6341 10485,760 bushelles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6342 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6343 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6344 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6345 <s xml:id="echoid-s715" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6346 262,144 acres
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6347 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6348 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6349 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6350 <s xml:id="echoid-s716" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6351 640 acres in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6352 a square mile
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6353 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6354 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6355 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6356 <s xml:id="echoid-s717" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6357 409 miles square
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6358 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6359 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6360 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6361 <s xml:id="echoid-s718" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6362 20 miles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6363 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6364 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6365 <pb file="add_6782_f281" o="281" n="562"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6366 <div xml:id="echoid-div201" type="page_commentary" level="2" n="201">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6367 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6368 <s xml:id="echoid-s719" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6369 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6370 <s xml:id="echoid-s719" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6371 Here Harriot calculates the square root of 4489, the cube root of 300763,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6372 the fourth root of 20151121, and the sixth root of 1350125107,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6373 demonstrating that the answer is 67 in each case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6374 This is the analysis, or taking apart, of what has been constructed on f. 278. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6375 Maurolico's treatment of cube roots begins on page 110 of his
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6376 <emph style="it">Arithmeticorum libri duo</emph> (1575).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6377 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6378 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6379 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6380 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6381 <head xml:id="echoid-head104" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6382 Analysis:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6383 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6384 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6385 <s xml:id="echoid-s721" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6386 Inde: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi><mi>d</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>b</mi><mo>+</mo><mn>3</mn><mi>d</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6387 ut Maurolicus et nos in alia charta demonstravimus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6388 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6389 Whence <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi><mi>d</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>b</mi><mo>+</mo><mn>3</mn><mi>d</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>, as in Maurolicus and as I have demonstrated in another sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6390 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6391 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6392 This note shows an alternative method of calculation, attributed to Maurolico,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6393 in which <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> is replaced by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6394 An asterisk against the note directs the reader to Maurolico's method of calculation, on the right.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6395 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6396 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6397 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6398 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6399 <s xml:id="echoid-s722" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6400 Maurolicus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6401 [???]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6402 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6403 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6404 <pb file="add_6782_f281v" o="281v" n="563"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6405 <pb file="add_6782_f282" o="282" n="564"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6406 <pb file="add_6782_f282v" o="282v" n="565"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6407 <pb file="add_6782_f283" o="283" n="566"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6408 <pb file="add_6782_f283v" o="283v" n="567"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6409 <pb file="add_6782_f284" o="284" n="568"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6410 <pb file="add_6782_f284v" o="284v" n="569"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6411 <pb file="add_6782_f285" o="285" n="570"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6412 <pb file="add_6782_f285v" o="285v" n="571"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6413 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6414 <s xml:id="echoid-s723" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6415 oppose?? <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6416 suum coniugatum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6417 eosdem habet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6418 numeros.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6419 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6420 their conjugates have the same numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6421 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6422 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6423 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6424 <s xml:id="echoid-s724" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6425 contrarium est <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6426 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>+</mo><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mo>-</mo><mo>=</mo><mo>+</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6427 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6428 the opposite is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>+</mo><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mo>-</mo><mo>=</mo><mo>+</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6429 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6430 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6431 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6432 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6433 <s xml:id="echoid-s725" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6434 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>r</mi></mstyle></math> quando:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6435 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6436 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>r</mi></mstyle></math> when:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6437 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6438 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6439 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6440 <s xml:id="echoid-s726" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6441 ut in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6442 2<emph style="super">o</emph> et 4<emph style="super">o</emph> casu <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6443 et ut in alia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6444 charta probatur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6445 universaliter.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6446 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6447 as in the 2nd and 4th cases and as it is proved generally in the other sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6448 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6449 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6450 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6451 <s xml:id="echoid-s727" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6452 tum <emph style="st">habetur</emph> unum (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>) ex consequenti <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6453 erit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mn>2</mn><mi>r</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6454 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6455 then as a consequence one value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>r</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6456 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6457 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6458 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6459 <s xml:id="echoid-s728" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6460 alterum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> habetur ex universalis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6461 methodo in alia charta.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6462 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6463 another value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is to be had by the general method in another sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6464 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6465 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6466 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6467 <pb file="add_6782_f286" o="286" n="572"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6468 <pb file="add_6782_f286v" o="286v" n="573"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6469 <pb file="add_6782_f287" o="287" n="574"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6470 <pb file="add_6782_f287v" o="287v" n="575"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6471 <pb file="add_6782_f288" o="288" n="576"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6472 <pb file="add_6782_f288v" o="288v" n="577"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6473 <pb file="add_6782_f289" o="289" n="578"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6474 <pb file="add_6782_f289v" o="289v" n="579"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6475 <pb file="add_6782_f290" o="290" n="580"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6476 <pb file="add_6782_f290v" o="290v" n="581"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6477 <pb file="add_6782_f291" o="291" n="582"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6478 <pb file="add_6782_f291v" o="291v" n="583"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6479 <pb file="add_6782_f292" o="292" n="584"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6480 <pb file="add_6782_f292v" o="292v" n="585"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6481 <pb file="add_6782_f293" o="293" n="586"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6482 <pb file="add_6782_f293v" o="293v" n="587"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6483 <pb file="add_6782_f294" o="294" n="588"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6484 <pb file="add_6782_f294v" o="294v" n="589"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6485 <pb file="add_6782_f295" o="295" n="590"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6486 <pb file="add_6782_f295v" o="295v" n="591"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6487 <pb file="add_6782_f296" o="296" n="592"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6488 <pb file="add_6782_f296v" o="296v" n="593"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6489 <pb file="add_6782_f297" o="297" n="594"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6490 <pb file="add_6782_f297v" o="297v" n="595"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6491 <pb file="add_6782_f298" o="298" n="596"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6492 <div xml:id="echoid-div202" type="page_commentary" level="2" n="202">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6493 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6494 <s xml:id="echoid-s729" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6495 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6496 <s xml:id="echoid-s729" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6497 On this folio Harriot gives rules for finding all the parameters of an arithmetic progression
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6498 given any three of them. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6499 The three parameters supposed given are listed in the second column, headed 'data',
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6500 where Harriot runs systematically through all the combinations <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mi>u</mi><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mi>u</mi><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mi>u</mi><mi>s</mi></mstyle></math>, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6501 Rules for finding the two remaining quantities in each case are given in the third column, headed 'quaesita'. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6502 For further details see Stedall 2007.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6503 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6504 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6505 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6506 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6507 <head xml:id="echoid-head105" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6508 Omnes casus arithmeticæ progressionis simplicis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6509 primi ordinis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6510 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6511 All cases of simple arithmetic progressions of the first order
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6512 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6513 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6514 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6515 <s xml:id="echoid-s731" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6516 casus. data. quæsita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6517 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6518 case. given. sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6519 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6520 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6521 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6522 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6523 <s xml:id="echoid-s732" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6524 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. primus numeris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6525 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6526 first number.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6527 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6528 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6529 <s xml:id="echoid-s733" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6530 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. ultimus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6531 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6532 last number.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6533 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6534 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6535 <s xml:id="echoid-s734" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6536 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. differentia. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6537 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6538 difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6539 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6540 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6541 <s xml:id="echoid-s735" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6542 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>. numeris locorum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6543 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6544 number of places.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6545 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6546 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6547 <s xml:id="echoid-s736" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6548 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>. summa.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6549 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6550 sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6551 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6552 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6553 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6554 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6555 <s xml:id="echoid-s737" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6556 6 et 9 casus qui <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6557 signantur * <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6558 soluuntur æquationibus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6559 quadraticis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6560 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6561 Cases 6 and 9 marked thus * are solved by quadratic equations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6562 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6563 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6564 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6565 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6566 <s xml:id="echoid-s738" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6567 Ex his terminis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6568 tribus datis, dantur reliqui.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6569 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6570 From any three terms given, the rest may be found.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6571 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6572 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6573 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6574 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6575 <s xml:id="echoid-s739" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6576 I. unitas.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6577 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6578 I. a unit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6579 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6580 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6581 <s xml:id="echoid-s740" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6582 II. quadratum unitatis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6583 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6584 II. the square of a unit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6585 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6586 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6587 <s xml:id="echoid-s741" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6588 III. cubus unitatis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6589 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6590 III. the cube of a unit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6591 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6592 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6593 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6594 <pb file="add_6782_f298v" o="298v" n="597"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6595 <pb file="add_6782_f299" o="299" n="598"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6596 <div xml:id="echoid-div203" type="page_commentary" level="2" n="203">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6597 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6598 <s xml:id="echoid-s742" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6599 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6600 <s xml:id="echoid-s742" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6601 Rough work, and some equations in words for arithmetic progressions.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6602 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6603 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6604 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6605 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6606 <head xml:id="echoid-head106" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6607 De progressione Arithmetica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6608 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6609 On arithmetic progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6610 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6611 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6612 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6613 <s xml:id="echoid-s744" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6614 In Arithmetica progressionis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6615 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6616 In arithmetic progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6617 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6618 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6619 <s xml:id="echoid-s745" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6620 [1.]) Numerus terminorum – 1 = Numerus differentiorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6621 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6622 The number of terms – 1 = the number of differences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6623 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6624 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6625 <s xml:id="echoid-s746" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6626 [2.]) Maximus terminorum – minimo = Summa differentiorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6627 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6628 The greatest term – the least term = the sum of the differences.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6629 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6630 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6631 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6632 <s xml:id="echoid-s747" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6633 [etc.]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6634 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6635 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6636 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6637 <s xml:id="echoid-s748" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6638 Terminus primorum vel ultimorum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6639 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6640 The term of the first or the last
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6641 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6642 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6643 <s xml:id="echoid-s749" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6644 excessus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6645 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6646 The excess.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6647 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6648 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6649 <s xml:id="echoid-s750" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6650 Summa. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6651 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6652 The sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6653 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6654 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6655 <s xml:id="echoid-s751" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6656 Numerus locorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6657 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6658 The number of places.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6659 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6660 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6661 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6662 <pb file="add_6782_f299v" o="299v" n="599"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6663 <pb file="add_6782_f300" o="300" n="600"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6664 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6665 <s xml:id="echoid-s752" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6666 The ground player <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6667 The persepctive player
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6668 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6669 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6670 <pb file="add_6782_f300v" o="300v" n="601"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6671 <pb file="add_6782_f301" o="301" n="602"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6672 <pb file="add_6782_f301v" o="301v" n="603"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6673 <pb file="add_6782_f302" o="302" n="604"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6674 <pb file="add_6782_f302v" o="302v" n="605"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6675 <pb file="add_6782_f303" o="303" n="606"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6676 <pb file="add_6782_f303v" o="303v" n="607"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6677 <pb file="add_6782_f304" o="304" n="608"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6678 <pb file="add_6782_f304v" o="304v" n="609"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6679 <pb file="add_6782_f305" o="305" n="610"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6680 <pb file="add_6782_f305v" o="305v" n="611"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6681 <pb file="add_6782_f306" o="306" n="612"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6682 <pb file="add_6782_f306v" o="306v" n="613"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6683 <pb file="add_6782_f307" o="307" n="614"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6684 <pb file="add_6782_f307v" o="307v" n="615"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6685 <pb file="add_6782_f308" o="308" n="616"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6686 <pb file="add_6782_f308v" o="308v" n="617"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6687 <pb file="add_6782_f309" o="309" n="618"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6688 <pb file="add_6782_f309v" o="309v" n="619"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6689 <pb file="add_6782_f310" o="310" n="620"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6690 <pb file="add_6782_f310v" o="310v" n="621"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6691 <pb file="add_6782_f311" o="311" n="622"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6692 <div xml:id="echoid-div204" type="page_commentary" level="2" n="204">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6693 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6694 <s xml:id="echoid-s753" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6695 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6696 <s xml:id="echoid-s753" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6697 This page refers to Stevin's <emph style="it">L'arithmétique … aussi l'algebre</emph> (1585), page 331,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6698 where Stevin discusses the equation 1(3) = 6(2) + 400 (in modern notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>=</mo><mn>6</mn><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>=</mo><mn>4</mn><mn>0</mn><mn>0</mn></mstyle></math>.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6699 Here Harriot works on the same equation, written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>4</mn><mn>0</mn><mn>0</mn></mstyle></math>. See also Add MS 6782, f. 311v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6700 The letters S,WL that appear in this page presumably refer to Harriot's friend Sir William Lower.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6701 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6702 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6703 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6704 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6705 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6706 <s xml:id="echoid-s755" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6707 a) Stevin. 331
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6708 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6709 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6710 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6711 <s xml:id="echoid-s756" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6712 S,WL
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6713 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6714 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6715 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6716 <s xml:id="echoid-s757" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6717 Ergo species non est universalis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6718 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6719 Therefore the rule is not general.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6720 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6721 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6722 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6723 <pb file="add_6782_f311v" o="311v" n="623"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6724 <div xml:id="echoid-div205" type="page_commentary" level="2" n="205">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6725 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6726 <s xml:id="echoid-s758" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6727 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6728 <s xml:id="echoid-s758" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6729 Further work relating to Add MS 6782, f. 311.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6730 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6731 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6732 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6733 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6734 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6735 <s xml:id="echoid-s760" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6736 Stevin. 331
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6737 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6738 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6739 <pb file="add_6782_f312" o="312" n="624"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6740 <div xml:id="echoid-div206" type="page_commentary" level="2" n="206">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6741 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6742 <s xml:id="echoid-s761" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6743 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6744 <s xml:id="echoid-s761" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6745 Further work based on Stevin's <emph style="it">L 19arithmétique … aussi l 19algebre</emph> (1585), page 331.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6746 Here Harriot works on general equations of the type <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>f</mi><mi>f</mi><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6747 The letters S,WL that appear on this page presumably refer to Harriot's friend Sir William Lower.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6748 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6749 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6750 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6751 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6752 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6753 <s xml:id="echoid-s763" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6754 b) Stevin. 331
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6755 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6756 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6757 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6758 <s xml:id="echoid-s764" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6759 species non universalis S,WL
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6760 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6761 The rule is not universal.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6762 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6763 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6764 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6765 <pb file="add_6782_f312v" o="312v" n="625"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6766 <pb file="add_6782_f313" o="313" n="626"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6767 <div xml:id="echoid-div207" type="page_commentary" level="2" n="207">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6768 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6769 <s xml:id="echoid-s765" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6770 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6771 <s xml:id="echoid-s765" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6772 The reference on this page is to Aulus Gellius, <emph style="it">Noctes atticae</emph>, (first printed 1469).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6773 Chapter 22 of Book II is entitled
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6774 'De vento iapyge deque aliorum ventorum vocabulis regionibusque accepta ex Favorini sermonibus'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6775 There Aulus Gellius names the winds from each direction; Harriot has placed them around the points of a compass.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6776 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6777 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6778 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6779 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6780 <head xml:id="echoid-head107" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6781 Ex Aulo Gellio. lib. 2. cap. 22. pag. 63.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6782 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6783 <pb file="add_6782_f313v" o="313v" n="627"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6784 <pb file="add_6782_f314" o="314" n="628"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6785 <div xml:id="echoid-div208" type="page_commentary" level="2" n="208">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6786 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6787 <s xml:id="echoid-s767" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6788 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6789 <s xml:id="echoid-s767" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6790 Canonical forms for equation with three or four positive roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6791 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6792 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6793 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6794 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6795 <head xml:id="echoid-head108" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6796 B)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6797 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6798 <pb file="add_6782_f314v" o="314v" n="629"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6799 <pb file="add_6782_f315" o="315" n="630"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6800 <div xml:id="echoid-div209" type="page_commentary" level="2" n="209">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6801 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6802 <s xml:id="echoid-s769" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6803 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6804 <s xml:id="echoid-s769" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6805 An examination of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mn>6</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>1</mn><mi>a</mi><mo>=</mo><mn>6</mn></mstyle></math>, which has roots 1, 2, 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6806 This is one of several equations with multiple roots treated by Viète in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6807 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6808 Harriot solves it in full on Add MS 6783, f. 187, and refers to it again in Add MS 6783, f. 188.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6809 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6810 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6811 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6812 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6813 <head xml:id="echoid-head109" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6814 C)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6815 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6816 <pb file="add_6782_f315v" o="315v" n="631"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6817 <div xml:id="echoid-div210" type="page_commentary" level="2" n="210">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6818 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6819 <s xml:id="echoid-s771" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6820 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6821 <s xml:id="echoid-s771" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6822 An examination of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mn>1</mn><mn>2</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>2</mn><mn>9</mn><mi>a</mi><mo>=</mo><mn>1</mn><mn>8</mn></mstyle></math>, which has roots 1, 2, 9.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6823 This is one of several equations with multiple roots treated by Viète in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6824 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6825 Harriot solves it in full on Add MS 6783, f. 187.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6826 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6827 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6828 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6829 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6830 <head xml:id="echoid-head110" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6831 D)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6832 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6833 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6834 <s xml:id="echoid-s773" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6835 Triens coefficientis longituidnis. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6836 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6837 A third of the longitudinal coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6838 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6839 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6840 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6841 <s xml:id="echoid-s774" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6842 Triplum quadratum. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>b</mi><mi>b</mi><mo>+</mo><mn>6</mn><mi>b</mi><mi>d</mi><mo>+</mo><mn>3</mn><mi>d</mi><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6843 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6844 Three times the square
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6845 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6846 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6847 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6848 <s xml:id="echoid-s775" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6849 maius est coefficientibus planis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6850 per <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>d</mi><mi>d</mi><mo>+</mo><mn>9</mn><mi>d</mi><mi>c</mi><mo>+</mo><mn>9</mn><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6851 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6852 greater than the plane coefficient by
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6853 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6854 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6855 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6856 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6857 <s xml:id="echoid-s776" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6858 Duplus cubus e triente. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6859 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6860 Twice the cube of a third of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6861 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6862 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6863 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6864 <s xml:id="echoid-s777" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6865 maior
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6866 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6867 greater than
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6868 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6869 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6870 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6871 <s xml:id="echoid-s778" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6872 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6873 in coefficientibus planibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6874 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6875 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math> times the plane coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6876 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6877 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6878 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6879 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6880 <s xml:id="echoid-s779" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6881 Excessus maximi laterus supra <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math> fit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6882 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6883 The excess of the greatest side over <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6884 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6885 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6886 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6887 <s xml:id="echoid-s780" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6888 reliqua duo sunt minora <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6889 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6890 the two remaining are less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6891 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6892 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6893 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6894 <s xml:id="echoid-s781" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6895 maxium latus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6896 erit
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6897 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6898 the greatest side will be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6899 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6900 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6901 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6902 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6903 <s xml:id="echoid-s782" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6904 Examinatio. Vide Charta B)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6905 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6906 Examination. See sheet B.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6907 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6908 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6909 Sheet B is Add MS 6782, f. 314.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6910 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6911 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6912 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6913 <s xml:id="echoid-s783" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6914 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6915 coefficientia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6916 plana.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6917 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6918 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> times the plane coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6919 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6920 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6921 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6922 <s xml:id="echoid-s784" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6923 Differentia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6924 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6925 Difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6926 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6927 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6928 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6929 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6930 <s xml:id="echoid-s785" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6931 Nota. Vide K in D.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6932 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6933 Note. See K in D.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6934 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6935 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6936 Sheet D.1 is Add MS 6782, f. 316.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6937 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6938 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6939 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6940 <pb file="add_6782_f316" o="316" n="632"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6941 <head xml:id="echoid-head111" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6942 D.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6943 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6944 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6945 <s xml:id="echoid-s786" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6946 D Nota K.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6947 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6948 Note K for sheet D.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6949 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6950 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6951 Sheet D is Add MS 6783, f. 315v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6952 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6953 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6954 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6955 <pb file="add_6782_f316v" o="316v" n="633"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6956 <pb file="add_6782_f317" o="317" n="634"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6957 <div xml:id="echoid-div211" type="page_commentary" level="2" n="211">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6958 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6959 <s xml:id="echoid-s787" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6960 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6961 <s xml:id="echoid-s787" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6962 An examination of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mn>9</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>2</mn><mn>4</mn><mi>a</mi><mo>=</mo><mn>2</mn><mn>0</mn></mstyle></math>, which has roots 2, 2, 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6963 This is one of several equations with multiple roots treated by Viète in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6964 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6965 Harriot solves it in full on Add MS 6783, f. 187.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6966 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6967 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6968 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6969 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6970 <head xml:id="echoid-head112" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6971 E)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6972 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6973 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6974 <s xml:id="echoid-s789" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6975 Triens coeff: long: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6976 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6977 A third of the longitudinal coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6978 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6979 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6980 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6981 <s xml:id="echoid-s790" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6982 Triplum quadrat: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>b</mi><mi>b</mi><mo>+</mo><mn>6</mn><mi>b</mi><mi>c</mi><mo>+</mo><mn>3</mn><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6983 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6984 Three times the square
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6985 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6986 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6987 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6988 <s xml:id="echoid-s791" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6989 maius est coefficientibus planis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6990 per <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6991 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6992 greater than the plane coefficient by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6993 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6994 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6995 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6996 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6997 <s xml:id="echoid-s792" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6998 Duplus cubus e triente. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	6999 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7000 Twice the cube of the third
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7001 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7002 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7003 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7004 <s xml:id="echoid-s793" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7005 maior
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7006 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7007 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7008 greater than
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7009 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7010 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7011 <s xml:id="echoid-s794" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7012 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7013 coefficientibus planibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7014 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7015 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> times the plane coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7016 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7017 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7018 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7019 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7020 <s xml:id="echoid-s795" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7021 Excessus maximi laterus supra <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7022 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7023 Let the excess of the greatest side over <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7024 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7025 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7026 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7027 <s xml:id="echoid-s796" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7028 reliqua duo sunt minora <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7029 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7030 the remaining two are less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7031 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7032 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7033 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7034 <s xml:id="echoid-s797" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7035 maxium latus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7036 erit
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7037 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7038 the greatest side will be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7039 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7040 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7041 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7042 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7043 <s xml:id="echoid-s798" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7044 Examinatio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7045 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7046 Examination
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7047 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7048 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7049 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7050 <s xml:id="echoid-s799" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7051 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7052 coeff
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7053 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7054 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> times the coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7055 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7056 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7057 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7058 <s xml:id="echoid-s800" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7059 Differentia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7060 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7061 Difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7062 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7063 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7064 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7065 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7066 <s xml:id="echoid-s801" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7067 Aliter casus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7068 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7069 Another case
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7070 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7071 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7072 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7073 <pb file="add_6782_f317v" o="317v" n="635"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7074 <pb file="add_6782_f318" o="318" n="636"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7075 <div xml:id="echoid-div212" type="page_commentary" level="2" n="212">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7076 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7077 <s xml:id="echoid-s802" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7078 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7079 <s xml:id="echoid-s802" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7080 An examination of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mn>1</mn><mn>8</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>9</mn><mn>5</mn><mi>a</mi><mo>=</mo><mn>1</mn><mn>2</mn><mn>6</mn></mstyle></math>, which has roots 2, 7, 9.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7081 This is one of several equations with multiple roots treated by Viète in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7082 <emph style="it">De potestatum numerosa resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7083 Harriot solves it in full on Add MS 6783, f. 187.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7084 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7085 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7086 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7087 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7088 <head xml:id="echoid-head113" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7089 F)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7090 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7091 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7092 <s xml:id="echoid-s804" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7093 Triens coefficientis longituidnis. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7094 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7095 A third of the longitudinal coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7096 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7097 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7098 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7099 <s xml:id="echoid-s805" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7100 Triplum quadratum. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>b</mi><mi>b</mi><mo>-</mo><mn>6</mn><mi>b</mi><mi>d</mi><mo>+</mo><mn>3</mn><mi>d</mi><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7101 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7102 Three times the square
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7103 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7104 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7105 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7106 <s xml:id="echoid-s806" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7107 maius est coefficientibus planis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7108 per <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>d</mi><mi>d</mi><mo>+</mo><mn>9</mn><mi>c</mi><mi>c</mi><mo>-</mo><mn>9</mn><mi>c</mi><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7109 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7110 greater than the plane coefficient by
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7111 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7112 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7113 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7114 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7115 <s xml:id="echoid-s807" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7116 Duplus cubus e triente. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7117 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7118 Twice the cube of the third
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7119 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7120 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7121 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7122 <s xml:id="echoid-s808" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7123 minor
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7124 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7125 less than
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7126 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7127 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7128 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7129 <s xml:id="echoid-s809" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7130 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7131 in coefficientibus planibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7132 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7133 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math> times the plane coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7134 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7135 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7136 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7137 <s xml:id="echoid-s810" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7138 Excessus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7139 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7140 Excess
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7141 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7142 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7143 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7144 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7145 <s xml:id="echoid-s811" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7146 medium et maximum latus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7147 excedunt. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7148 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7149 medium and maximum sides exceed
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7150 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7151 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7152 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7153 <s xml:id="echoid-s812" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7154 sit unus vel alter excessu, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7155 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7156 let one or other excess be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7157 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7158 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7159 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7160 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7161 <s xml:id="echoid-s813" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7162 erit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>=</mo><mi>d</mi></mstyle></math>, excessus medij 1. adde <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math> erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> medium. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7163 erit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>=</mo><mn>3</mn><mi>c</mi><mo>-</mo><mn>2</mn><mi>d</mi></mstyle></math>, excessus maximi 3. adde <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math> erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mn>3</mn><mi>c</mi><mo>-</mo><mn>2</mn><mi>d</mi></mstyle></math> maximum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7164 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7165 if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>=</mo><mi>d</mi></mstyle></math>, the excess of the medium, add <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> will be the medium; <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7166 if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>=</mo><mn>3</mn><mi>c</mi><mo>-</mo><mn>2</mn><mi>d</mi></mstyle></math>, the excess of the maximum, add <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>d</mi></mstyle></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mn>3</mn><mi>c</mi><mo>-</mo><mn>3</mn><mi>d</mi></mstyle></math> will be the maximum;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7167 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7168 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7169 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7170 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7171 <s xml:id="echoid-s814" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7172 Examinatio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7173 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7174 Examination
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7175 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7176 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7177 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7178 <s xml:id="echoid-s815" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7179 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>c</mi></mstyle></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7180 in coeff planis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7181 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7182 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>c</mi></mstyle></math> times <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>d</mi></mstyle></math> times the plane coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7183 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7184 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7185 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7186 <s xml:id="echoid-s816" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7187 cubus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>c</mi><mo>-</mo><mn>2</mn><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7188 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7189 The cube of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>c</mi><mo>-</mo><mn>2</mn><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7190 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7191 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7192 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7193 <s xml:id="echoid-s817" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7194 Differentia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7195 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7196 Difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7197 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7198 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7199 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7200 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7201 <s xml:id="echoid-s818" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7202 Operationes sunt <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7203 in dorso D.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7204 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7205 The working is on the back of D.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7206 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7207 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7208 The back of sheet D.1 is Add MS 6782, f. 316v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7209 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7210 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7211 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7212 <pb file="add_6782_f318v" o="318v" n="637"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7213 <pb file="add_6782_f319" o="319" n="638"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7214 <div xml:id="echoid-div213" type="page_commentary" level="2" n="213">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7215 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7216 <s xml:id="echoid-s819" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7217 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7218 <s xml:id="echoid-s819" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7219 An examination of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mn>6</mn><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>2</mn><mi>a</mi><mo>=</mo><mn>8</mn></mstyle></math>, which has roots 2, 2, 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7220 This is one of several equations with multiple roots treated by Viète in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7221 <emph style="it">De potestatum numerosa resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7222 Harriot solves it in full on Add MS 6783, f. 187, and refers to it again in Add MS 6783, f. 188.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7223 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7224 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7225 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7226 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7227 <head xml:id="echoid-head114" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7228 G)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7229 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7230 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7231 <s xml:id="echoid-s821" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7232 Triens coeff: long: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7233 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7234 A third of the longitudinal coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7235 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7236 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7237 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7238 <s xml:id="echoid-s822" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7239 Triplum quadrat: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>b</mi><mi>b</mi><mo>=</mo><mn>3</mn><mi>b</mi><mi>b</mi></mstyle></math> coeff. planis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7240 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7241 Three times the square is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mi>b</mi><mi>b</mi><mn>4</mn><mo>,</mo><mi>t</mi><mi>h</mi><mi>e</mi><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>e</mi><mi>f</mi><mi>f</mi><mi>i</mi><mi>c</mi><mi>i</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>.</mo></mstyle></math></emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7242 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7243 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7244 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7245 <s xml:id="echoid-s823" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7246 Duplus cubus e triente. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7247 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7248 Twice the cube of the third
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7249 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7250 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7251 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7252 <s xml:id="echoid-s824" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7253 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7254 in coeff: planib.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7255 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7256 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> times the plane coefficient
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7257 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7258 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7259 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7260 <s xml:id="echoid-s825" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7261 Tria latera igitur
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7262 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7263 Therefore the three sides are
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7264 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7265 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7266 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7267 <pb file="add_6782_f319v" o="319v" n="639"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7268 <pb file="add_6782_f320" o="320" n="640"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7269 <div xml:id="echoid-div214" type="page_commentary" level="2" n="214">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7270 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7271 <s xml:id="echoid-s826" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7272 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7273 <s xml:id="echoid-s826" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7274 This set of pages, lettered <emph style="it">aa</emph> to <emph style="it">au</emph> is connected to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7275 Harriot's treatise 'De generatione aequationum canonicarum' in Add MS 6783, f. 183 to f. 163. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7276 On this first page, Harriot works out the multiplications
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7277 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7278 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mi>a</mi><mo>-</mo><mi>b</mi><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mi>a</mi><mo>-</mo><mi>b</mi><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mi>a</mi><mo>+</mo><mi>b</mi><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7279 In each case he writes down the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> that reduce the resulting product to zero.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7280 For the second multiplication, for instance, he shows that the product becomes zero when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7281 but not when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7282 For similar content see Add MS 6782, f. 182 (d.2), f. 181 (d.3), f. 180 (d.4), and f. 178 (d.6).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7283 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7284 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7285 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7286 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7287 <head xml:id="echoid-head115" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7288 aa)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7289 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7290 <pb file="add_6782_f320v" o="320v" n="641"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7291 <pb file="add_6782_f321" o="321" n="642"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7292 <div xml:id="echoid-div215" type="page_commentary" level="2" n="215">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7293 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7294 <s xml:id="echoid-s828" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7295 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7296 <s xml:id="echoid-s828" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7297 This page contains multiplications similar to those on the previous page (Add MS 6782, f. 320)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7298 but now with the terms written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>-</mo><mi>a</mi><mo maxsize="1">)</mo></mstyle></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo maxsize="1">)</mo></mstyle></math>, and so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7299 Both versions are treated in Add MS 6782, f. 182 (d.2).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7300 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7301 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7302 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7303 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7304 <head xml:id="echoid-head116" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7305 ab)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7306 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7307 <pb file="add_6782_f321v" o="321v" n="643"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7308 <pb file="add_6782_f322" o="322" n="644"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7309 <head xml:id="echoid-head117" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7310 ac)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7311 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7312 <div xml:id="echoid-div216" type="page_commentary" level="2" n="216">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7313 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7314 <s xml:id="echoid-s830" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7315 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7316 <s xml:id="echoid-s830" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7317 A treatment of the equation arising from the multiplication <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, with a numerical example.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7318 For a more detailed treatment of the same equation see Add MS 6782, f. 181 (d.3).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7319 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7320 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7321 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7322 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7323 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7324 <s xml:id="echoid-s832" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7325 Fundamentum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7326 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7327 Foundation
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7328 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7329 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7330 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7331 <pb file="add_6782_f322v" o="322v" n="645"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7332 <pb file="add_6782_f323" o="323" n="646"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7333 <div xml:id="echoid-div217" type="page_commentary" level="2" n="217">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7334 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7335 <s xml:id="echoid-s833" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7336 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7337 <s xml:id="echoid-s833" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7338 A continuation from Add MS 6782, f. 322 of work on the equation arising from the multiplication
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7339 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7340 Harriot states without proof the special form the equation will take when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7341 when the term in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi></mstyle></math> vanishes. For a full derivation see Add MS 6782, f. 181 (d.3).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7342 Harriot calls this form of the cubic equation an 'elliptic' or 'Bombellian' equation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7343 The special case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mi>c</mi></mstyle></math> he calls 'parabolic'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7344 For Harriot's definitions of the hyperbolic, elliptic, and parabolic forms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7345 of a cubic equation without a square term, see Add MS 6783, f. 106 (e.8). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7346 On this page Harriot also gives the form the equation will take when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>d</mi><mo>+</mo><mi>c</mi><mi>d</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7347 when the term in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> vanishes. For a full derivation see Add MS 6782, f. 181 (d.3).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7348 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7349 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7350 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7351 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7352 <head xml:id="echoid-head118" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7353 ad)
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7357 In charta ac)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7358 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7359 In sheet <emph style="it">ac</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7360 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7361 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7362 Sheet ac is Add MS 6782, f. 322.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7363 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7364 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7365 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7366 <s xml:id="echoid-s836" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7367 Eliptica. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7368 seu Bombellica si <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7369 convertitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7370 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7371 Elliptic, or the Bombellian kind if the signs are changed.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7372 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7373 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7374 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7375 <s xml:id="echoid-s837" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7376 Vide D.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7377 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7378 See D.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7379 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7380 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7381 Sheet D. is Add MS 6783, f. 272.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7382 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7383 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7384 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7385 <s xml:id="echoid-s838" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7386 æquatio parabolica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7387 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7388 parabolic equation
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7389 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7390 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7391 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7392 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7393 <s xml:id="echoid-s839" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7394 parabolica
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7395 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7396 parabolic
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7397 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7398 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7399 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7400 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7401 <s xml:id="echoid-s840" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7402 solummodo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7403 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7404 only
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7405 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7406 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7407 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7408 <pb file="add_6782_f323v" o="323v" n="647"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7409 <pb file="add_6782_f324" o="324" n="648"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7410 <div xml:id="echoid-div218" type="page_commentary" level="2" n="218">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7411 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7412 <s xml:id="echoid-s841" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7413 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7414 <s xml:id="echoid-s841" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7415 On this page Harriot works with the multiplication from Add MS 6782, f. 322 and f. 323, namely,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7416 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, but now with the signs changed so that it becomes <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7417 As in Add MS 6782, f. 323, he gives the special form of the equation that arises when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7418 when the term in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi></mstyle></math> vanishes. For a full derivation see Add MS 6782, f. 180 (d.4).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7419 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7420 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7421 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7422 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7423 <head xml:id="echoid-head119" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7424 ae) Conversiones
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7425 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7426 Changes of sign
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7427 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7428 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7429 <pb file="add_6782_f324v" o="324v" n="649"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7430 <pb file="add_6782_f325" o="325" n="650"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7431 <pb file="add_6782_f325v" o="325v" n="651"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7432 <head xml:id="echoid-head120" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7433 f.8
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7434 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7435 <pb file="add_6782_f326" o="326" n="652"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7436 <pb file="add_6782_f326v" o="326v" n="653"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7437 <head xml:id="echoid-head121" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7438 f.8
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7439 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7440 <pb file="add_6782_f327" o="327" n="654"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7441 <pb file="add_6782_f327v" o="327v" n="655"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7442 <head xml:id="echoid-head122" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7443 f.8
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7444 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7445 <pb file="add_6782_f328" o="328" n="656"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7446 <pb file="add_6782_f328v" o="328v" n="657"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7447 <pb file="add_6782_f329" o="329" n="658"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7448 <pb file="add_6782_f329v" o="329v" n="659"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7449 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7450 <s xml:id="echoid-s843" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7451 Archimedes de quadrat: parabola <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7452 prop: 23. pa: 21.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7453 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7454 Archimedes, De quadratura parabola, Proposition 23, page 21.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7455 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7456 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7457 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7458 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7459 <s xml:id="echoid-s844" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7460 decrescentes
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7461 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7462 decreasing
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7463 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7464 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7465 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7466 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7467 <s xml:id="echoid-s845" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7468 crescentes
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7469 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7470 increasing
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7471 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7472 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7473 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7474 <pb file="add_6782_f330" o="330" n="660"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7475 <div xml:id="echoid-div219" type="page_commentary" level="2" n="219">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7476 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7477 <s xml:id="echoid-s846" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7478 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7479 <s xml:id="echoid-s846" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7480 This page is a continuation of Add MS 6783, f. 44v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7481 Note 3 gives the triangular numbers in general algebraic notation:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7482 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo maxsize="1">)</mo></mrow><mrow><mn>1</mn><mo>×</mo><mn>2</mn></mrow></mfrac></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo maxsize="1">)</mo></mrow><mrow><mn>1</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>3</mn></mrow></mfrac></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7483 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>n</mi><mo>+</mo><mn>3</mn><mo maxsize="1">)</mo></mrow><mrow><mn>1</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>4</mn></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7484 On the right these formula are given labels that in modern subscript notation would be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7485 <emph style="it">p</emph><emph style="sub">1</emph>, <emph style="it">p</emph><emph style="sub">2</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7486 <emph style="it">p</emph><emph style="sub">3</emph>, and so on. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7487 In the fourth notation, in the lower half of the page,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7488 <emph style="it">p</emph> has been replaced by <emph style="it">v</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7489 and the terms have been multiplied out to give a one-line expression (or in Harriot's terms, an equation)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7490 instead of a fraction. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7491 See also page 1 of the 'Magisteria' (Add MS 6782, f. 108).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7492 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7493 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7494 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7495 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7496 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7497 <s xml:id="echoid-s848" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7498 3. Generalis notatio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7499 triangularium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7500 in notis generalibus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7501 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7502 3. General notation for triangular numbers in general symbols.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7503 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7504 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7505 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7506 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7507 <s xml:id="echoid-s849" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7508 Melius ad continuam <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7509 additionem triangularium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7510 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7511 Better for continual addition of triangular numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7512 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7513 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7514 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7515 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7516 <s xml:id="echoid-s850" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7517 4. Quarta notatio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7518 per æquationes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7519 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7520 4. Fourth notation, by means of equations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7521 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7522 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7523 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7524 <pb file="add_6782_f330v" o="330v" n="661"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7525 <div xml:id="echoid-div220" type="page_commentary" level="2" n="220">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7526 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7527 <s xml:id="echoid-s851" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7528 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7529 <s xml:id="echoid-s851" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7530 This page contains two magic squares. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7531 It also shows the digits 0 to 9 written in their Arabic form and in characters composed only of straight lines
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7532 (see also Add MS 6782, f. 30v).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7533 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7534 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7535 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7536 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7537 <pb file="add_6782_f331" o="331" n="662"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7538 <div xml:id="echoid-div221" type="page_commentary" level="2" n="221">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7539 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7540 <s xml:id="echoid-s853" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7541 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7542 <s xml:id="echoid-s853" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7543 This appears to be the 'other paper' referred to on Add MS 6782, f. 38,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7544 since the table at the top of this page is the same as the one that appears there. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7545 On the right, the first few entries from the third and fourth columns are written in factorial form,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7546 showing why the ratios of the entries in the first two rows are 1 : 6 and 2 : 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7547 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7548 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7549 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7550 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7551 <head xml:id="echoid-head123" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7552 Of combinations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7553 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7554 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7555 <s xml:id="echoid-s855" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7556 Questi minuti numerator <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7557 multiplicatur per 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7558 & denominator per 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7559 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7560 The numerator of these fractions is multiplied by 2 etc., the denominator by 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7561 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7562 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7563 <s xml:id="echoid-s856" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7564 Ergo tertius et quartus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7565 habent ratione ut 2 ad 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7566 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7567 Therefore the third and the fourth have a ratio of 2 to 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7568 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7569 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7570 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7571 <s xml:id="echoid-s857" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7572 unde ratio in omnibus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7573 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7574 whence the ratio in all of them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7575 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7576 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7577 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7578 <pb file="add_6782_f331v" o="331v" n="663"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7579 <pb file="add_6782_f332" o="332" n="664"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7580 <div xml:id="echoid-div222" type="page_commentary" level="2" n="222">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7581 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7582 <s xml:id="echoid-s858" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7583 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7584 <s xml:id="echoid-s858" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7585 A table of factorials from 1! = 1, to 25! = 15,511,210,043,330,985,984,000,000.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7586 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7587 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7588 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7589 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7590 <head xml:id="echoid-head124" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7591 For Transpositions.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7592 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7593 <pb file="add_6782_f332v" o="332v" n="665"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7594 <pb file="add_6782_f333" o="333" n="666"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7595 <pb file="add_6782_f333v" o="333v" n="667"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7596 <pb file="add_6782_f334" o="334" n="668"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7597 <pb file="add_6782_f334v" o="334v" n="669"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7598 <pb file="add_6782_f335" o="335" n="670"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7599 <div xml:id="echoid-div223" type="page_commentary" level="2" n="223">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7600 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7601 <s xml:id="echoid-s860" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7602 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7603 <s xml:id="echoid-s860" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7604 The same information as in Add MS 6782, f. 336, now presented slightly differently.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7605 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7606 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7607 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7608 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7609 <head xml:id="echoid-head125" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7610 Progressiones crescentes; quarum principia sunt quivis numeri.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7611 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7612 Increasing progressions; of which the first terms are any numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7613 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7614 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7615 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7616 <s xml:id="echoid-s862" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7617 Melior forma <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7618 sive optime.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7619 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7620 A better form, perhaps the best.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7621 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7622 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7623 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7624 <pb file="add_6782_f335v" o="335v" n="671"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7625 <pb file="add_6782_f336" o="336" n="672"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7626 <div xml:id="echoid-div224" type="page_commentary" level="2" n="224">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7627 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7628 <s xml:id="echoid-s863" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7629 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7630 <s xml:id="echoid-s863" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7631 General formulae for the entries in a table generated from a constant difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7632 where every column is increasing (as signified by the symbols Δ above each column). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7633 The first entry in column 1 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7634 The first entry in column 2 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>p</mi><mn>2</mn></msup></mrow></mstyle></math> (where 2 is a superscript, not a power). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7635 The first entry in column 3 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>p</mi><mn>3</mn></msup></mrow></mstyle></math> (where 3 is a superscript, not a power). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7636 And so on.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7637 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7638 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7639 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7640 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7641 <head xml:id="echoid-head126" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7642 progressiones crescentes, quarum principia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7643 sunt quibus numeri.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7644 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7645 increasing progressions, of which the first terms are any numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7646 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7647 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7648 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7649 <s xml:id="echoid-s865" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7650 Vide meliorem <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7651 formam in alia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7652 Charta.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7653 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7654 See a better form in the other sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7655 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7656 <sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7657 The other sheet mentioned here is Add MS 6782, f. 355.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7658 </sc>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7659 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7660 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7661 <pb file="add_6782_f336v" o="336v" n="673"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7662 <pb file="add_6782_f337" o="337" n="674"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7663 <div xml:id="echoid-div225" type="page_commentary" level="2" n="225">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7664 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7665 <s xml:id="echoid-s866" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7666 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7667 <s xml:id="echoid-s866" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7668 These are the symbols Harriot devised in 1585 for writing down the native Indian language of Algonquin.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7669 In the right-hand column there are 12 vowels followed by 24 consonants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7670 In the left-hand column are words representing each sound.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7671 The sounds and then the words are transcribed here from Harriot's notes on another copy of this page,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7672 now held at Westminster School, London, and reproduced in Stedall 2007.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7673 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7674 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7675 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7676 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7677 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7678 <s xml:id="echoid-s868" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7679 [sounds] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7680 as (a) in all, tall, fall, call <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7681 as (o) in ore, for, core <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7682 as (a) in arrow, man, pan <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7683 as (u) in us, upon, but, cut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7684 as (a) in ape, ale, any , are <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7685 as (e) in erbe, end, the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7686 as (i) in ise, ire, pipe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7687 as (e) in he, shee, or (ee) in thee, eele. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7688 [penultimate pair of vowels]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7689 (in barbarouse wordes only and not to be expressed viva voce.) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7690 as (o) in so, no, otes. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7691 as (o) in do, to, shoe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7692 as (y) in yea, yes, day <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7693 as (w) in way, was, now, sow <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7694 as (r) in roote <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7695 as (l) in lake <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7696 as (z) in zone, zachary <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7697 as the French (i) in je, jeter, or as (g) in hodge, iudge <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7698 as (s) in sault, samon <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7699 as (sh) in she, shoe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7700 as (m) in man <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7701 as (n) in not <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7702 as (ng) in king, fling, thing (or (n) in knave) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7703 as (v) in vine, geve <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7704 as (th) in the, thine, there <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7705 as (gh) in some barabrouse wordes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7706 as (f) in fling, fear, of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7707 as (th) in thing, thorne <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7708 as (ch) in some barbarouse wordes or as the Greeke <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>χ</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7709 as (h) in hat, he, oh <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7710 as (b) in borde, but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7711 as (d) in do, grudge, good <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7712 as (g) in good, god, geve, hog <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7713 as (p) in pan <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7714 as (t) in tooth, to, ten, hat <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7715 as (c) in corne or as (k) in keepe
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7716 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7717 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7718 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7719 <s xml:id="echoid-s869" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7720 [words] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7721 armes. ore. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7722 arow. urchin. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7723 aye. err. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7724 ice. eele. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7725 (in barbarous words only and not to be expressed viva voce.) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7726 oates. oon. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7727 ye. ne. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7728 root. lake. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7729 zone. je. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7730 sault. shoo. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7731 men. nete. gna. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7732 vine. thing. ghi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7733 flinge. thorne. chi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7734 bore. drudge. gold. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7735 pan. toothe corne.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7736 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7737 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7738 <pb file="add_6782_f337v" o="337v" n="675"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7739 <pb file="add_6782_f338" o="338" n="676"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7740 <pb file="add_6782_f338v" o="338v" n="677"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7741 <pb file="add_6782_f339" o="339" n="678"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7742 <pb file="add_6782_f339v" o="339v" n="679"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7743 <pb file="add_6782_f340" o="340" n="680"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7744 <pb file="add_6782_f340v" o="340v" n="681"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7745 <pb file="add_6782_f341" o="341" n="682"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7746 <pb file="add_6782_f341v" o="341v" n="683"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7747 <pb file="add_6782_f342" o="342" n="684"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7748 <pb file="add_6782_f342v" o="342v" n="685"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7749 <pb file="add_6782_f343" o="343" n="686"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7750 <pb file="add_6782_f343v" o="343v" n="687"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7751 <pb file="add_6782_f344" o="344" n="688"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7752 <pb file="add_6782_f344v" o="344v" n="689"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7753 <pb file="add_6782_f345" o="345" n="690"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7754 <pb file="add_6782_f345v" o="345v" n="691"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7755 <pb file="add_6782_f346" o="346" n="692"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7756 <pb file="add_6782_f346v" o="346v" n="693"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7757 <pb file="add_6782_f347" o="347" n="694"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7758 <div xml:id="echoid-div226" type="page_commentary" level="2" n="226">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7759 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7760 <s xml:id="echoid-s870" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7761 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7762 <s xml:id="echoid-s870" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7763 The table from page 12 of the 'Magisteria' (Add MS 6782, f. 119).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7764 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7765 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7766 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7767 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7768 <pb file="add_6782_f347v" o="347v" n="695"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7769 <pb file="add_6782_f348" o="348" n="696"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7770 <div xml:id="echoid-div227" type="page_commentary" level="2" n="227">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7771 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7772 <s xml:id="echoid-s872" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7773 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7774 <s xml:id="echoid-s872" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7775 See page 5 of the 'Magisteria' (Add MS 6782, f. 112), which contains the same numerical tables.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7776 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7777 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7778 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7779 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7780 <pb file="add_6782_f348v" o="348v" n="697"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7781 <div xml:id="echoid-div228" type="page_commentary" level="2" n="228">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7782 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7783 <s xml:id="echoid-s874" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7784 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7785 <s xml:id="echoid-s874" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7786 See page 7 of the 'Magisteria' (Add MS 6782, f. 114), which contains the first two numerical tables.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7787 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7788 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7789 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7790 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7791 <pb file="add_6782_f349" o="349" n="698"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7792 <div xml:id="echoid-div229" type="page_commentary" level="2" n="229">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7793 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7794 <s xml:id="echoid-s876" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7795 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7796 <s xml:id="echoid-s876" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7797 Formulae for entries in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> columns of a difference table;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7798 see page 16 of the 'Magisteria' (Add MS 6782, f. 123).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7799 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7800 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7801 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7802 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7803 <pb file="add_6782_f349v" o="349v" n="699"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7804 <pb file="add_6782_f350" o="350" n="700"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7805 <pb file="add_6782_f350v" o="350v" n="701"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7806 <pb file="add_6782_f351" o="351" n="702"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7807 <pb file="add_6782_f351v" o="351v" n="703"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7808 <pb file="add_6782_f352" o="352" n="704"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7809 <pb file="add_6782_f352v" o="352v" n="705"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7810 <pb file="add_6782_f353" o="353" n="706"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7811 <pb file="add_6782_f353v" o="353v" n="707"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7812 <pb file="add_6782_f354" o="354" n="708"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7813 <div xml:id="echoid-div230" type="page_commentary" level="2" n="230">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7814 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7815 <s xml:id="echoid-s878" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7816 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7817 <s xml:id="echoid-s878" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7818 Squares of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>f</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7819 The page also shows the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo><mo maxsize="1">(</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7820 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7821 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7822 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7823 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7824 <head xml:id="echoid-head127" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7825 Quadrata e polynomia radice
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7826 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7827 Squares from polynomial roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7828 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7829 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7830 <pb file="add_6782_f354v" o="354v" n="709"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7831 <pb file="add_6782_f355" o="355" n="710"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7832 <div xml:id="echoid-div231" type="page_commentary" level="2" n="231">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7833 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7834 <s xml:id="echoid-s880" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7835 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7836 <s xml:id="echoid-s880" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7837 Squares of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>–</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>–</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>–</mo><mi>c</mi><mo>–</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7838 and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>–</mo><mi>f</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>–</mo><mi>d</mi><mo>–</mo><mi>f</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>–</mo><mi>c</mi><mo>–</mo><mi>d</mi><mo>–</mo><mi>f</mi><mo maxsize="1">)</mo></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>–</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>–</mo><mi>f</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7839 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7840 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7841 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7842 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7843 <head xml:id="echoid-head128" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7844 Quadrata e polynomia radice
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7845 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7846 Squares from polynomial roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7847 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7848 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7849 <pb file="add_6782_f355v" o="355v" n="711"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7850 <pb file="add_6782_f356" o="356" n="712"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7851 <div xml:id="echoid-div232" type="page_commentary" level="2" n="232">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7852 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7853 <s xml:id="echoid-s882" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7854 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7855 <s xml:id="echoid-s882" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7856 The square and cube of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7857 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7858 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7859 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7860 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7861 <pb file="add_6782_f356v" o="356v" n="713"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7862 <pb file="add_6782_f357" o="357" n="714"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7863 <div xml:id="echoid-div233" type="page_commentary" level="2" n="233">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7864 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7865 <s xml:id="echoid-s884" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7866 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7867 <s xml:id="echoid-s884" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7868 Powers of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo></mstyle></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mrow><msup><mo maxsize="1">)</mo><mn>6</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7869 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7870 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7871 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7872 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7873 <head xml:id="echoid-head129" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7874 potentia e binomia radice
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7875 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7876 powers from binomial roots
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7877 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7878 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7879 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7880 <s xml:id="echoid-s886" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7881 solidum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7882 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7883 solid
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7884 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7885 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7886 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7887 <pb file="add_6782_f357v" o="357v" n="715"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7888 <pb file="add_6782_f358" o="358" n="716"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7889 <div xml:id="echoid-div234" type="page_commentary" level="2" n="234">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7890 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7891 <s xml:id="echoid-s887" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7892 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7893 <s xml:id="echoid-s887" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7894 Cubes of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>f</mi><mo maxsize="1">)</mo></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>f</mi><mo>+</mo><mi>g</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7895 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7896 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7897 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7898 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7899 <pb file="add_6782_f358v" o="358v" n="717"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7900 <pb file="add_6782_f359" o="359" n="718"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7901 <pb file="add_6782_f359v" o="359v" n="719"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7902 <pb file="add_6782_f360" o="360" n="720"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7903 <pb file="add_6782_f360v" o="360v" n="721"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7904 <pb file="add_6782_f361" o="361" n="722"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7905 <pb file="add_6782_f361v" o="361v" n="723"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7906 <pb file="add_6782_f362" o="362" n="724"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7907 <div xml:id="echoid-div235" type="page_commentary" level="2" n="235">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7908 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7909 <s xml:id="echoid-s889" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7910 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7911 <s xml:id="echoid-s889" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7912 This page refers to Aristotle's <emph style="it">Physics</emph>, Books V and VI,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7913 defines what it means for things to be together or apart, in contact, or continuous.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7914 The definitions may be paraphrased as follows.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7915 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7916 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7917 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7918 Things are said to be together if they are in one place, apart if they are in different places. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7919 Things are said to be in contact if their extremities are together. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7920 Things are said to be continuous if the touching limits of each become one and the same.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7921 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7922 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7923 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7924 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7925 <head xml:id="echoid-head130" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7926 De infinitis. De continuo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7927 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7928 On infinity. On the continuum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7929 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7930 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7931 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7932 <s xml:id="echoid-s891" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7933 Aristotle in the beginning of his 6th booke of his physicks, & in the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7934 26th treatise of the 5th booke, defineth those thinges to be <foreign xml:lang="lat">continua <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7935 quorum extrema sunt unum.</foreign> And in the 22nd treatise of the said 5th booke <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7936 that: <foreign xml:lang="lat">tangentia sunt, quorum extrema sunt simul</foreign>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7937 <foreign xml:lang="lat">Simul qua in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7938 uno loco sunt primo</foreign>. <foreign xml:lang="lat">Separatim qui sunt in altero.</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7939 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7940 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7941 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7942 <s xml:id="echoid-s892" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7943 Now for the <emph style="st">understanding</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7944 <emph style="super">better explication</emph> of the
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7945 <emph style="super">meaning of the</emph> definitions as also of their truth. Let us <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7946 understand first two <emph style="super">materiall</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7947 cubes A & B to be separate, that is, to be in diverse <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7948 planes, extremes & all.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7949 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7950 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7951 <pb file="add_6782_f362v" o="362v" n="725"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7952 <pb file="add_6782_f363" o="363" n="726"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7953 <head xml:id="echoid-head131" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7954 De Infinitis progressionibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7955 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7956 On infinite progressions
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7957 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7958 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7959 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7960 <s xml:id="echoid-s893" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7961 In progressions that be infinite be they increasing or decreasing. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7962 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7963 <s xml:id="echoid-s894" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7964 There are these passes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7965 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7966 <s xml:id="echoid-s895" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7967 First to a quantity that haveth no
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7968 <emph style="st">proportion</emph> rate <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7969 to the first quantity given, or rather because betwixt positive quantityes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7970 there is a positive rate, I may call that rate infinite either in great-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7971 ness or litle<emph style="super">nes</emph>s according to the
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7972 <emph style="st">proportion</emph> <emph style="super">progression</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7973 in respect of the first quantity <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7974 given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7975 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7976 <s xml:id="echoid-s896" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7977 Yet in respecte of the progression following it is divisible or mul-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7978 tiplicable till the progression being infinite hath for his second passe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7979 also a quantity <emph style="super">of an[???]</emph> infinite rate.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7980 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7981 <s xml:id="echoid-s897" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7982 Which is not only infinite in respecte of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7983 the first quantity of the last progression; but infinitely infinite in respect <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7984 of <emph style="st">of</emph> the first in the first progresse.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7985 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7986 <s xml:id="echoid-s898" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7987 And also the summe of the second pro-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7988 gression is infinite <emph style="st">infi</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7989 in respect of the first summe of the first pro-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7990 gression, or the first quantity of all.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7991 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7992 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7993 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7994 <s xml:id="echoid-s899" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7995 And so a third, fourth & infinite other progressions and passes; of which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7996 any quantity or the summe of all infinitely all, is of an infinite <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7997 quantity in greatness of litleness in respect, of the summe or <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7998 first quantity of the first progression.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	7999 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8000 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8001 <s xml:id="echoid-s900" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8002 And yet <emph style="st">at</emph> <emph style="super">for a</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8003 last in decreasing progressions we must needes under-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8004 stand a quantity absolutely indivisible; but multiplicable infinitely <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8005 infinite <emph style="st">to make the [¿]prime[?]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8006 from where the rest are issued</emph> till a quantity <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8007 absolutely immultiplicable be produced which I may call universally infinite.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8008 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8009 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8010 <s xml:id="echoid-s901" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8011 And in increasing progressions we must needes understand that <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8012 <emph style="st">at</emph> <emph style="super">for a</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8013 last there must be a quantity immultiplicable absolute, but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8014 divisible infinitely infinite till that quantity be issued that is <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8015 absolutely indivisble.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8016 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8017 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8018 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8019 <s xml:id="echoid-s902" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8020 That such <emph style="st">a</emph> quantity which I call universally infinite: hath not only <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8021 act rationall, by supposition, or by consequence from
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8022 <emph style="super">mere</emph> supposition: but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8023 also act reall, or existence: in an instant, having
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8024 <emph style="super">[???] perfect</emph> actuall being, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8025 or in time, passed by motion <emph style="st">fini</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8026 both finite & infinite: with many reall <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8027 consequences or properties consequent; & accidents adioyning: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8028 shalbe declared in the papers following.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8029 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8030 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8031 <pb file="add_6782_f363v" o="363v" n="727"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8032 <pb file="add_6782_f364" o="364" n="728"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8033 <head xml:id="echoid-head132" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8034 De Infinitis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8035 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8036 On infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8037 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8038 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8039 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8040 <s xml:id="echoid-s903" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8041 Seing that any finite line will <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8042 subtend an angle at summe distance; <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8043 as let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> subtend the <emph style="st">the</emph> angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8044 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8045 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8046 <s xml:id="echoid-s904" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8047 Then a line double to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, which let be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8048 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math>, will subtend the same angle at a <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8049 double distance, so that <emph style="it"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math></emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>d</mi></mstyle></math> will be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8050 aequall to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8051 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8052 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8053 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8054 <s xml:id="echoid-s905" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8055 In those subtensions I understand that the poynt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be <emph style="super">in a</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8056 perpendicular <emph style="super">line</emph> to the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8057 middle of the subtendent lines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8058 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8059 <s xml:id="echoid-s906" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8060 as also in all the others which follow.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8061 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8062 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8063 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8064 <s xml:id="echoid-s907" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8065 Now I suppose <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> to be removed to a further distance from the poynt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8066 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8067 <s xml:id="echoid-s908" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8068 Then the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi><mi>c</mi></mstyle></math> subtended must be lesse than before.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8069 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8070 <s xml:id="echoid-s909" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8071 And <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8072 shall <emph style="st">[???]</emph> subtend the same angle at a double distance as before.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8073 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8074 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8075 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8076 <s xml:id="echoid-s910" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8077 And this is true <emph style="st">generally</emph> continually that the further
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8078 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> is removed <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8079 the lesse angle it subtendeth & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> always must subtend the same <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8080 angle at a double distance.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8081 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8082 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8083 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8084 <s xml:id="echoid-s911" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8085 Then I suppose <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> to be removed to an infinite distance; at which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8086 distance the supposition altereth not the quantity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. but the
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8087 <emph style="st">quantity </emph>consequence <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8088 is of the angle.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8089 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8090 <s xml:id="echoid-s912" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8091 Which wilbe, that the angle <emph style="st">wh</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8092 then subtended <emph style="it">[???]</emph> to be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8093 of an infinite quantity in litleness in respecte of the former angles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8094 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8095 <s xml:id="echoid-s913" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8096 Yet it <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8097 cannot be sayd to be no angle negatively because it is positive. & it <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8098 must also follow that the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> must subtend the same positive angle <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8099 at a double distance.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8100 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8101 <s xml:id="echoid-s914" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8102 Which is Double to the former infinite distance.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8103 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8104 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8105 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8106 <s xml:id="echoid-s915" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8107 Also, let the distance of the subtendents be nearer <emph style="st">[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8108 <emph style="super">to</emph> infinite,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8109 <emph style="st">[???]</emph>it cannot be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8110 otherwise inferred but that the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>g</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8111 <emph style="st">being infinit</emph> though infinite, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8112 be <foreign xml:lang="lat ">ad diversas partes, & in diversis locis</foreign>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8113 because <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> are betweene them, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8114 & have agreement or concurrence but only in the poynt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8115 <emph style="st">[???]</emph> <emph style="super">or</emph> in no distance <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8116 out of the poynt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8117 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8118 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8119 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8120 <s xml:id="echoid-s916" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8121 And yet the nearness of there congruence &
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8122 con<emph style="super">cu</emph>rrence in all other partes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8123 [???] at the utmost is such, that although they be remote; the angle <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8124 is of no proportion explicable by nomber finite, but infinite
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8125 [¿]unknown[?], to any <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8126 <emph style="st">angles</emph> other angle which we call finite.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8127 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8128 <s xml:id="echoid-s917" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8129 The like inexplicable proportion <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8130 is of the <emph style="super">subtendent</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8131 lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, to there infinite distance position from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8132 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8133 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8134 <s xml:id="echoid-s918" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8135 And yet the sayd lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. as also that infinite litle or improportio-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8136 nable angle is divisible still <foreign xml:lang="lat">in infinitum</foreign>. &
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8137 still, although improportionable <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8138 yet in an other respect, that is to say of his owne partes, is proportionable.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8139 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8140 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8141 <pb file="add_6782_f364v" o="364v" n="729"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8142 <pb file="add_6782_f365" o="365" n="730"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8143 <head xml:id="echoid-head133" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8144 De Infinitis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8145 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8146 On infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8147 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8148 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8149 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8150 <s xml:id="echoid-s919" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8151 That in a finite time an infinite space <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8152 may be moved
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8153 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8154 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8155 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8156 <s xml:id="echoid-s920" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8157 It is now convenient <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8158 that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>f</mi></mstyle></math> be in this line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8159 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8160 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8161 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8162 <s xml:id="echoid-s921" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8163 Suppose the <emph style="st">the</emph> line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>e</mi><mi>f</mi></mstyle></math> <foreign xml:lang="lat">et ultra</foreign> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8164 to be infinite, & the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> suppose <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8165 to revolve & describe a circle <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8166 in a finite time, fro <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> towards <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8167 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> doth first respect <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8168 after <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, & so forth successively no poynt <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8169 in the infinite line is <emph style="st">not</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8170 unrespected by that time the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> cometh <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8171 to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>g</mi></mstyle></math> where then the line is parallel & cutteth not the former <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8172 line infinite.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8173 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8174 <s xml:id="echoid-s922" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8175 Now seing that a motion may be of any thing <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8176 according <emph style="super">to</emph> the continuall succession of a poynt,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8177 as well in respect <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8178 of <emph style="st">[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8179 <foreign xml:lang="lat">mobile ab motus</foreign>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8180 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8181 <s xml:id="echoid-s923" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8182 Whatsoever may be or not be in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8183 respect of the moment, it maketh no matter: the purpose is <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8184 manifest.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8185 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8186 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8187 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8188 <s xml:id="echoid-s924" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8189 Consequentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8190 Accidentis quædam huius motus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8191 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8192 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8193 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8194 <s xml:id="echoid-s925" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8195 The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> having moved till he comes to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>h</mi></mstyle></math> that is <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8196 parallel to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>f</mi></mstyle></math>. & so that continuing his motion of revolution:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8197 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8198 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8199 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8200 <s xml:id="echoid-s926" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8201 The lines are parallel but in one instant.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8202 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8203 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8204 <s xml:id="echoid-s927" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8205 They never cut at an infinite distance but at that instant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8206 they are parallel.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8207 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8208 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8209 <s xml:id="echoid-s928" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8210 And if they cut then, they must cut
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8211 <foreign xml:lang="lat">ad utrasque partes</foreign> & then <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8212 being right lines there must be no space betwixte them, but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8213 there distance by supposition is more than the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8214 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8215 <s xml:id="echoid-s929" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8216 Which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8217 implies contradiction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8218 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8219 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8220 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8221 <s xml:id="echoid-s930" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8222 And yet there must be a cutting at an infinite distance or else all <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8223 the poyntes of the infinite line could not have been respected. &
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8224 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8225 <s xml:id="echoid-s931" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8226 if <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8227 that be not some part of the infinite line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8228 that is some quantity <emph style="st">which</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8229 <emph style="st">it is</emph> finite is only cut;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8230 & that is at a finite distance; & then it maketh an <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8231 angle <emph style="super">of quantity</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8232 at the greatest distance of such cutting: from that cutting the line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8233 by motion came to be parallel: That motion is made in an instant or <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8234 in time.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8235 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8236 <s xml:id="echoid-s932" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8237 If in time, then in half the time the cutting must be further <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8238 than the supposed furthest;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8239 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8240 <s xml:id="echoid-s933" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8241 If in an instant, our line wilbe in <emph style="st">two places</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8242 two places in one <emph style="st">[???]</emph> instant;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8243 <foreign xml:lang="lat">quæ implicant</foreign>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8244 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8245 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8246 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8247 <s xml:id="echoid-s934" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8248 The lines therefore must cut at an infinite distance before they come to <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8249 be parallel.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8250 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8251 <s xml:id="echoid-s935" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8252 And that must be in time before or in an instant before. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8253 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8254 <s xml:id="echoid-s936" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8255 If in time, then in half the time they cut at greater distance than infinite or <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8256 are parallel before they are parallel.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8257 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8258 <s xml:id="echoid-s937" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8259 Which both do imply contradiction. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8260 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8261 <s xml:id="echoid-s938" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8262 If in an instant before; the two instants are one or different.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8263 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8264 <s xml:id="echoid-s939" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8265 If one, <foreign xml:lang="lat">implicat</foreign>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8266 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8267 <s xml:id="echoid-s940" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8268 If two there must be no other betwixt them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8269 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8270 <s xml:id="echoid-s941" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8271 And then there [???] be a time greater <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8272 than an instant & lesse than any time of quantity that is indivisible, that is <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8273 agayne, indivisible into partes of quantity. & so also like of poyntes &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8274 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8275 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8276 <pb file="add_6782_f365v" o="365v" n="731"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8277 <pb file="add_6782_f366" o="366" n="732"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8278 <head xml:id="echoid-head134" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8279 De Infinitis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8280 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8281 On infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8282 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8283 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8284 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8285 <s xml:id="echoid-s942" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8286 <emph style="st">If the</emph> <emph style="super">The</emph> line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> by his revolution <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8287 cometh at length to be parallel to <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8288 the infinite line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8289 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8290 <s xml:id="echoid-s943" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8291 Which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8292 motion being from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> suppose <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8293 to have been æqually.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8294 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8295 <s xml:id="echoid-s944" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8296 The <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8297 degree of the motion let be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8298 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mi>n</mi></mstyle></math>. the time <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>p</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8299 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8300 <s xml:id="echoid-s945" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8301 The beginning of the time or first instant <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8302 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8303 <s xml:id="echoid-s946" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8304 The last instant wherein the line is <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8305 parallel, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. Now seing that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> must cut at <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8306 an infinite distance & <emph style="super">that</emph> his last cutting must be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8307 before the instant <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8308 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8309 <s xml:id="echoid-s947" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8310 Which suppose <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8311 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8312 <s xml:id="echoid-s948" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8313 That <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi></mstyle></math> as it is argued by the premises <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8314 must differe from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math> by an indivisible time, so that <emph style="st">it </emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8315 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi></mstyle></math> must be the next instant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8316 to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. & no other between.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8317 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8318 <s xml:id="echoid-s949" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8319 In which instant <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> must not be parallel but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8320 make his last cutting at an infinite distance.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8321 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8322 <s xml:id="echoid-s950" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8323 And therefore it must have <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8324 a certayne <foreign xml:lang="lat">situs</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8325 at that instant out of the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> towards <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, which let be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math>, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8326 as it maketh his last section.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8327 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8328 <s xml:id="echoid-s951" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8329 In which situation the motion ordering it hath <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8330 the sayd degree <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mi>n</mi></mstyle></math>, as in all other situations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8331 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8332 <s xml:id="echoid-s952" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8333 From the which situation to the situation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8334 of being parallel it must be moved unto (as it is sayd) in the next instant.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8335 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8336 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8337 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8338 <s xml:id="echoid-s953" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8339 Now suppose (as it may be) that the motion from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> be in half the time <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8340 of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>p</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8341 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8342 <s xml:id="echoid-s954" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8343 Then doth it follow necessarily that the degree of motion or velo-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8344 city be double to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mi>n</mi></mstyle></math>. And therefore, what space or parte of a space, (be it <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8345 finite or infinite, so it be positive,) it moved before according to <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8346 the degree of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mi>n</mi></mstyle></math>. it moveth the same now, in half the time. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8347 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8348 <s xml:id="echoid-s955" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8349 Therefore in this second motion when <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> cometh to have his situation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8350 at <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> to make the sayd last section; seing that then it hath double <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8351 degree of velocity; it must afterward be parallel in half an instant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8352 that is to say, <emph style="st">that</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8353 in half that time which was sayd to be indivisible. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8354 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8355 <s xml:id="echoid-s956" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8356 Which doth imply contradiction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8357 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8358 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8359 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8360 <s xml:id="echoid-s957" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8361 Agayne if it be sayd that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> at that instant
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8362 <emph style="st">& in the position</emph> (when & <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8363 where it maketh his last section with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math> before it be parallel)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8364 <emph style="st">then</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8365 be <foreign xml:lang="lat">deinceps</foreign> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>h</mi></mstyle></math>. or that the poynts <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8366 <foreign xml:lang="lat">deinceps</foreign> at an infinite <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8367 distance so that no point can be between.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8368 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8369 <s xml:id="echoid-s958" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8370 Yet from the poynt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> may <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8371 be interposed a line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>f</mi></mstyle></math>. and also from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>l</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>. & by the doctrine of Elements <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8372 the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>k</mi><mi>h</mi></mstyle></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>l</mi><mi>h</mi></mstyle></math> must be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8373 <emph style="st">greater</emph> <emph style="super">lesser</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8374 than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>a</mi><mi>h</mi></mstyle></math>. & therefore lesse than that <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8375 which was sayd to be least or indivisible. & therefore the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>h</mi></mstyle></math>, or the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8376 poynts <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> be not <foreign xml:lang="lat">deinceps. quæ implicant</foreign>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8377 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8378 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8379 <pb file="add_6782_f366v" o="366v" n="733"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8380 <pb file="add_6782_f367" o="367" n="734"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8381 <head xml:id="echoid-head135" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8382 De Infinitis. Ratio Achilles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8383 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8384 On infinity. The ratio of Achilles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8385 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8386 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8387 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8388 <s xml:id="echoid-s959" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8389 There is a reason <emph style="super">of Zeno</emph> in Aristotle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8390 (in the 6th booke of his phisickes. text. 78.) which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8391 for the sorce it seemeth to carry is called Achilles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8392 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8393 <s xml:id="echoid-s960" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8394 And for that cause, no doubt, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8395 is <emph style="super">the</emph> name also Achilles used in the example to expresse the reason.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8396 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8397 <s xml:id="echoid-s961" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8398 The which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8399 because it is against Aristotles doctrine
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8400 & for that it compryseth matter <emph style="super">pregnant</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8401 of greater consequence concerning the doctrine of infinites, it being there <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8402 but briefly & obscurely set downe with an answere uncertayne: I thinke good <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8403 to set <emph style="st">[???]</emph>downe more [???] & largely:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8404 with Aristotles Answere as he hath <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8405 it in the place allwayes, as also at full according to his owne doctrine in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8406 other places.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8407 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8408 <s xml:id="echoid-s962" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8409 To the end that comparing one with the other, the truth may appear, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8410 & perhaps [¿]seem[?] otherwise to be,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8411 then yet hath been by the peripateticles either noted or <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8412 observed.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8413 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8414 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8415 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8416 <s xml:id="echoid-s963" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8417 The proposition of Zeno is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8418 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8419 <s xml:id="echoid-s964" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8420 The swift runner (runne he never so <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8421 swiftly) shall never overtake the slow runner <emph style="super">mover</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8422 (runne <emph style="super">move</emph> he never <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8423 so slowly.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8424 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8425 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8426 <s xml:id="echoid-s965" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8427 That there may be <emph style="super">no</emph> doubte of the meaning of the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8428 proposition we will declare what thinges are therein supposed.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8429 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8430 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8431 <s xml:id="echoid-s966" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8432 <emph style="st">The suppositions for the reason are adjoyned.</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8433 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8434 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8435 <s xml:id="echoid-s967" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8436 ffirst, (as it ought to be, else the proposition were ridiculous) The motion <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8437 of the runner & slow mover are understood to be both one way & in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8438 one right line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8439 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8440 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8441 <s xml:id="echoid-s968" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8442 Secondly <emph style="st">the [???] of [???] must be of some [???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8443 The <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8444 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8445 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8446 <pb file="add_6782_f367v" o="367v" n="735"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8447 <pb file="add_6782_f368" o="368" n="736"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8448 <head xml:id="echoid-head136" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8449 Ratio Achilles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8450 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8451 The ratio of Achilles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8452 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8453 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8454 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8455 <s xml:id="echoid-s969" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8456 Let Achilles be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8457 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8458 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8459 <s xml:id="echoid-s970" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8460 Testudo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8461 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8462 The tortoise <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8463 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8464 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8465 <s xml:id="echoid-s971" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8466 The Motion of Achilles from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8467 in the time <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi></mstyle></math>. of Testudo from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>C</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8468 in the <emph style="super">same</emph> time <emph style="st">fg</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8469 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8470 <s xml:id="echoid-s972" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8471 <emph style="st">Which let be the</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8472 <emph style="st">half parte of the time ef</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8473 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8474 <s xml:id="echoid-s973" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8475 Which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8476 space of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi><mi>C</mi></mstyle></math> let be the tenth parte <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8477 of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>B</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8478 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8479 <s xml:id="echoid-s974" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8480 Now the quaestion is, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8481 both these motions being continued in the same proportion as 10 to 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8482 where & when shall <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> overtake <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>. <emph style="st">Suppose at d</emph>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8483 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8484 <s xml:id="echoid-s975" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8485 At some point or other it must really be.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8486 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8487 <s xml:id="echoid-s976" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8488 Suppose that <emph style="super">X</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8489 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8490 <s xml:id="echoid-s977" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8491 There must be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8492 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>, <emph style="st">[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8493 at the same instant of time.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8494 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8495 <s xml:id="echoid-s978" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8496 And therefore the time wherein <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8497 <emph style="st">that</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8498 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> hath moved to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> must be the same wherein <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> hath moved to <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8499 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8500 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8501 <s xml:id="echoid-s979" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8502 But the space <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>d</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi><mi>d</mi></mstyle></math> must be as 10 to 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8503 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8504 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8505 <s xml:id="echoid-s980" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8506 Now by the supposition it must follow
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8507 (because these motions be proportionall <emph style="super">(as 10 to 1)</emph>) <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8508 * As <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>B</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi><mi>C</mi></mstyle></math>. so: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>d</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi><mi>d</mi></mstyle></math>. which same termes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8509 proportionall call by these <emph style="st">same</emph> letters & in the same order.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8510 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8511 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8512 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8513 <s xml:id="echoid-s981" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8514 As <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi></mstyle></math> is known to be 1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>γ</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8515 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mo>+</mo><mi>α</mi></mstyle></math> is unknown. & so is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8516 yet this is known that. <emph style="st">is æquall to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ɛ</mi></mstyle></math>.</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8517 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8518 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8519 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8520 <s xml:id="echoid-s982" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8521 * Now what other proportion is this than if a man <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8522 should say as <emph style="st">all</emph> the first to the second so <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8523 all the antecedents to all the consequents which <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8524 in this be infinite in nomber.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8525 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8526 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8527 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8528 <s xml:id="echoid-s983" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8529 X To find that poynt geometrically is set downe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8530 in my other papers <foreign xml:lang="lat">de infinitis</foreign>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8531 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8532 on infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8533 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8534 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8535 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8536 <pb file="add_6782_f368v" o="368v" n="737"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8537 <pb file="add_6782_f369" o="369" n="738"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8538 <head xml:id="echoid-head137" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8539 De Infinitis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8540 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8541 On infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8542 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8543 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8544 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8545 <s xml:id="echoid-s984" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8546 Now will I propound some dfficultyes to be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8547 considered of.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8548 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8549 <s xml:id="echoid-s985" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8550 Seing that every line is compounded <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8551 of atomes, & therefore the periphery of a circle. <emph style="st">that <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8552 is to say</emph> one
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8553 <foreign xml:lang="lat">atomus</foreign> is succeeding one an other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8554 infinitely in such manner as <emph style="it">that</emph> the perifery is at <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8555 last compounded and made.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8556 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8557 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8558 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8559 <s xml:id="echoid-s986" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8560 Now also seing that the whole <foreign xml:lang="lat">periferies</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8561 is compounded of <foreign xml:lang="lat">atomis undiquaque <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8562 sitis</foreign> about the poynt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. so many times infinitely, & to that number of them <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8563 infinitely, till the circle supposed be accomplished.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8564 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8565 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8566 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8567 <s xml:id="echoid-s987" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8568 I demand <emph style="st">therefore</emph> <emph style="super">then</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8569 what wilbe the nomber of <foreign xml:lang="lat">atomi</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8570 that are <foreign xml:lang="lat">deinceps</foreign> about the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8571 point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8572 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8573 <s xml:id="echoid-s988" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8574 Infinite they must needes be, or else infinite lines could not <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8575 be <emph style="st">dra</emph> supposed actually from the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> to the perifery.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8576 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8577 <s xml:id="echoid-s989" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8578 And infinite also <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8579 are <emph style="super">also</emph> in the perifery.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8580 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8581 <s xml:id="echoid-s990" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8582 But now I demande whether they are aequally infinite <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8583 or not.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8584 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8585 <s xml:id="echoid-s991" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8586 If about the center are lesse infinite then there cannot from the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8587 center <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> to every poynt in the perifery be understood a right line but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8588 we must understand those <emph style="super"><foreign xml:lang="lat">atomi</foreign> about the center</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8589 that we supposed indivisible, divisble <emph style="super">which were absurd</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8590 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8591 <s xml:id="echoid-s992" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8592 and <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8593 if they be æqually infinite: then <emph style="st">the same nomber of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8594 <foreign xml:lang="lat">atomi</foreign></emph> in a great <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8595 place, (where the nomber, although infinite, yet in them selves definite; because <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8596 they being supposed to have <emph style="st">[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8597 acte there is not one more nor lesse.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8598 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8599 <s xml:id="echoid-s993" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8600 Neither <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8601 can there be more because <emph style="st">[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8602 they being <foreign xml:lang="lat">deinceps</foreign> one more cannot <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8603 be between there being no distance: & if there <emph style="st">be supposed</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8604 <emph style="super">might be</emph> one lesse; there <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8605 lacketh of the supposed actaull, & definite & positive number although infinite. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8606 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8607 <s xml:id="echoid-s994" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8608 Then I say in a greate place where there could be no more or lesse, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8609 in a lesse place there are an æquall nomber; which seemeth to imply.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8610 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8611 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8612 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8613 <s xml:id="echoid-s995" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8614 An other difficulty riseth from the square.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8615 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8616 <s xml:id="echoid-s996" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8617 If a line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8618 be compounded of <foreign xml:lang="lat">atomis</foreign>, the diametrall line wilbe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8619 found to be aæquall to the side.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8620 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8621 <s xml:id="echoid-s997" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8622 ffor suppose the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8623 to be drawne <emph style="st">from the poynt[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8624 from the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> <emph style="super">of the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math>,</emph> to <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8625 the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, of <emph style="st">th</emph> the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. Then from the next point <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8626 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, which is <foreign xml:lang="lat">deinceps</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8627 to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> in the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math>, draw a line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8628 to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> the next point to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> in the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8629 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8630 <s xml:id="echoid-s998" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8631 So likewise from every <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8632 next point in the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math>, to every next point in the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8633 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8634 <s xml:id="echoid-s999" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8635 Now the lines so drawne must needs be the least & most that may be, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8636 because they are <foreign xml:lang="lat">deinceps</foreign> & all.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8637 & they all cut the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> & of the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8638 there can be <emph style="st">between</emph> no point betwixt
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8639 <emph style="st">the</emph> two of the former lines
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8640 <emph style="super">because they are
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8641 <foreign xml:lang="lat">deinceps</foreign></emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8642 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8643 <s xml:id="echoid-s1000" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8644 And therefore <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8645 the nomber of the poynts of the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8646 <emph style="super">are</emph> aequally infinite to the poynts of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> & <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8647 <foreign xml:lang="lat">per</foreign> consequence the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> & <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> aequall.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8648 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8649 <s xml:id="echoid-s1001" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8650 But this difficulty wilbe made more <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8651 playne by the next following, which <emph style="st">[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8652 wilbe found the meanes for the solution <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8653 of all.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8654 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8655 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8656 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8657 <s xml:id="echoid-s1002" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8658 An other question is. where two
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8659 <foreign xml:lang="lat">atomi</foreign> are
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8660 <foreign xml:lang="lat">deinceps</foreign>. whether an other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8661 (the <emph style="st">other</emph> <emph style="super">first two</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8662 not disioyned) may either passe or have situation betwixt them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8663 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8664 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8665 <pb file="add_6782_f369v" o="369v" n="739"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8666 <pb file="add_6782_f370" o="370" n="740"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8667 <head xml:id="echoid-head138" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8668 De Infinitis. Notanda.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8669 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8670 On infinity. To be noted.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8671 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8672 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8673 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8674 <s xml:id="echoid-s1003" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8675 De tactu duorum corporum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8676 per superficies. an duæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8677 superficies sint realiter distantes <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8678 in corporum contactu.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8679 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8680 On the contact of two bodies at their surfaces,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8681 but the two surfaces are in reality separate in the contact of the bodies.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8682 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8683 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8684 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8685 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8686 <s xml:id="echoid-s1004" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8687 Because <foreign xml:lang="lat">discretum</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8688 is negative to <foreign xml:lang="lat">continuum</foreign> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8689 in respect of that thing <emph style="st">that</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8690 <emph style="super">which</emph> may be sayd to be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8691 either.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8692 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8693 <s xml:id="echoid-s1005" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8694 If yet <emph style="super">that</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8695 which is <foreign xml:lang="lat">discretum</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8696 is not <foreign xml:lang="lat">continuum</foreign> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8697 & that which is <foreign xml:lang="lat">continuum</foreign>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8698 is not <foreign xml:lang="lat">discretum</foreign>. therefore <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8699 the one being knowne the other cannot be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8700 unknowne what it is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8701 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8702 <s xml:id="echoid-s1006" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8703 Now although there <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8704 be great controversy of the essence & quality <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8705 of <foreign xml:lang="lat">continuum</foreign>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8706 yet there is no such of <foreign xml:lang="lat">discretum</foreign>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8707 we will therefore lay downe what is manifest <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8708 of it, that the ratio & essence of <foreign xml:lang="lat">continuum</foreign> may appeare.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8709 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8710 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8711 <pb file="add_6782_f370v" o="370v" n="741"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8712 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8713 <s xml:id="echoid-s1007" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8714 Willaim Sprat a wolle draper <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8715 at the sign of the rope in Watlin <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8716 street at Soper Lane corner. serveth <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8717 for a [???] for his wifes brother <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8718 for [???]. there are 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8719 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8720 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8721 <pb file="add_6782_f371" o="371" n="742"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8722 <head xml:id="echoid-head139" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8723 De Infinitis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8724 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8725 On infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8726 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8727 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8728 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8729 <s xml:id="echoid-s1008" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8730 That there may be two magnitudes given, of which the one shalbe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8731 infinite in respect of the other, & yet in respect of two other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8732 magnitudes they shalbe finite.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8733 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8734 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8735 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8736 <s xml:id="echoid-s1009" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8737 That a line finite, cannot have his partes, of a finite magnitude; but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8738 they must be of a finite nomber.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8739 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8740 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8741 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8742 <s xml:id="echoid-s1010" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8743 That a finite line may have an infinite nomber of partes,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8744 & if <emph style="super">all</emph> the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8745 partes be in continuall proportion: the nomber must be compounded <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8746 of an infinite nomber of finite partes; & an infinite nomber of <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8747 infinite partes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8748 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8749 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8750 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8751 <s xml:id="echoid-s1011" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8752 If a line be understood to be compounded of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8753 <emph style="st">infinite</emph> poyntes: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8754 the nomber of them is infinite of the first passe, second or <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8755 any nomber of passes finite or infinite.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8756 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8757 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8758 <pb file="add_6782_f371v" o="371v" n="743"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8759 <pb file="add_6782_f372" o="372" n="744"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8760 <head xml:id="echoid-head140" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8761 De Infinitis. Ratio Clava Herculis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8762 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8763 On infinity. The ratio of the key of Hercules
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8764 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8765 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8766 <pb file="add_6782_f372v" o="372v" n="745"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8767 <pb file="add_6782_f373" o="373" n="746"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8768 <head xml:id="echoid-head141" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8769 De Infinitis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8770 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8771 On infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8772 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8773 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8774 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8775 <s xml:id="echoid-s1012" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8776 Suppose the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> doth touch the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8777 the circle in the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. & touching <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8778 in that point <emph style="super">in</emph> it only & in no other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8779 point <emph style="st">it</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8780 <emph style="super">it</emph> toucheth, as Euclide suffi-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8781 ciently demonstrateth. Now I say <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8782 there is (a point <foreign xml:lang="lat">deinceps</foreign>) a next <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8783 poynt that doth not touch the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8784 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8785 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8786 <pb file="add_6782_f373v" o="373v" n="747"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8787 <pb file="add_6782_f374" o="374" n="748"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8788 <head xml:id="echoid-head142" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8789 De Infinitis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8790 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8791 On infinity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8792 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8793 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8794 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8795 <s xml:id="echoid-s1013" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8796 Minimum. That will kill men by <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8797 piercing & running through. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8798 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8799 <s xml:id="echoid-s1014" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8800 Maximum. That which will presse men <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8801 to death.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8802 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8803 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8804 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8805 <s xml:id="echoid-s1015" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8806 Unitas. Numeris unitatum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8807 finitis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8808 infinitis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8809 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8810 Unity. The number of a unit. Finite. Infinite.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8811 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8812 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8813 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8814 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8815 <s xml:id="echoid-s1016" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8816 Finites finitorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8817 Infinites finitorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8818 finites Infinitorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8819 Infinites Infinitorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8820 Infiniti infinitorum infinitum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8821 Infiniti infinitorum finitum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8822 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8823 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8824 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8825 <s xml:id="echoid-s1017" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8826 finitorum minimum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8827 Infinitorum minimum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8828 finitus minimorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8829 Infinites minimorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8830 finites finiti minimorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8831 Infinites finiti minimorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8832 Infinites finiti maximorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8833 Infinites infiniti maximorum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8834 finiti. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8835 finitorum maximum .1. Infinitorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8836 Infinitorum maximum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8837 Infiniti.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8838 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8839 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8840 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8841 <s xml:id="echoid-s1018" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8842 Ratio Achilles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8843 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8844 The ratio of Achilles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8845 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8846 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8847 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8848 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8849 <s xml:id="echoid-s1019" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8850 All the mistery of infinites lieth <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8851 in <foreign xml:lang="lat">formati ratione
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8852 <emph style="super">unius</emph> unitatis</foreign> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8853 which is only respective, & from <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8854 where the knowledge & import <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8855 of <foreign xml:lang="lat">formalis ratio</foreign> of quantity <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8856 doth spring.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8857 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8858 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8859 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8860 <s xml:id="echoid-s1020" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8861 A finite space may be moved in infinite time.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8862 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8863 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8864 <s xml:id="echoid-s1021" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8865 There is a [¿]conditioned[?]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8866 motion that a finite space <emph style="super">given</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8867 cannot be moved <emph style="super">in a finite time</emph> but in an infinite time.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8868 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8869 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8870 <s xml:id="echoid-s1022" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8871 Also: that a finite space given cannot be moved
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8872 <emph style="super">in a finite time nor</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8873 in an infinite time.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8874 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8875 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8876 <s xml:id="echoid-s1023" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8877 Also: that an infinite space may be moved <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8878 in a finite time.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8879 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8880 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8881 <s xml:id="echoid-s1024" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8882 Also: that an infinite space <emph style="super">given</emph> may be moved not in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8883 a finite time but in an infinite time.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8884 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8885 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8886 <s xml:id="echoid-s1025" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8887 Also: that an infinite space given, may not be <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8888 moved either in an infinite time nor finite.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8889 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8890 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8891 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8892 <s xml:id="echoid-s1026" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8893 Of contradictions that spring from diverse suppositions <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8894 it cannot truly <emph style="st">[???]</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8895 <emph style="super">be</emph> sayd that the one parte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8896 <emph style="st">doth [???]</emph> or <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8897 other is false, for they are true consequently from <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8898 there suppositions & in that respect are both true. but <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8899 that which followeth is, that one of the suppositions <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8900 is necessarily false, from where one of the <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8901 partes of the contradiction was inferred.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8902 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8903 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8904 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8905 <s xml:id="echoid-s1027" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8906 As in the reason Achilles & other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8907 reasons of Zeno &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8908 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8909 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8910 <pb file="add_6782_f374v" o="374v" n="749"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8911 <pb file="add_6782_f375" o="375" n="750"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8912 <pb file="add_6782_f375v" o="375v" n="751"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8913 <pb file="add_6782_f376" o="376" n="752"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8914 <pb file="add_6782_f376v" o="376v" n="753"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8915 <pb file="add_6782_f377" o="377" n="754"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8916 <pb file="add_6782_f377v" o="377v" n="755"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8917 <pb file="add_6782_f378" o="378" n="756"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8918 <pb file="add_6782_f378v" o="378v" n="757"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8919 <pb file="add_6782_f379" o="379" n="758"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8920 <pb file="add_6782_f379v" o="379v" n="759"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8921 <pb file="add_6782_f380" o="380" n="760"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8922 <head xml:id="echoid-head143" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8923 Proponatur, per Artem Analyticam solvere et inde <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8924 componere, hoc problema:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8925 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8926 It is proposed, by the analytic are to solve and thence compose this problem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8927 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8928 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8929 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8930 <s xml:id="echoid-s1028" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8931 <emph style="ul">Datam rectam terminatum: extrema ac media ratione secare.</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8932 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8933 Given a finite straight line, to cut it in extreme and mean ratio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8934 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8935 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8936 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8937 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8938 <s xml:id="echoid-s1029" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8939 Sit data recta terminata <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. et <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8940 ponatur secari in puncto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> ita ut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8941 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math> sit minor pars, et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8942 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8943 Let the given finite straight line be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> and let it be cut in the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8944 so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math> is the lesser part and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> the greater.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8945 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8946 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8947 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8948 <s xml:id="echoid-s1030" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8949 Quoniam utraque pars ignota est, duæ possunt esse zeteses; etsi una <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8950 sufficiat ad solutionem problematis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8951 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8952 Since both parts are unkown, there are two possible zeteses, but one suffices for the solution of the problem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8953 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8954 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8955 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8956 <head xml:id="echoid-head144" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8957 Zetesis. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8958 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8959 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8960 <s xml:id="echoid-s1031" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8961 ponatur primo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math> esse notum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8962 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8963 first suppose <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math> is known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8964 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8965 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8966 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8967 <s xml:id="echoid-s1032" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8968 Tum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8969 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8970 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8971 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8972 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8973 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8974 <s xml:id="echoid-s1033" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8975 Tres igitur proportionales erunt: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8976 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8977 Therefore three proportionals are: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8978 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8979 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8980 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8981 <s xml:id="echoid-s1034" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8982 Inde resoluta analogia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8983 æaquatio erit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8984 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8985 Whence having resolved the proportion, the equation will be:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8986 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8987 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8988 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8989 <s xml:id="echoid-s1035" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8990 Et: per Antithesin:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8991 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8992 And by antithesis:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8993 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8994 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8995 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8996 <s xml:id="echoid-s1036" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8997 Inde: Analogia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8998 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	8999 Whence, the ratio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9000 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9001 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9002 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9003 <s xml:id="echoid-s1037" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9004 Ubi datur media proportionalis et adgregatum exremarum, <emph style="st">per</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9005 ad Exegesin:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9006 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9007 Where there is given the mean proportional and the sum of the extremes, the resolution:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9008 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9009 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9010 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9011 <head xml:id="echoid-head145" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9012 Zetesis. 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9013 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9014 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9015 <s xml:id="echoid-s1038" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9016 ponatur secundo, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> esse notam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9017 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9018 suppose the second, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, is known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9019 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9020 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9021 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9022 <s xml:id="echoid-s1039" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9023 Tum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math> erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>a</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9024 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9025 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math> will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>a</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9026 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9027 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9028 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9029 <s xml:id="echoid-s1040" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9030 Tres igitur proportionales erunt. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>a</mi><mi>c</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9031 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9032 Therefore three proportionals will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>-</mo><mi>a</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9033 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9034 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9035 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9036 <s xml:id="echoid-s1041" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9037 Inde: resoluta analogia: erit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9038 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9039 Whence the resolution of the ratio will be:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9040 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9041 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9042 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9043 <s xml:id="echoid-s1042" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9044 Et: per Antithesin.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9045 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9046 And by antihesis:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9047 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9048 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9049 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9050 <s xml:id="echoid-s1043" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9051 Inde: analogia: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9052 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9053 Whence the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi></mstyle></math> : <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> : <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> : <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9054 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9055 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9056 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9057 <s xml:id="echoid-s1044" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9058 Ubi datur media proportionalis et differentia extremarum, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9059 ad Exegesin.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9060 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9061 Where there is given a mean proportional and the difference of the extremes, the resolution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9062 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9063 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9064 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9065 <pb file="add_6782_f380v" o="380v" n="761"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9066 <pb file="add_6782_f381" o="381" n="762"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9067 <pb file="add_6782_f381v" o="381v" n="763"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9068 <pb file="add_6782_f382" o="382" n="764"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9069 <pb file="add_6782_f382v" o="382v" n="765"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9070 <pb file="add_6782_f383" o="383" n="766"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9071 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9072 <s xml:id="echoid-s1045" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9073 to devide which by <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9074 [???] a mean <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9075 proportional. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9076 [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9077 the first being given is <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9078 the same [???] all 3 to [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9079 the proportionals.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9080 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9081 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9082 <pb file="add_6782_f383v" o="383v" n="767"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9083 <pb file="add_6782_f384" o="384" n="768"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9084 <pb file="add_6782_f384v" o="384v" n="769"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9085 <pb file="add_6782_f385" o="385" n="770"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9086 <pb file="add_6782_f385v" o="385v" n="771"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9087 <pb file="add_6782_f386" o="386" n="772"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9088 <pb file="add_6782_f386v" o="386v" n="773"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9089 <pb file="add_6782_f387" o="387" n="774"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9090 <pb file="add_6782_f387v" o="387v" n="775"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9091 <pb file="add_6782_f388" o="388" n="776"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9092 <div xml:id="echoid-div236" type="page_commentary" level="2" n="236">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9093 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9094 <s xml:id="echoid-s1046" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9095 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9096 <s xml:id="echoid-s1046" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9097 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9098 The example on this page is a quartic equation with a fourth power, a linear term and a square,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9099 the equation from Problem 6 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9100 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9101 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9102 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9103 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9104 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9105 <head xml:id="echoid-head146" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9106 12.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9107 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9108 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9109 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9110 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9111 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9112 <s xml:id="echoid-s1048" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9113 prob. 6. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>f</mi><mi>f</mi><mi>f</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9114 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9115 Problem 6. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>f</mi><mi>f</mi><mi>f</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9116 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9117 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9118 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9119 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9120 <s xml:id="echoid-s1049" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9121 Unicum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9122 Vietæ exemplum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9123 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9124 Viète's only example.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9125 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9126 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9127 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9128 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9129 <s xml:id="echoid-s1050" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9130 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>2</mn><mn>0</mn><mn>0</mn><mo>,</mo><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mn>0</mn><mi>a</mi><mo>=</mo><mn>4</mn><mn>4</mn><mn>9</mn><mn>3</mn><mn>7</mn><mn>6</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9131 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9132 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9133 <s xml:id="echoid-s1051" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9134 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9135 canonica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9136 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9137 Canonical form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9138 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9139 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9140 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9141 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9142 <s xml:id="echoid-s1052" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9143 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9144 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9145 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9146 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9147 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9148 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9149 <pb file="add_6782_f388v" o="388v" n="777"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9150 <pb file="add_6782_f389" o="389" n="778"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9151 <div xml:id="echoid-div237" type="page_commentary" level="2" n="237">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9152 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9153 <s xml:id="echoid-s1053" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9154 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9155 <s xml:id="echoid-s1053" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9156 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9157 The example on this page is a quartic equation with only a fourth power and a cube term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9158 the equation from Problem 5 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9159 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9160 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9161 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9162 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9163 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9164 <head xml:id="echoid-head147" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9165 11.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9166 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9167 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9168 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9169 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9170 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9171 <s xml:id="echoid-s1055" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9172 prob. 5. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9173 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9174 Problem 5. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9175 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9176 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9177 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9178 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9179 <s xml:id="echoid-s1056" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9180 Unicum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9181 Vietæ exemplum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9182 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9183 Viète's only exmaple.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9184 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9185 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9186 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9187 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9188 <s xml:id="echoid-s1057" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9189 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mo>,</mo><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mn>0</mn><mi>a</mi><mo>=</mo><mn>4</mn><mn>7</mn><mn>0</mn><mn>0</mn><mn>1</mn><mn>6</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9190 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9191 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9192 <s xml:id="echoid-s1058" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9193 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9194 canonica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9195 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9196 Canonical form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9197 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9198 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9199 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9200 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9201 <s xml:id="echoid-s1059" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9202 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9203 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9204 solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9205 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9206 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9207 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9208 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9209 <s xml:id="echoid-s1060" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9210 Alterum exemplum nostrum: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9211 quod per divisionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9212 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9213 Another example of my own, done by division.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9214 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9215 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9216 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9217 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9218 <s xml:id="echoid-s1061" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9219 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9220 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9221 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9222 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9223 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9224 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9225 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9226 <s xml:id="echoid-s1062" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9227 pro 1<emph style="super">a</emph> figura <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9228 Divide 44 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9229 per. 3 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9230 quotiens. 14. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9231 cuius maximus cubus 8 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9232 latus 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9233 pro 1<emph style="super">a</emph> figura <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9234 si caetera <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9235 consentiunt
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9236 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9237 For the first figure, divide 44 by 3; the quotient is 14, whose greatest cube is 8, with side 2,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9238 [to be taken] for the first figure, if the rest agree.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9239 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9240 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9241 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9242 <pb file="add_6782_f389v" o="389v" n="779"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9243 <pb file="add_6782_f390" o="390" n="780"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9244 <div xml:id="echoid-div238" type="page_commentary" level="2" n="238">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9245 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9246 <s xml:id="echoid-s1063" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9247 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9248 <s xml:id="echoid-s1063" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9249 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9250 The example on this page is a quartic equation with only a fourth power and a linear term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9251 the second equation from Problem 4 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9252 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9253 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9254 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9255 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9256 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9257 <head xml:id="echoid-head148" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9258 10.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9259 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9260 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9261 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9262 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9263 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9264 <s xml:id="echoid-s1065" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9265 prob. 4. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9266 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9267 Problem 4. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9268 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9269 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9270 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9271 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9272 <s xml:id="echoid-s1066" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9273 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9274 Vietæ exemplum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9275 quod Per divisionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9276 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9277 Viète's second example, done by division.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9278 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9279 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9280 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9281 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9282 <s xml:id="echoid-s1067" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9283 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>7</mn><mn>3</mn><mn>1</mn><mo>,</mo><mn>7</mn><mn>7</mn><mn>6</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9284 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9285 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9286 <s xml:id="echoid-s1068" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9287 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9288 canonica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9289 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9290 Canonical form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9291 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9292 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9293 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9294 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9295 <s xml:id="echoid-s1069" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9296 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9297 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9298 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9299 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9300 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9301 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9302 <pb file="add_6782_f390v" o="390v" n="781"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9303 <pb file="add_6782_f391" o="391" n="782"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9304 <div xml:id="echoid-div239" type="page_commentary" level="2" n="239">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9305 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9306 <s xml:id="echoid-s1070" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9307 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9308 <s xml:id="echoid-s1070" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9309 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9310 The example on this page is a quartic equation with only a fourth power and a linear term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9311 the first equation from Problem 4 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9312 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9313 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9314 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9315 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9316 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9317 <head xml:id="echoid-head149" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9318 9.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9319 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9320 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9321 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9322 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9323 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9324 <s xml:id="echoid-s1072" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9325 prob. 4. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9326 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9327 Problem 4. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9328 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9329 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9330 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9331 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9332 <s xml:id="echoid-s1073" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9333 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9334 Vietæ exemplum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9335 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9336 Viète's first example.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9337 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9338 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9339 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9340 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9341 <s xml:id="echoid-s1074" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9342 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>3</mn><mn>5</mn><mn>5</mn><mo>,</mo><mn>7</mn><mn>7</mn><mn>6</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9343 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9344 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9345 <s xml:id="echoid-s1075" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9346 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9347 canonica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9348 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9349 Canonical form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9350 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9351 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9352 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9353 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9354 <s xml:id="echoid-s1076" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9355 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9356 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9357 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9358 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9359 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9360 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9361 <pb file="add_6782_f391v" o="391v" n="783"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9362 <pb file="add_6782_f392" o="392" n="784"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9363 <div xml:id="echoid-div240" type="page_commentary" level="2" n="240">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9364 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9365 <s xml:id="echoid-s1077" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9366 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9367 <s xml:id="echoid-s1077" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9368 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9369 The example on this page is a cubic equation without a linear term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9370 the second equation from Problem 3 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9371 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9372 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9373 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9374 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9375 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9376 <head xml:id="echoid-head150" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9377 8.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9378 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9379 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9380 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9381 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9382 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9383 <s xml:id="echoid-s1079" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9384 prob. 3. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9385 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9386 Problem 3. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9387 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9388 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9389 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9390 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9391 <s xml:id="echoid-s1080" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9392 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9393 Vietæ exemplum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9394 quod per divisionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9395 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9396 Viète's second example, done by division.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9397 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9398 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9399 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9400 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9401 <s xml:id="echoid-s1081" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9402 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>1</mn><mn>0</mn><mo>,</mo><mn>0</mn><mn>0</mn><mn>0</mn><mo>,</mo><mi>a</mi><mi>a</mi><mo>=</mo><mn>5</mn><mo>,</mo><mn>7</mn><mn>7</mn><mn>3</mn><mo>,</mo><mn>8</mn><mn>2</mn><mn>4</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9403 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9404 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9405 <s xml:id="echoid-s1082" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9406 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9407 canonica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9408 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9409 Canonical form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9410 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9411 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9412 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9413 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9414 <s xml:id="echoid-s1083" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9415 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9416 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9417 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9418 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9419 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9420 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9421 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9422 <s xml:id="echoid-s1084" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9423 Nota.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9424 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9425 Note.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9426 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9427 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9428 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9429 <s xml:id="echoid-s1085" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9430 prima figura acquiritur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9431 per divisionem ac si <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9432 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9433 esset: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>d</mi><mo>+</mo><mi>b</mi><mo maxsize="1">)</mo><mo>×</mo><mi>b</mi><mi>b</mi></mstyle></math> quæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>b</mi><mi>b</mi><mi>d</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9434 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9435 the first figure is acquired by division as if the canonical form were <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>d</mi><mo>+</mo><mi>b</mi><mo maxsize="1">)</mo><mo>×</mo><mi>b</mi><mi>b</mi></mstyle></math> quæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>b</mi><mi>b</mi><mi>d</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9436 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9437 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9438 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9439 <s xml:id="echoid-s1086" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9440 hoc est si <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>+</mo><mi>b</mi></mstyle></math> sit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9441 divisor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9442 Quotiens erit, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9443 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9444 that is, if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>+</mo><mi>b</mi></mstyle></math> is the divisor, the quotient will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9445 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9446 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9447 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9448 <s xml:id="echoid-s1087" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9449 Et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> latus erit 1<emph style="super">a</emph> figura
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9450 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9451 And the square-root <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> will be the first figure.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9452 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9453 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9454 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9455 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9456 <s xml:id="echoid-s1088" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9457 Ut hic Quotiens est 5. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9458 cuius latus <emph style="super">quadratum</emph> 2. pro <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9459 prima figura.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9460 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9461 As here the quotient is 5, whose square-root is 2 for the first figure.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9462 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9463 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9464 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9465 <s xml:id="echoid-s1089" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9466 Vide Vietam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9467 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9468 See Viète.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9469 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9470 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9471 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9472 <pb file="add_6782_f392v" o="392v" n="785"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9473 <pb file="add_6782_f393" o="393" n="786"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9474 <div xml:id="echoid-div241" type="page_commentary" level="2" n="241">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9475 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9476 <s xml:id="echoid-s1090" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9477 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9478 <s xml:id="echoid-s1090" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9479 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9480 The example on this page is a cubic equation without a linear term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9481 the first equation from Problem 3 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9482 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9483 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9484 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9485 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9486 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9487 <head xml:id="echoid-head151" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9488 7.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9489 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9490 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9491 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9492 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9493 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9494 <s xml:id="echoid-s1092" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9495 prob. 3. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9496 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9497 Problem 3. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9498 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9499 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9500 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9501 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9502 <s xml:id="echoid-s1093" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9503 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9504 Vietæ exemplum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9505 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9506 Viète's first example
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9507 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9508 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9509 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9510 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9511 <s xml:id="echoid-s1094" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9512 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>3</mn><mn>0</mn><mo>,</mo><mi>a</mi><mi>a</mi><mo>=</mo><mn>8</mn><mn>6</mn><mo>,</mo><mn>2</mn><mn>2</mn><mn>0</mn><mo>,</mo><mn>2</mn><mn>8</mn><mn>8</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9513 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9514 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9515 <s xml:id="echoid-s1095" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9516 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9517 canonica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9518 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9519 Canonical form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9520 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9521 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9522 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9523 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9524 <s xml:id="echoid-s1096" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9525 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9526 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9527 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9528 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9529 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9530 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9531 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9532 <s xml:id="echoid-s1097" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9533 Jam 43. fiat <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9534 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9535 Now <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> becomes 43.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9536 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9537 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9538 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9539 <pb file="add_6782_f393v" o="393v" n="787"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9540 <pb file="add_6782_f394" o="394" n="788"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9541 <div xml:id="echoid-div242" type="page_commentary" level="2" n="242">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9542 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9543 <s xml:id="echoid-s1098" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9544 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9545 <s xml:id="echoid-s1098" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9546 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9547 The example on this page is a cubic equation without a square term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9548 the second equation from Problem 2 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9549 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9550 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9551 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9552 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9553 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9554 <head xml:id="echoid-head152" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9555 6.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9556 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9557 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9558 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9559 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9560 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9561 <s xml:id="echoid-s1100" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9562 prob. 2. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9563 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9564 Problem 2. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9565 </emph>]<lb/></s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9566 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9567 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9568 <s xml:id="echoid-s1101" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9569 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9570 Vietæ exemplum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9571 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9572 Viète's second example.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9573 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9574 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9575 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9576 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9577 <s xml:id="echoid-s1102" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9578 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>9</mn><mn>5</mn><mn>4</mn><mn>0</mn><mn>0</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>8</mn><mn>1</mn><mn>9</mn><mo>,</mo><mn>4</mn><mn>5</mn><mn>9</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9579 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9580 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9581 <s xml:id="echoid-s1103" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9582 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9583 canonica
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9584 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9585 Canonical form
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9586 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9587 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9588 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9589 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9590 <s xml:id="echoid-s1104" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9591 Resolutio:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9592 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9593 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9594 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9595 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9596 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9597 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9598 <s xml:id="echoid-s1105" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9599 per divisionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9600 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9601 By division.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9602 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9603 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9604 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9605 <pb file="add_6782_f394v" o="394v" n="789"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9606 <pb file="add_6782_f395" o="395" n="790"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9607 <div xml:id="echoid-div243" type="page_commentary" level="2" n="243">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9608 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9609 <s xml:id="echoid-s1106" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9610 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9611 <s xml:id="echoid-s1106" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9612 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9613 The example on this page is a cubic equation without a square term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9614 the first equation from Problem 2 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9615 <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9616 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9617 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9618 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9619 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9620 <head xml:id="echoid-head153" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9621 5.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9622 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9623 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9624 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9625 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9626 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9627 <s xml:id="echoid-s1108" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9628 prob. 2. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9629 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9630 Problem 2. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9631 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9632 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9633 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9634 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9635 <s xml:id="echoid-s1109" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9636 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9637 Vietæ exemplum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9638 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9639 Viète's first example.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9640 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9641 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9642 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9643 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9644 <s xml:id="echoid-s1110" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9645 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>3</mn><mn>0</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>1</mn><mn>4</mn><mn>3</mn><mn>5</mn><mn>6</mn><mn>1</mn><mn>9</mn><mn>7</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9646 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9647 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9648 <s xml:id="echoid-s1111" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9649 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9650 canonica.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9651 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9652 Canonical form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9653 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9654 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9655 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9656 <s xml:id="echoid-s1112" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9657 Vel:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9658 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9659 Or:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9660 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9661 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9662 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9663 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9664 <s xml:id="echoid-s1113" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9665 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9666 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9667 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9668 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9669 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9670 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9671 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9672 <s xml:id="echoid-s1114" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9673 Vide supra. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9674 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9675 See above at A.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9676 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9677 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9678 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9679 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9680 <s xml:id="echoid-s1115" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9681 Jam 24 fiat. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9682 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9683 Now <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> becomes 24.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9684 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9685 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9686 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9687 <pb file="add_6782_f395v" o="395v" n="791"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9688 <pb file="add_6782_f396" o="396" n="792"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9689 <div xml:id="echoid-div244" type="page_commentary" level="2" n="244">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9690 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9691 <s xml:id="echoid-s1116" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9692 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9693 <s xml:id="echoid-s1116" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9694 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9695 Here the method is applied to a cubic equation without a square term.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9696 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9697 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9698 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9699 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9700 <head xml:id="echoid-head154" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9701 4.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9702 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9703 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9704 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9705 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9706 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9707 <s xml:id="echoid-s1118" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9708 prob. 2. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9709 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9710 Problem 2. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9711 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9712 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9713 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9714 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9715 <s xml:id="echoid-s1119" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9716 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mi>a</mi><mo>+</mo><mn>3</mn><mn>5</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>2</mn><mn>2</mn><mn>9</mn><mn>3</mn><mn>2</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9717 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9718 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9719 <s xml:id="echoid-s1120" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9720 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9721 canonica
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9722 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9723 Canonical form
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9724 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9725 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9726 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9727 <s xml:id="echoid-s1121" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9728 Hoc est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9729 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9730 That is:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9731 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9732 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9733 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9734 <s xml:id="echoid-s1122" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9735 Vel.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9736 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9737 Or.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9738 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9739 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9740 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9741 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9742 <s xml:id="echoid-s1123" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9743 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9744 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9745 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9746 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9747 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9748 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9749 <pb file="add_6782_f396v" o="396v" n="793"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9750 <pb file="add_6782_f397" o="397" n="794"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9751 <div xml:id="echoid-div245" type="page_commentary" level="2" n="245">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9752 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9753 <s xml:id="echoid-s1124" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9754 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9755 <s xml:id="echoid-s1124" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9756 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9757 In the example on this page, the large size of the coefficient in relation to the root means that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9758 the term <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mn>6</mn><mn>2</mn><mi>b</mi></mstyle></math> must be taken into account in determining the first digit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9759 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9760 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9761 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9762 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9763 <head xml:id="echoid-head155" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9764 3.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9765 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9766 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9767 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9768 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9769 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9770 <s xml:id="echoid-s1126" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9771 prob. 1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9772 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9773 Problem 1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9774 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9775 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9776 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9777 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9778 <s xml:id="echoid-s1127" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9779 Casus 2<emph style="super">a</emph>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9780 per divisionem
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9781 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9782 Case 2, by division
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9783 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9784 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9785 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9786 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9787 <s xml:id="echoid-s1128" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9788 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mn>7</mn><mn>6</mn><mn>2</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>2</mn><mn>2</mn><mn>1</mn><mn>2</mn><mn>0</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9789 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9790 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9791 <s xml:id="echoid-s1129" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9792 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9793 canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9794 ut supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9795 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9796 Canonical form as above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9797 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9798 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9799 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9800 <s xml:id="echoid-s1130" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9801 Vel:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9802 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9803 Or:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9804 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9805 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9806 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9807 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9808 <s xml:id="echoid-s1131" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9809 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9810 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9811 Solution
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9812 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9813 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9814 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9815 <s xml:id="echoid-s1132" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9816 Quoniam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>></mo><mn>2</mn></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9817 fiat devolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9818 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9819 Because <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>7</mn><mo>></mo><mn>2</mn></mstyle></math> it becomes a devolution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9820 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9821 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9822 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9823 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9824 <s xml:id="echoid-s1133" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9825 Vietæ exemplum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9826 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mn>9</mn><mn>5</mn><mn>4</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>1</mn><mn>8</mn><mn>4</mn><mn>8</mn><mn>7</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9827 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9828 Viète's example, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mn>9</mn><mn>5</mn><mn>4</mn><mi>a</mi><mo>=</mo><mn>1</mn><mn>8</mn><mn>4</mn><mn>8</mn><mn>7</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9829 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9830 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9831 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9832 <pb file="add_6782_f397v" o="397v" n="795"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9833 <pb file="add_6782_f398" o="398" n="796"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9834 <div xml:id="echoid-div246" type="page_commentary" level="2" n="246">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9835 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9836 <s xml:id="echoid-s1134" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9837 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9838 <s xml:id="echoid-s1134" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9839 For a general explanation of the method see Add MS 6782, f. 399. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9840 The equation on this page has a 3-digit solution. The first digit is found by inspection to be 2 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>2</mn><mn>0</mn><mn>0</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9841 The second digit, is found to be 4 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>4</mn><mn>0</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9842 The process is now repeated, treating <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> as a single quantity, to find the third digit, again labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9843 This is found to be 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9844 For Harriot's owon description of this process see Add MS 6784, f. 408.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9845 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9846 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9847 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9848 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9849 <head xml:id="echoid-head156" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9850 2.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9851 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9852 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9853 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9854 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9855 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9856 <s xml:id="echoid-s1136" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9857 prob. 1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9858 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9859 Problem 1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9860 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9861 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9862 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9863 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9864 <s xml:id="echoid-s1137" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9865 Exemplum primum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9866 Vietæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9867 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9868 Viète's first example
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9869 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9870 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9871 This is Problem 1 from Viète's <emph style="it">De numerosa potestatum resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9872 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9873 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9874 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9875 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9876 <s xml:id="echoid-s1138" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9877 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mn>7</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>6</mn><mn>0</mn><mn>7</mn><mn>5</mn><mn>0</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9878 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9879 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9880 <s xml:id="echoid-s1139" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9881 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9882 canonica. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9883 ut supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9884 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9885 Canonical form as above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9886 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9887 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9888 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9889 <s xml:id="echoid-s1140" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9890 hoc est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9891 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9892 that is:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9893 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9894 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9895 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9896 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9897 <s xml:id="echoid-s1141" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9898 Resolutio Vietana. paucis mutatis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9899 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9900 Viète's solution, a little changed
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9901 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9902 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9903 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9904 <pb file="add_6782_f398v" o="398v" n="797"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9905 <pb file="add_6782_f399" o="399" n="798"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9906 <div xml:id="echoid-div247" type="page_commentary" level="2" n="247">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9907 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9908 <s xml:id="echoid-s1142" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9909 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9910 <s xml:id="echoid-s1142" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9911 This is the first of a set of 12 pages on extracting roots of positively affected equations,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9912 that is, equations where all the powers following the first are positive.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9913 Such equations have one, and only one, positive root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9914 The work is closely based on Problems 1 to 6 in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9915 Viète, <emph style="it">De numerosa potestatum ad exegesin resolutione</emph> (1600);
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9916 Harriot's heading 'De numerosa potestatum resolutione' directly echoes Viète's. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9917 The method works by finding each digit of the root in turn.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9918 Suppose that a required root <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> of is of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9919 where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> represents multiples of 10 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> represents units.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9920 The first digit is found by inspection. The canonical form then shows how to estimate <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9921 In the problem on this page, for example, Harriot first takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> to be 40, but quickly finds that this is too large.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9922 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> must be 30. Subtracting the known values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math> (= 900) and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>d</mi></mstyle></math> (= 720) from 2356
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9923 leaves him with 736, which according to the canonical form must correspond to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>d</mi><mo>+</mo><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9924 A first estimate for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is found by dividing 736 by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>b</mi><mo>+</mo><mi>d</mi></mstyle></math> (= 84). The integer part of the quotient is 8.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9925 In fact <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>8</mn></mstyle></math> satisfies the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>d</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>=</mo><mn>7</mn><mn>3</mn><mn>6</mn></mstyle></math> exactly and so the process is complete. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9926 Later examples become more complicated but follow the same basic procedure. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9927 For further discussion see See Stedall 2003, 45–62 and 292, and Stedall 2011, 29–31.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9928 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9929 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9930 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9931 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9932 <head xml:id="echoid-head157" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9933 1.) De numerosa potestatum resolutione. Vieta. fol. 7. b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9934 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9935 On the numerical resolution of powers. Viète, folio 7b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9936 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9937 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9938 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9939 <s xml:id="echoid-s1144" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9940 prob. 1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9941 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9942 Problem 1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>a</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9943 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9944 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9945 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9946 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9947 <s xml:id="echoid-s1145" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9948 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi><mo>+</mo><mn>2</mn><mn>4</mn><mo>,</mo><mi>a</mi><mo>=</mo><mn>2</mn><mn>3</mn><mn>5</mn><mn>6</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9949 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9950 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9951 <s xml:id="echoid-s1146" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9952 Species <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9953 canonica
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9954 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9955 Canonical form
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9956 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9957 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9958 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9959 <s xml:id="echoid-s1147" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9960 Hoc est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9961 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9962 That is:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9963 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9964 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9965 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9966 <s xml:id="echoid-s1148" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9967 vel:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9968 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9969 or:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9970 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9971 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9972 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9973 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9974 <s xml:id="echoid-s1149" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9975 Genesis Vulgaris
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9976 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9977 Common derivation
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9978 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9979 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9980 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9981 <s xml:id="echoid-s1150" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9982 Genesis Specialis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9983 seu canonica
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9984 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9985 Specific or canonical derivation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9986 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9987 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9988 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9989 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9990 <s xml:id="echoid-s1151" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9991 Resolutio secundum methodum Vietanam, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9992 paucis mutatis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9993 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9994 Solution according to the method of Viète, a little changed
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9995 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9996 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9997 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9998 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	9999 <s xml:id="echoid-s1152" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10000 non potest auferri. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10001 operatio igitur iteranda <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10002 et fiat <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. minor. videlicet. 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10003 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10004 cannot be subtracted; the work must therefore be repeated making <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> smaller, namely, 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10005 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10006 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10007 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10008 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10009 <s xml:id="echoid-s1153" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10010 Aliter.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10011 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10012 Another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10013 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10014 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10015 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10016 <pb file="add_6782_f399v" o="399v" n="799"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10017 <pb file="add_6782_f400" o="400" n="800"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10018 <div xml:id="echoid-div248" type="page_commentary" level="2" n="248">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10019 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10020 <s xml:id="echoid-s1154" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10021 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10022 <s xml:id="echoid-s1154" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10023 Following from the general treatment in Add MS 6782, f. 403, f. 402, f. 401,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10024 of avulsed quartics with no square or linear term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10025 Harriot here solves the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>4</mn><mn>8</mn><mn>1</mn><mn>5</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>6</mn><mn>5</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> for both roots (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn><mn>8</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>5</mn><mn>7</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10026 He also shows how either root may be obtained from the other. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10027 The equation is taken from Problem 20 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10028 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10029 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10030 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10031 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10032 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10033 <head xml:id="echoid-head158" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10034 c.17.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10035 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10036 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10037 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10038 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10039 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10040 <s xml:id="echoid-s1156" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10041 prob. 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10042 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10043 Problem 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10044 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10045 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10046 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10047 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10048 <s xml:id="echoid-s1157" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10049 canon ad <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10050 resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10051 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10052 Canonical form for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10053 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10054 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10055 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10056 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10057 <s xml:id="echoid-s1158" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10058 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10059 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10060 Solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10061 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10062 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10063 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10064 <s xml:id="echoid-s1159" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10065 Eductio radicis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10066 minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10067 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10068 Extraction of the smaller root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10069 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10070 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10071 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10072 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10073 <s xml:id="echoid-s1160" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10074 Radix igitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10075 minor. 38.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10076 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10077 Therefore the smaller root is 38.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10078 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10079 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10080 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10081 <s xml:id="echoid-s1161" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10082 Quæratur maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10083 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10084 The larger root is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10085 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10086 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10087 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10088 <s xml:id="echoid-s1162" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10089 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10090 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10091 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10092 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> the larger.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10093 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10094 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10095 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10096 <s xml:id="echoid-s1163" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10097 Vieta aliter <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10098 ut pag: supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10099 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10100 Viète otherwise, as in the page above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10101 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10102 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10103 The page above is Add MS 6782, f. 402.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10104 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10105 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10106 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10107 <s xml:id="echoid-s1164" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10108 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. 57.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10109 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10110 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>5</mn><mn>7</mn></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10111 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10112 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10113 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10114 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10115 <s xml:id="echoid-s1165" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10116 Eductio radicis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10117 maioris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10118 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10119 Extraction of the larger root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10120 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10121 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10122 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10123 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10124 <s xml:id="echoid-s1166" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10125 Radix igitur maior. 57.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10126 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10127 Therefore the larger root is 57.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10128 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10129 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10130 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10131 <s xml:id="echoid-s1167" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10132 Quæratur iam minor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10133 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10134 Now the smaller root is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10135 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10136 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10137 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10138 <s xml:id="echoid-s1168" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10139 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> minor, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> minor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10140 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10141 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> the larger.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10142 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10143 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10144 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10145 <s xml:id="echoid-s1169" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10146 Vieta aliter <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10147 ut pag: supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10148 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10149 Viète otherwise as in the page above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10150 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10151 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10152 The page above is Add MS 6782, f. 402.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10153 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10154 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10155 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10156 <s xml:id="echoid-s1170" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10157 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. 38.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10158 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10159 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>3</mn><mn>8</mn></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10160 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10161 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10162 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10163 <pb file="add_6782_f400v" o="400v" n="801"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10164 <pb file="add_6782_f401" o="401" n="802"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10165 <div xml:id="echoid-div249" type="page_commentary" level="2" n="249">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10166 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10167 <s xml:id="echoid-s1171" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10168 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10169 <s xml:id="echoid-s1171" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10170 In this final page of Section c, Harriot argues that the first figure of the larger root must be 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10171 Assuming that it is either 4 or 6 will lead to a contradiction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10172 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10173 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10174 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10175 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10176 <head xml:id="echoid-head159" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10177 c.18.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10178 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10179 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10180 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10181 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10182 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10183 <s xml:id="echoid-s1173" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10184 prob. 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>,</mo><mn>4</mn><mn>8</mn><mn>1</mn><mo>,</mo><mn>5</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>6</mn><mn>5</mn><mo>,</mo><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10185 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10186 Problem 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>4</mn><mn>8</mn><mn>1</mn><mn>5</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>6</mn><mn>5</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10187 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10188 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10189 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10190 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10191 <s xml:id="echoid-s1174" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10192 <emph style="st">Additementum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10193 nostrum</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10194 Absurdum consequens in eductione lateris maioris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10195 si prima figura sit minor vel maior. 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10196 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10197 Nonsensical consequences in the extraction of the larger root if the first figure is less than or greater than 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10198 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10199 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10200 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10201 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10202 <s xml:id="echoid-s1175" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10203 B. Divisor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mn>4</mn><mn>1</mn><mn>0</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10204 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10205 The divisor is 5410.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10206 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10207 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10208 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10209 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10210 <s xml:id="echoid-s1176" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10211 Absurdum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10212 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10213 Contradiction
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10214 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10215 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10216 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10217 <s xml:id="echoid-s1177" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10218 Nam cum Residuum supra <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10219 habent signum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10220 et Divisor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>+</mo></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10221 Parabola erit etiam, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10222 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10223 For with the above residue we have a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math> sign, while the divisor is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>+</mo></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10224 so the comparison is also <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10225 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10226 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10227 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10228 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10229 <s xml:id="echoid-s1178" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10230 Prima figura igitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10231 non est 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10232 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10233 Therefore the first figure is not 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10234 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10235 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10236 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10237 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10238 <s xml:id="echoid-s1179" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10239 B. Divisor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo><mn>1</mn><mn>7</mn><mn>2</mn><mn>0</mn><mn>7</mn><mn>5</mn></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10240 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10241 The divisor is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo><mn>1</mn><mn>7</mn><mn>2</mn><mn>0</mn><mn>7</mn><mn>5</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10242 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10243 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10244 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10245 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10246 <s xml:id="echoid-s1180" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10247 Absurdum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10248 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10249 Contradiction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10250 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10251 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10252 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10253 <s xml:id="echoid-s1181" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10254 Nam cum residuum supra <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10255 habent signum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>+</mo></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10256 et divisor, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10257 parabola erit etiam, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10258 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10259 For while the above residue has the sign <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>+</mo></mstyle></math> and the divisor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math>, the comparison is also <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10260 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10261 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10262 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10263 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10264 <s xml:id="echoid-s1182" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10265 Prima figura igitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10266 non est, 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10267 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10268 Therefore the first figure is not 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10269 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10270 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10271 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10272 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10273 <s xml:id="echoid-s1183" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10274 Erit igitur 5. per limitum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10275 præfinitiones, sicut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10276 per exemplum est explicatum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10277 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10278 Therefore it will be 5, by the determinations of limits, as explained by the example.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10279 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10280 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10281 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10282 <head xml:id="echoid-head160" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10283 Nota.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10284 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10285 Note
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10286 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10287 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10288 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10289 <s xml:id="echoid-s1184" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10290 Operatio pro eductione lateris maioris aliquando secundum partem <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10291 est similis operationem pro eductione lateris minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10292 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10293 In the operation for extracting the larger root,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10294 sometimes the second part is similar to the operation for extracting the smaller root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10295 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10296 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10297 <s xml:id="echoid-s1185" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10298 Nimirum si <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10299 utraque latera consentiant in primus figurus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10300 <emph style="super">et numero figurum</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10301 Evidently, if both roots agree in the first figure and the number of figures.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10302 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10303 <s xml:id="echoid-s1186" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10304 Ut si latus minus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10305 sit 23. maius 24.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10306 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10307 As if the smaller root is 23, the larger is 24.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10308 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10309 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10310 <s xml:id="echoid-s1187" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10311 Ita si minus 343, maius 347. est sic de cæteris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10312 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10313 Thus if the smaller root is 343, the larger 347, and so on for others.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10314 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10315 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10316 <s xml:id="echoid-s1188" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10317 Sed si dissentiant in primum figura: dissimiles erunt operationes totaliter <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10318 ut in exemplis antecedentis, in his chartis expositis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10319 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10320 But if they do not agree in the first figure, the operations will be completely different,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10321 as in the preceding examples explained in these sheets.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10322 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10323 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10324 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10325 <pb file="add_6782_f401v" o="401v" n="803"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10326 <pb file="add_6782_f402" o="402" n="804"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10327 <div xml:id="echoid-div250" type="page_commentary" level="2" n="250">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10328 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10329 <s xml:id="echoid-s1189" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10330 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10331 <s xml:id="echoid-s1189" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10332 On this page Harriot compares his own method with that of Viète, in Problem 20 of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10333 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10334 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10335 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10336 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10337 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10338 <head xml:id="echoid-head161" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10339 c.16.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10340 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10341 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10342 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10343 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10344 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10345 <s xml:id="echoid-s1191" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10346 prob. 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10347 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10348 Problem 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10349 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10350 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10351 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10352 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10353 <s xml:id="echoid-s1192" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10354 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10355 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10356 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10357 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10358 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10359 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10360 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10361 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10362 <s xml:id="echoid-s1193" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10363 Aliter quam supra, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10364 et ut Vieta.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10365 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10366 Another way from that above, and as Viète.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10367 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10368 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10369 By 'above' Harriot means the working given in Add MS 6782, f. 404, f. 403.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10370 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10371 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10372 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10373 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10374 <s xml:id="echoid-s1194" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10375 Si una radix sit nota, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10376 altera erit cognita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10377 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10378 If one roots is known, the other will be known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10379 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10380 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10381 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10382 <s xml:id="echoid-s1195" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10383 4<emph style="super">or</emph> continue proportionales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10384 Four continued proportionals.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10385 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10386 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10387 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10388 <s xml:id="echoid-s1196" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10389 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10390 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10391 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10392 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10393 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10394 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10395 <s xml:id="echoid-s1197" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10396 Sint continue proportionales
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10397 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10398 Let there be continued proportinals
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10399 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10400 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10401 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10402 <s xml:id="echoid-s1198" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10403 datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> et inde <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10404 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10405 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is given and thence <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10406 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10407 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10408 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10409 <s xml:id="echoid-s1199" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10410 erit: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10411 inde:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10412 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10413 We will have: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10414 thence:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10415 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10416 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10417 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10418 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10419 <s xml:id="echoid-s1200" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10420 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10421 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10422 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10423 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10424 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10425 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10426 <s xml:id="echoid-s1201" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10427 Sint continue proportionales
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10428 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10429 Let there be continued proportinals
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10430 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10431 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10432 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10433 <s xml:id="echoid-s1202" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10434 datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> et inde, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10435 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10436 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is given, and thence <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10437 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10438 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10439 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10440 <s xml:id="echoid-s1203" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10441 erit: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10442 inde:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10443 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10444 We will have: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10445 thence:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10446 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10447 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10448 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10449 <pb file="add_6782_f402v" o="402v" n="805"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10450 <pb file="add_6782_f403" o="403" n="806"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10451 <div xml:id="echoid-div251" type="page_commentary" level="2" n="251">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10452 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10453 <s xml:id="echoid-s1204" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10454 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10455 <s xml:id="echoid-s1204" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10456 On this page, Harriot continues his general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10457 begun on the previous page. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10458 The numerical example at the end, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>4</mn><mn>8</mn><mn>1</mn><mn>5</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>6</mn><mn>5</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>, is from Problem 20 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10459 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10460 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10461 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10462 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10463 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10464 <head xml:id="echoid-head162" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10465 c.15.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10466 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10467 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10468 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10469 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10470 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10471 <s xml:id="echoid-s1206" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10472 prob. 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10473 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10474 Problem 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10475 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10476 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10477 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10478 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10479 <s xml:id="echoid-s1207" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10480 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10481 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10482 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10483 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10484 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10485 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10486 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10487 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10488 <s xml:id="echoid-s1208" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10489 Si una radix sit nota, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10490 altera erit cognita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10491 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10492 If one root is known, the other will be known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10493 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10494 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10495 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10496 <s xml:id="echoid-s1209" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10497 sit, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> nota. Quæaeritur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10498 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10499 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10500 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10501 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10502 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10503 <s xml:id="echoid-s1210" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10504 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10505 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10506 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10507 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10508 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10509 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10510 <s xml:id="echoid-s1211" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10511 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10512 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10513 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10514 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10515 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10516 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10517 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10518 <s xml:id="echoid-s1212" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10519 sit, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> nota. Quæaeritur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10520 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10521 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10522 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10523 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10524 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10525 <s xml:id="echoid-s1213" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10526 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10527 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10528 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10529 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10530 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10531 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10532 <s xml:id="echoid-s1214" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10533 Unde eadem æquatio:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10534 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10535 Whence the same equation:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10536 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10537 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10538 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10539 <s xml:id="echoid-s1215" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10540 Datur <emph style="st">igitur</emph> igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10541 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10542 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10543 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10544 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10545 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10546 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10547 <s xml:id="echoid-s1216" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10548 Poristicum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10549 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10550 Proof
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10551 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10552 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10553 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10554 <s xml:id="echoid-s1217" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10555 Quod,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10556 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10557 Because
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10558 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10559 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10560 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10561 <s xml:id="echoid-s1218" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10562 Est enim: est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10563 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10564 Indeed it is. Therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10565 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10566 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10567 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10568 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10569 <s xml:id="echoid-s1219" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10570 Pro exemplo ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10571 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10572 According to this example for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10573 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10574 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10575 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10576 <s xml:id="echoid-s1220" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10577 In numeris, sit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>.</mo><mn>3</mn><mn>8</mn></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>.</mo><mn>5</mn><mn>7</mn><mo>.</mo></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10578 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10579 In numbers let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>3</mn><mn>8</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>5</mn><mn>7</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10580 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10581 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10582 <s xml:id="echoid-s1221" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10583 Hoc est: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10584 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>,</mo><mn>4</mn><mn>8</mn><mn>1</mn><mo>,</mo><mn>5</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>6</mn><mn>5</mn><mo>,</mo><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10585 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10586 That is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>4</mn><mn>8</mn><mn>1</mn><mn>5</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>6</mn><mn>5</mn><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10587 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10588 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10589 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10590 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10591 <s xml:id="echoid-s1222" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10592 Limites radicum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10593 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10594 The limits of the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10595 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10596 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10597 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10598 <pb file="add_6782_f403v" o="403v" n="807"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10599 <pb file="add_6782_f404" o="404" n="808"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10600 <div xml:id="echoid-div252" type="page_commentary" level="2" n="252">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10601 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10602 <s xml:id="echoid-s1223" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10603 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10604 <s xml:id="echoid-s1223" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10605 On this page Harriot begins a general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>d</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10606 with no square or linear term.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10607 In order to preserve dimensions, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math> is used as a placeholder for a general 4-dimensional quantity.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10608 All coeffcients are assumed to be positive.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10609 Equations of this kind have two positive roots or none at all, depending on the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10610 For Harriot's derivation of the canonical form for unequal roots, see Add MS 6783, f. 173.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10611 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10612 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10613 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10614 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10615 <head xml:id="echoid-head163" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10616 c.14.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10617 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10618 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10619 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10620 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10621 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10622 <s xml:id="echoid-s1225" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10623 prob. 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10624 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10625 Problem 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10626 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10627 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10628 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10629 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10630 <s xml:id="echoid-s1226" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10631 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10632 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10633 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10634 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10635 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10636 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10637 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10638 <s xml:id="echoid-s1227" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10639 Nam: Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>. erit:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10640 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10641 For if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math> then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10642 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10643 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10644 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10645 <s xml:id="echoid-s1228" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10646 Et ita est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10647 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10648 And so it is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10649 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10650 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10651 <s xml:id="echoid-s1229" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10652 Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10653 erit:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10654 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10655 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math> then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10656 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10657 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10658 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10659 <s xml:id="echoid-s1230" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10660 est igitur
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10661 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10662 Therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10663 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10664 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10665 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10666 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10667 <s xml:id="echoid-s1231" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10668 Species ad radices <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10669 æquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10670 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10671 Canonical form for equal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10672 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10673 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10674 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10675 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10676 <s xml:id="echoid-s1232" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10677 Sunt continue proportionalia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10678 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10679 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10680 There are continued proportionals <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10681 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10682 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10683 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10684 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10685 <s xml:id="echoid-s1233" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10686 Sit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, minor radix. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10687 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10688 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> the larger.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10689 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10690 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10691 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10692 <s xml:id="echoid-s1234" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10693 fiat: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mo>,</mo><mn>3</mn><mo>:</mo><mi>d</mi><mo>,</mo><mfrac><mrow><mn>3</mn><mi>d</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10694 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10695 let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mo>:</mo><mn>3</mn><mo>=</mo><mi>d</mi><mo>:</mo><mfrac><mrow><mn>3</mn><mi>d</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10696 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10697 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10698 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10699 <s xml:id="echoid-s1235" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10700 Dico quod:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10701 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10702 I say that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10703 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10704 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10705 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10706 <s xml:id="echoid-s1236" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10707 Est enim. est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10708 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10709 Indeed it is. Therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10710 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10711 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10712 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10713 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10714 <s xml:id="echoid-s1237" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10715 Dico quod: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10716 vel:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10717 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10718 I say that: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10719 or:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10720 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10721 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10722 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10723 <s xml:id="echoid-s1238" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10724 Est enim. est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10725 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10726 Indeed it is. Therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10727 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10728 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10729 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10730 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10731 <s xml:id="echoid-s1239" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10732 Dico quod: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10733 vel:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10734 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10735 I say that: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10736 or:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10737 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10738 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10739 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10740 <s xml:id="echoid-s1240" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10741 Est enim. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10742 Est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10743 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10744 Indeed it is. Therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10745 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10746 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10747 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10748 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10749 <s xml:id="echoid-s1241" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10750 ergo. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>></mo><mi>a</mi></mstyle></math>. Hoc est qualibet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10751 radice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10752 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10753 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>></mo><mi>a</mi></mstyle></math>. This is so whatever the root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10754 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10755 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10756 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10757 <pb file="add_6782_f404v" o="404v" n="809"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10758 <pb file="add_6782_f405" o="405" n="810"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10759 <div xml:id="echoid-div253" type="page_commentary" level="2" n="253">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10760 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10761 <s xml:id="echoid-s1242" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10762 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10763 <s xml:id="echoid-s1242" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10764 Following from the general treatment in Add MS 6782, f. 407, f. 406,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10765 of avulsed quartics with no cube or square term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10766 Harriot here solves the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>1</mn><mn>7</mn><mn>9</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>2</mn><mn>7</mn><mn>7</mn><mn>5</mn><mn>5</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> for both roots (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>8</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10767 He also shows how either root may be obtained from the other. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10768 The equation is taken from Problem 19 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10769 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10770 Viète gave rules for the relationship between the two roots but did not explain how he had arrived at them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10771 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10772 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10773 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10774 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10775 <head xml:id="echoid-head164" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10776 c.13.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10777 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10778 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10779 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10780 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10781 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10782 <s xml:id="echoid-s1244" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10783 prob. 19. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10784 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10785 Problem 19. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10786 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10787 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10788 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10789 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10790 <s xml:id="echoid-s1245" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10791 Canon ad <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10792 resolutionem
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10793 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10794 Canonical form for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10795 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10796 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10797 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10798 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10799 <s xml:id="echoid-s1246" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10800 Resolutio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10801 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10802 Solution
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10803 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10804 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10805 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10806 <s xml:id="echoid-s1247" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10807 Eductio radicis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10808 Minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10809 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10810 Extraction of the smaller root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10811 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10812 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10813 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10814 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10815 <s xml:id="echoid-s1248" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10816 Radix igitur minor est 8.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10817 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10818 Therefore the smaller root is 8.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10819 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10820 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10821 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10822 <s xml:id="echoid-s1249" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10823 Quæratur iam maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10824 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10825 Now the larger root is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10826 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10827 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10828 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10829 <s xml:id="echoid-s1250" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10830 Sit minor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. maior <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10831 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10832 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> the larger.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10833 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10834 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10835 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10836 <s xml:id="echoid-s1251" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10837 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. 27.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10838 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10839 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10840 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10841 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10842 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10843 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10844 <s xml:id="echoid-s1252" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10845 Eductio radicis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10846 Maioris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10847 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10848 Extraction of the larger root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10849 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10850 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10851 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10852 <pb file="add_6782_f405v" o="405v" n="811"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10853 <pb file="add_6782_f406" o="406" n="812"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10854 <div xml:id="echoid-div254" type="page_commentary" level="2" n="254">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10855 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10856 <s xml:id="echoid-s1253" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10857 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10858 <s xml:id="echoid-s1253" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10859 On this page, Harriot continues his general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10860 begun on the previous page. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10861 The numerical example at the end, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>1</mn><mn>7</mn><mn>9</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>2</mn><mn>7</mn><mn>7</mn><mn>5</mn><mn>5</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>, is from Problem 19 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10862 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10863 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10864 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10865 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10866 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10867 <head xml:id="echoid-head165" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10868 c.12.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10869 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10870 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10871 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10872 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10873 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10874 <s xml:id="echoid-s1255" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10875 prob. 19. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10876 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10877 Problem 19. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10878 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10879 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10880 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10881 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10882 <s xml:id="echoid-s1256" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10883 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10884 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10885 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10886 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10887 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10888 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10889 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10890 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10891 <s xml:id="echoid-s1257" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10892 Si una radix sit nota, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10893 altera erit cognita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10894 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10895 If one root is known, the other will be known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10896 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10897 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10898 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10899 <s xml:id="echoid-s1258" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10900 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10901 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10902 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10903 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10904 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10905 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10906 <s xml:id="echoid-s1259" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10907 Datur igitur, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10908 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10909 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10910 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10911 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10912 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10913 <s xml:id="echoid-s1260" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10914 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10915 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10916 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10917 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10918 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10919 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10920 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10921 <s xml:id="echoid-s1261" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10922 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10923 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10924 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10925 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10926 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10927 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10928 <s xml:id="echoid-s1262" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10929 datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10930 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10931 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10932 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10933 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10934 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10935 <s xml:id="echoid-s1263" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10936 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10937 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10938 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10939 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10940 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10941 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10942 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10943 <s xml:id="echoid-s1264" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10944 Pro exemplo ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10945 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10946 According to this example for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10947 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10948 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10949 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10950 <s xml:id="echoid-s1265" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10951 In numeris. Sit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. 8. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. 27
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10952 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10953 In numbers, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>8</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10954 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10955 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10956 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10957 <s xml:id="echoid-s1266" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10958 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>1</mn><mn>7</mn><mo>,</mo><mn>9</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>2</mn><mn>7</mn><mo>,</mo><mn>7</mn><mn>5</mn><mn>5</mn><mo>,</mo><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10959 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10960 That is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>1</mn><mn>7</mn><mn>9</mn><mn>4</mn><mn>4</mn><mo>=</mo><mn>2</mn><mn>7</mn><mn>7</mn><mn>5</mn><mn>5</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10961 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10962 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10963 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10964 <s xml:id="echoid-s1267" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10965 Limites radicum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10966 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10967 Limits of the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10968 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10969 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10970 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10971 <pb file="add_6782_f406v" o="406v" n="813"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10972 <pb file="add_6782_f407" o="407" n="814"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10973 <div xml:id="echoid-div255" type="page_commentary" level="2" n="255">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10974 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10975 <s xml:id="echoid-s1268" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10976 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10977 <s xml:id="echoid-s1268" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10978 On this page Harriot begins a general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>d</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10979 with no cube or square term.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10980 In order to preserve dimensions, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math> is used as a placeholder for a general 4-dimensional quantity;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10981 similarly <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi><mi>d</mi></mstyle></math> is a placeholder for a 3-dimensional quantity, not necessarily a cube.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10982 All coefficients are assumed to be positive.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10983 Equations of this kind have two positive roots or none at all, depending on the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10984 For Harriot's derivation of the canonical form for unequal roots, see Add MS 6783, f. 174.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10985 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10986 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10987 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10988 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10989 <head xml:id="echoid-head166" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10990 c.11.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10991 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10992 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10993 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10994 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10995 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10996 <s xml:id="echoid-s1270" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10997 prob. 19. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10998 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	10999 Problem 19. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11000 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11001 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11002 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11003 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11004 <s xml:id="echoid-s1271" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11005 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11006 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11007 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11008 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11009 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11010 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11011 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11012 <s xml:id="echoid-s1272" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11013 nam: Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>. erit:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11014 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11015 for if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>+</mo><mi>b</mi></mstyle></math> then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11016 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11017 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11018 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11019 <s xml:id="echoid-s1273" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11020 et ita est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11021 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11022 and so it is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11023 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11024 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11025 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11026 <s xml:id="echoid-s1274" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11027 Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>. erit:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11028 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11029 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math> then:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11030 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11031 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11032 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11033 <s xml:id="echoid-s1275" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11034 est enim.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11035 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11036 Indeed it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11037 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11038 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11039 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11040 <s xml:id="echoid-s1276" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11041 est igitur
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11042 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11043 Therefore it is so
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11044 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11045 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11046 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11047 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11048 <s xml:id="echoid-s1277" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11049 Species ad radices <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11050 æquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11051 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11052 The case of equal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11053 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11054 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11055 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11056 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11057 <s xml:id="echoid-s1278" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11058 Sunt continue proportionalia. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11059 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11060 et: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>b</mi><mi>c</mi><mo>,</mo><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>,</mo><mi>b</mi><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11061 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11062 There are continued proportionals <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11063 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11064 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11065 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11066 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11067 <s xml:id="echoid-s1279" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11068 Sit, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> minor radix. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11069 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11070 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> the larger.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11071 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11072 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11073 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11074 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11075 <s xml:id="echoid-s1280" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11076 Dico etiam quod:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11077 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11078 I also say that:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11079 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11080 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11081 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11082 <s xml:id="echoid-s1281" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11083 Est enim. Est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11084 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11085 Indeed it is. Therefore is is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11086 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11087 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11088 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11089 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11090 <s xml:id="echoid-s1282" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11091 Ergo, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mo maxsize="1">[</mo></msqrt><mn>3</mn><mo maxsize="1">]</mo><mrow><mi>d</mi><mi>d</mi><mi>d</mi></mrow><mo>></mo><mi>a</mi></mstyle></math>. Hoc est qualibet radice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11092 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11093 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mo maxsize="1">[</mo></msqrt><mn>3</mn><mo maxsize="1">]</mo><mrow><mi>d</mi><mi>d</mi><mi>d</mi></mrow><mo>></mo><mi>a</mi></mstyle></math>; this is so whatever the root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11094 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11095 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11096 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11097 <pb file="add_6782_f407v" o="407v" n="815"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11098 <pb file="add_6782_f408" o="408" n="816"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11099 <div xml:id="echoid-div256" type="page_commentary" level="2" n="256">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11100 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11101 <s xml:id="echoid-s1283" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11102 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11103 <s xml:id="echoid-s1283" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11104 Following from the general treatment in Add MS 6782, f. 410, f. 109, of avulsed cubics with no linear term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11105 Harriot here solves the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>4</mn><mn>3</mn><mn>0</mn><mn>0</mn><mo>=</mo><mn>5</mn><mn>7</mn><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> for both roots (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>3</mn><mn>0</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>4</mn><mn>5</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11106 He also shows how either root may be obtained from the other. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11107 The equation is taken from Problem 18 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11108 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11109 Viète gave rules for the relationship between the two roots but did not explain how he had arrived at them. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11110 This page demonstrates clearly two kinds of canonical forms used by Harriot in this treatise.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11111 The first, the 'canonical form for unequal roots' is the general form of an avulsed cubic without a linear term;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11112 in this case <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> are the two positive roots of the equation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11113 The second, the 'canonical form for the solution' is the form arrived at by assuming the root <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11114 takes the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>0</mn><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math>, that is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is the first integer in the solution, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> the second.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11115 Thus the meanings of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> in the two forms are thus quite different.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11116 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11117 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11118 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11119 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11120 <head xml:id="echoid-head167" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11121 c.10.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11122 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11123 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11124 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11125 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11126 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11127 <s xml:id="echoid-s1285" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11128 prob. 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11129 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11130 Problem 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11131 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11132 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11133 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11134 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11135 <s xml:id="echoid-s1286" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11136 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11137 Here <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> are the two positive roots of the equation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11138 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11139 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11140 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11141 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11142 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11143 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11144 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11145 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11146 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11147 <s xml:id="echoid-s1287" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11148 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11149 Here <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> are the first and second integers of any solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11150 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11151 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11152 ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11153 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11154 Canonical form for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11155 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11156 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11157 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11158 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11159 <s xml:id="echoid-s1288" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11160 Resolutio:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11161 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11162 Solution:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11163 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11164 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11165 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11166 <s xml:id="echoid-s1289" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11167 Eductio lateris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11168 Minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11169 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11170 Extraction of the smaller root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11171 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11172 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11173 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11174 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11175 <s xml:id="echoid-s1290" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11176 Radix igitur minor, est 30.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11177 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11178 Therefore the smaller root is 30.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11179 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11180 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11181 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11182 <s xml:id="echoid-s1291" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11183 Quæratur iam maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11184 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11185 The larger root is now sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11186 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11187 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11188 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11189 <s xml:id="echoid-s1292" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11190 Sit minor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. maior <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11191 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11192 Let the smaller root be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, the larger <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11193 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11194 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11195 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11196 <s xml:id="echoid-s1293" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11197 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. 45.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11198 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11199 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>4</mn><mn>5</mn></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11200 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11201 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11202 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11203 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11204 <s xml:id="echoid-s1294" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11205 Si quæratur minor radix. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11206 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11207 If the smaller root <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11208 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11209 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11210 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11211 <s xml:id="echoid-s1295" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11212 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. 30.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11213 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11214 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>3</mn><mn>0</mn></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11215 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11216 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11217 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11218 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11219 <s xml:id="echoid-s1296" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11220 Eductio lateris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11221 Maioris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11222 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11223 Solution and extraction of the larger root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11224 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11225 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11226 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11227 <s xml:id="echoid-s1297" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11228 Radix igitur maior 45.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11229 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11230 Therefore the larger root is 45.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11231 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11232 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11233 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11234 <pb file="add_6782_f408v" o="408v" n="817"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11235 <pb file="add_6782_f409" o="409" n="818"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11236 <div xml:id="echoid-div257" type="page_commentary" level="2" n="257">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11237 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11238 <s xml:id="echoid-s1298" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11239 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11240 <s xml:id="echoid-s1298" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11241 On this page Harriot compares his own method with that of Viète, in Problem 18 of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11242 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11243 showing that the two methods are essentially the same.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11244 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11245 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11246 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11247 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11248 <head xml:id="echoid-head168" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11249 c.9.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11250 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11251 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11252 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11253 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11254 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11255 <s xml:id="echoid-s1300" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11256 prob. 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11257 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11258 Problem 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11259 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11260 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11261 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11262 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11263 <s xml:id="echoid-s1301" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11264 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11265 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11266 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11267 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11268 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11269 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11270 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11271 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11272 <s xml:id="echoid-s1302" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11273 Aliter quam supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11274 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11275 Another way from that above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11276 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11277 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11278 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11279 <s xml:id="echoid-s1303" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11280 si una radix sit nota, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11281 altera erit cognita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11282 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11283 If one root is known, the other will be known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11284 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11285 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11286 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11287 <s xml:id="echoid-s1304" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11288 tres continue proportionales. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11289 prima et secunda <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11290 secunda et tertia. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11291 tertia. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11292 prima.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11293 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11294 Three continued proportionals. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11295 first and second <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11296 second and third <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11297 third <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11298 first
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11299 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11300 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11301 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11302 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11303 <s xml:id="echoid-s1305" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11304 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11305 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11306 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11307 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11308 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11309 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11310 <s xml:id="echoid-s1306" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11311 sint continue proportionales. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11312 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>e</mi><mi>e</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11313 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11314 Let there be continued proportionals <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>e</mi><mi>e</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>.]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11315 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11316 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11317 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11318 <s xml:id="echoid-s1307" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11319 Datur igitur. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11320 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11321 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11322 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11323 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11324 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11325 <s xml:id="echoid-s1308" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11326 Datur igitur. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11327 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11328 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11329 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11330 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11331 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11332 <s xml:id="echoid-s1309" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11333 Sed in Vieta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11334 iisdem præmissis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11335 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11336 But in Viète from the same premises.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11337 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11338 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11339 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11340 <s xml:id="echoid-s1310" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11341 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11342 The other sheet referred to here is Add MS 6782, f. 410.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11343 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11344 eadem quæ altera charta.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11345 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11346 The same as in the other sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11347 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11348 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11349 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11350 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11351 <s xml:id="echoid-s1311" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11352 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11353 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11354 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11355 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11356 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11357 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11358 <s xml:id="echoid-s1312" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11359 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11360 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11361 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11362 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11363 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11364 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11365 <s xml:id="echoid-s1313" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11366 datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11367 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11368 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11369 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11370 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11371 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11372 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11373 <s xml:id="echoid-s1314" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11374 sed in Vieta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11375 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11376 But in Viete
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11377 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11378 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11379 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11380 <s xml:id="echoid-s1315" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11381 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>c</mi><mo>=</mo><mo>-</mo><mi>g</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11382 eadem quæ nostra in altera charta.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11383 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11384 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>c</mi><mo>=</mo><mo>-</mo><mi>g</mi><mi>b</mi><mo>=</mo><mi>b</mi><mi>b</mi></mstyle></math>, the same as mine in the other sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11385 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11386 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11387 The other sheet referred to here is Add MS 6782, f. 410.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11388 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11389 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11390 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11391 <pb file="add_6782_f409v" o="409v" n="819"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11392 <pb file="add_6782_f410" o="410" n="820"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11393 <div xml:id="echoid-div258" type="page_commentary" level="2" n="258">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11394 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11395 <s xml:id="echoid-s1316" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11396 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11397 <s xml:id="echoid-s1316" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11398 On this page, Harriot continues his general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11399 begun on the previous page. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11400 The numerical example at the end, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>4</mn><mn>3</mn><mn>0</mn><mn>0</mn><mo>=</mo><mn>5</mn><mn>7</mn><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>, is from Problem 18 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11401 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11402 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11403 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11404 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11405 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11406 <head xml:id="echoid-head169" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11407 c.8.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11408 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11409 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11410 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11411 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11412 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11413 <s xml:id="echoid-s1318" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11414 prob. 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11415 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11416 Problem 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11417 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11418 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11419 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11420 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11421 <s xml:id="echoid-s1319" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11422 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11423 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11424 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11425 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11426 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11427 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11428 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11429 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11430 <s xml:id="echoid-s1320" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11431 Si una radix sit nota, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11432 altera erit cognita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11433 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11434 If one root is known, the other will be known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11435 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11436 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11437 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11438 <s xml:id="echoid-s1321" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11439 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11440 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11441 <s xml:id="echoid-s1322" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11442 Dabitur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11443 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11444 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> will be given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11445 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11446 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11447 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11448 <s xml:id="echoid-s1323" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11449 Datur igitur, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11450 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11451 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11452 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11453 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11454 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11455 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11456 <s xml:id="echoid-s1324" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11457 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11458 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11459 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11460 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11461 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11462 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11463 <s xml:id="echoid-s1325" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11464 Dabitur ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11465 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11466 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> will be given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11467 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11468 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11469 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11470 <s xml:id="echoid-s1326" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11471 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11472 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11473 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11474 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11475 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11476 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11477 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11478 <s xml:id="echoid-s1327" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11479 pro exemplo ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11480 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11481 According to this example for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11482 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11483 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11484 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11485 <s xml:id="echoid-s1328" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11486 In numeris sit. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11487 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. 30. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11488 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. 45.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11489 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11490 In numbers, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>3</mn><mn>0</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>4</mn><mn>5</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11491 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11492 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11493 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11494 <s xml:id="echoid-s1329" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11495 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>4</mn><mn>3</mn><mn>0</mn><mn>0</mn><mo>=</mo><mn>5</mn><mn>7</mn><mo>,</mo><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11496 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11497 That is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>4</mn><mn>3</mn><mn>0</mn><mn>0</mn><mo>=</mo><mn>5</mn><mn>7</mn><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11498 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11499 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11500 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11501 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11502 <s xml:id="echoid-s1330" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11503 Limites radicum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11504 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11505 Limits of the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11506 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11507 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11508 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11509 <pb file="add_6782_f410v" o="410v" n="821"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11510 <pb file="add_6782_f411" o="411" n="822"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11511 <div xml:id="echoid-div259" type="page_commentary" level="2" n="259">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11512 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11513 <s xml:id="echoid-s1331" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11514 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11515 <s xml:id="echoid-s1331" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11516 On this page Harriot begins a general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11517 with no linear term. All coefficients are assumed to be positive.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11518 Equations of this kind have two positive roots or none at all, depending on the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11519 For Harriot's derivation of the canonical form for unequal roots, see Add MS 6783, f. 181.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11520 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11521 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11522 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11523 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11524 <head xml:id="echoid-head170" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11525 c.7.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11526 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11527 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11528 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11529 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11530 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11531 <s xml:id="echoid-s1333" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11532 prob. 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11533 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11534 Problem 18. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11535 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11536 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11537 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11538 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11539 <s xml:id="echoid-s1334" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11540 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11541 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11542 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11543 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11544 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11545 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11546 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11547 <s xml:id="echoid-s1335" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11548 Nam: Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11549 erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>b</mi><mo>-</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>c</mi></mstyle></math>. Et ita est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11550 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11551 For if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math> then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>b</mi><mo>-</mo><mi>b</mi><mi>b</mi><mi>b</mi><mi>c</mi></mstyle></math>; and so it is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11552 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11553 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11554 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11555 <s xml:id="echoid-s1336" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11556 Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11557 erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>c</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>c</mi><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>. est enim.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11558 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11559 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math> then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>c</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>c</mi><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>; indeed it is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11560 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11561 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11562 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11563 <s xml:id="echoid-s1337" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11564 est igitur
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11565 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11566 Therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11567 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11568 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11569 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11570 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11571 <s xml:id="echoid-s1338" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11572 Species ad radices <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11573 æquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11574 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11575 The case of equal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11576 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11577 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11578 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11579 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11580 <s xml:id="echoid-s1339" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11581 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math> sunt continue proportionalia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11582 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11583 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math> are in continued proportion.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11584 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11585 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11586 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11587 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11588 <s xml:id="echoid-s1340" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11589 Dico etiam quod:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11590 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11591 I say also that:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11592 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11593 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11594 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11595 <s xml:id="echoid-s1341" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11596 ponatur: est igitur:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11597 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11598 This supposed, then
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11599 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11600 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11601 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11602 <s xml:id="echoid-s1342" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11603 est enim, est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11604 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11605 Indded it is; therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11606 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11607 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11608 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11609 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11610 <s xml:id="echoid-s1343" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11611 est igitur: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>></mo><mi>a</mi></mstyle></math>. hoc est qualibet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11612 radice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11613 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11614 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>></mo><mi>a</mi></mstyle></math>; this is so whatever the root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11615 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11616 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11617 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11618 <pb file="add_6782_f411v" o="411v" n="823"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11619 <pb file="add_6782_f412" o="412" n="824"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11620 <div xml:id="echoid-div260" type="page_commentary" level="2" n="260">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11621 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11622 <s xml:id="echoid-s1344" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11623 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11624 <s xml:id="echoid-s1344" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11625 Following on from Add MS 6782, f. 415, f. 414, f. 413, Harriot here solves the equation
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11626 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>5</mn><mn>5</mn><mn>5</mn><mn>2</mn><mn>0</mn><mo>=</mo><mn>1</mn><mn>3</mn><mn>1</mn><mn>0</mn><mn>4</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> for the larger root (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>1</mn><mn>0</mn><mn>8</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11627 He then shows how the smaller roots (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>1</mn><mn>2</mn></mstyle></math>) may be derived from the larger one.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11628 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11629 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11630 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11631 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11632 <head xml:id="echoid-head171" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11633 c.6.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11634 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11635 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11636 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11637 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11638 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11639 <s xml:id="echoid-s1346" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11640 prob. 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11641 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11642 Problem 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11643 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11644 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11645 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11646 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11647 <s xml:id="echoid-s1347" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11648 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11649 ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11650 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11651 Canonical form for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11652 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11653 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11654 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11655 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11656 <s xml:id="echoid-s1348" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11657 Resolutio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11658 et eductio lateris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11659 Maioris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11660 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11661 Solution and extraction of the larger root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11662 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11663 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11664 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11665 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11666 <s xml:id="echoid-s1349" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11667 Radix <emph style="super">igitur</emph> maior est 108.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11668 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11669 Therefore the larger root is 108.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11670 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11671 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11672 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11673 <s xml:id="echoid-s1350" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11674 Quæratur iam minor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11675 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11676 Now there is sought the smaller root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11677 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11678 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11679 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11680 <s xml:id="echoid-s1351" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11681 Sit maior <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. minor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11682 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11683 Let the larger root be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, the smaller <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11684 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11685 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11686 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11687 <s xml:id="echoid-s1352" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11688 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11689 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11690 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>1</mn><mn>2</mn></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11691 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11692 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11693 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11694 <pb file="add_6782_f412v" o="412v" n="825"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11695 <pb file="add_6782_f413" o="413" n="826"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11696 <div xml:id="echoid-div261" type="page_commentary" level="2" n="261">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11697 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11698 <s xml:id="echoid-s1353" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11699 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11700 <s xml:id="echoid-s1353" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11701 Following from the general treatment in Add MS 6782, f. 415, f. 414, of avulsed cubics with no square term,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11702 Harriot here solves the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>5</mn><mn>5</mn><mn>5</mn><mn>2</mn><mn>0</mn><mo>=</mo><mn>1</mn><mn>3</mn><mn>1</mn><mn>0</mn><mn>4</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math> for the smaller root (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>1</mn><mn>2</mn></mstyle></math>).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11703 He then shows how the larger roots (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>1</mn><mn>0</mn><mn>8</mn></mstyle></math>) may be derived from the smaller one. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11704 The equation is taken from Problem 17 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11705 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11706 Viète gave rules for the relationship between the two roots but did not explain how he had arrived at them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11707 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11708 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11709 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11710 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11711 <head xml:id="echoid-head172" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11712 c.5.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11713 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11714 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11715 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11716 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11717 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11718 <s xml:id="echoid-s1355" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11719 prob. 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11720 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11721 Problem 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11722 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11723 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11724 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11725 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11726 <s xml:id="echoid-s1356" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11727 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11728 ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11729 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11730 Canonical form for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11731 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11732 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11733 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11734 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11735 <s xml:id="echoid-s1357" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11736 Resolutio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11737 et eductio lateris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11738 minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11739 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11740 Solution and extraction of the smaller root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11741 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11742 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11743 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11744 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11745 <s xml:id="echoid-s1358" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11746 Radix igitur minor est, 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11747 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11748 Therefore the smaller root is 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11749 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11750 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11751 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11752 <s xml:id="echoid-s1359" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11753 Radix <emph style="super">minor</emph> sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. maior <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11754 Et quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11755 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11756 The smaller root is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, the larger <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>; and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11757 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11758 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11759 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11760 <s xml:id="echoid-s1360" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11761 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. 108.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11762 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11763 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>1</mn><mn>0</mn><mn>8</mn></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11764 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11765 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11766 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11767 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11768 <s xml:id="echoid-s1361" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11769 A. Poristicum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11770 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11771 Proof
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11772 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11773 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11774 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11775 <s xml:id="echoid-s1362" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11776 Quod: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi><mo>-</mo><mi>b</mi><mi>b</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mi>x</mi><mi>z</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11777 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11778 Because <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi><mo>-</mo><mi>b</mi><mi>b</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mi>x</mi><mi>z</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11779 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11780 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11781 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11782 <s xml:id="echoid-s1363" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11783 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11784 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11785 That is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11786 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11787 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11788 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11789 <s xml:id="echoid-s1364" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11790 Est enim. est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11791 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11792 Indeed it is; therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11793 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11794 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11795 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11796 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11797 <s xml:id="echoid-s1365" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11798 Etiam. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi><mo>-</mo><mi>c</mi><mi>c</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mi>x</mi><mi>z</mi></mrow><mrow><mi>c</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11799 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11800 Also <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi><mo>-</mo><mi>c</mi><mi>c</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mi>x</mi><mi>z</mi></mrow><mrow><mi>c</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11801 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11802 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11803 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11804 <s xml:id="echoid-s1366" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11805 hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11806 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11807 That is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11808 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11809 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11810 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11811 <s xml:id="echoid-s1367" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11812 Est enim. est igitur.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11813 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11814 Indeed it is; therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11815 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11816 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11817 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11818 <pb file="add_6782_f413v" o="413v" n="827"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11819 <pb file="add_6782_f414" o="414" n="828"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11820 <div xml:id="echoid-div262" type="page_commentary" level="2" n="262">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11821 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11822 <s xml:id="echoid-s1368" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11823 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11824 <s xml:id="echoid-s1368" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11825 On this page, Harriot continues his general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11826 begun on the previous page. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11827 The numerical example at the end, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>5</mn><mn>5</mn><mn>5</mn><mn>2</mn><mn>0</mn><mo>=</mo><mn>1</mn><mn>3</mn><mn>1</mn><mn>0</mn><mn>4</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>, is from Problem 17 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11828 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11829 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11830 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11831 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11832 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11833 <head xml:id="echoid-head173" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11834 c.4.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11835 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11836 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11837 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11838 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11839 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11840 <s xml:id="echoid-s1370" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11841 prob. 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11842 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11843 Problem 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11844 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11845 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11846 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11847 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11848 <s xml:id="echoid-s1371" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11849 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11850 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11851 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11852 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11853 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11854 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11855 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11856 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11857 <s xml:id="echoid-s1372" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11858 Si una radix sit nota, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11859 altera erit cognita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11860 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11861 If one root is known, the other will be known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11862 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11863 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11864 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11865 <s xml:id="echoid-s1373" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11866 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11867 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11868 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11869 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11870 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11871 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11872 <s xml:id="echoid-s1374" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11873 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11874 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11875 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11876 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11877 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11878 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11879 <s xml:id="echoid-s1375" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11880 vel:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11881 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11882 or:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11883 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11884 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11885 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11886 <s xml:id="echoid-s1376" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11887 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11888 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11889 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11890 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11891 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11892 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11893 <s xml:id="echoid-s1377" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11894 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> nota. Quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11895 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11896 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11897 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11898 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11899 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11900 <s xml:id="echoid-s1378" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11901 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11902 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11903 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11904 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11905 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11906 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11907 <s xml:id="echoid-s1379" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11908 vel:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11909 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11910 or:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11911 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11912 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11913 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11914 <s xml:id="echoid-s1380" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11915 Datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11916 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11917 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11918 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11919 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11920 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11921 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11922 <s xml:id="echoid-s1381" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11923 Pro exemplo ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11924 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11925 According to this example for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11926 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11927 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11928 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11929 <s xml:id="echoid-s1382" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11930 In numeris. Sit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. 12. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>. 108.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11931 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11932 In numbers, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>1</mn><mn>2</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>1</mn><mn>0</mn><mn>8</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11933 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11934 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11935 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11936 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11937 <s xml:id="echoid-s1383" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11938 Limites radicum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11939 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11940 Limits of the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11941 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11942 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11943 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11944 <pb file="add_6782_f414v" o="414v" n="829"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11945 <pb file="add_6782_f415" o="415" n="830"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11946 <div xml:id="echoid-div263" type="page_commentary" level="2" n="263">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11947 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11948 <s xml:id="echoid-s1384" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11949 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11950 <s xml:id="echoid-s1384" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11951 On this page Harriot begins a general treatment of equations of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11952 with no square term. To preserve dimensions, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math> is used as a placeholder for a general 3-dimensional quantity;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11953 similarly <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>d</mi></mstyle></math> is a placeholder for a 2-dimensional quantity, not necessarily a square.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11954 All coefficients are assumed to be positive.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11955 Equations of this kind have two positive roots or none at all, depending on the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11956 For Harriot's derivation of the canonical form for unequal roots, see Add MS 6783, f. 181.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11957 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11958 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11959 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11960 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11961 <head xml:id="echoid-head174" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11962 c.3.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11963 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11964 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11965 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11966 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11967 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11968 <s xml:id="echoid-s1386" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11969 prob. 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11970 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11971 Problem 17. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11972 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11973 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11974 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11975 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11976 <s xml:id="echoid-s1387" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11977 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11978 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11979 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11980 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11981 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11982 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11983 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11984 <s xml:id="echoid-s1388" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11985 Nam: Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>. erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>. Et ita est:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11986 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11987 For if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math> then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>b</mi><mi>b</mi></mstyle></math>; and so it is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11988 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11989 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11990 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11991 <s xml:id="echoid-s1389" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11992 Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>. erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>. est enim.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11993 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11994 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math> then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mi>c</mi><mo>-</mo><mi>c</mi><mi>c</mi><mi>c</mi></mstyle></math>; and indeed it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11995 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11996 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11997 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11998 <s xml:id="echoid-s1390" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	11999 est igitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12000 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12001 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12002 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12003 Therefore it is so, that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12004 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12005 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12006 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12007 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12008 <s xml:id="echoid-s1391" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12009 Species ad radices <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12010 æquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12011 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12012 The case of equal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12013 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12014 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12015 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12016 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12017 <s xml:id="echoid-s1392" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12018 si: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>d</mi><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12019 erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12020 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12021 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>d</mi><mi>d</mi></mstyle></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo>=</mo><mi>x</mi><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12022 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12023 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12024 If the cubic has two positive roots <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, then the third root must be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo><mi>b</mi><mo>-</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12025 Hence the product of the roots is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo><mo maxsize="1">(</mo><mi>b</mi><mi>b</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>c</mi><mi>c</mi><mo maxsize="1">)</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12026 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12027 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12028 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12029 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12030 <s xml:id="echoid-s1393" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12031 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math>. sunt continue <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12032 proportionalia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12033 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12034 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math>, are in continued proportion.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12035 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12036 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12037 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12038 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12039 <s xml:id="echoid-s1394" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12040 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, minor radix. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12041 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12042 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> the larger.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12043 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12044 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12045 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12046 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12047 <s xml:id="echoid-s1395" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12048 Ergo qualibet radix non <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12049 habet plures figuras <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12050 quam sunt in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>d</mi><mi>d</mi></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12051 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12052 Therefore whatever the root, it has no more figures than are in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mi>d</mi><mi>d</mi></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12053 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12054 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12055 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12056 <pb file="add_6782_f415v" o="415v" n="831"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12057 <pb file="add_6782_f416" o="416" n="832"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12058 <div xml:id="echoid-div264" type="page_commentary" level="2" n="264">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12059 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12060 <s xml:id="echoid-s1396" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12061 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12062 <s xml:id="echoid-s1396" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12063 On the previous page, Add MS 6782, f. 417, Harriot discussed equations of the general form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12064 On that page, as an example, he calculated limits for the two positive roots of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>9</mn><mn>2</mn><mn>6</mn><mn>1</mn><mo>=</mo><mn>3</mn><mn>7</mn><mn>0</mn><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12065 On this page he solves the same equation fully for both roots. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12066 The equation is taken from Problem 16 of Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12067 <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12068 Viète gave rules for the relationship between the two roots but did not explain how he had arrived at them.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12069 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12070 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12071 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12072 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12073 <head xml:id="echoid-head175" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12074 c.2.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12075 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12076 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12077 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12078 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12079 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12080 <s xml:id="echoid-s1398" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12081 prob. 16. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12082 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12083 Problem 16. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12084 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12085 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12086 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12087 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12088 <s xml:id="echoid-s1399" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12089 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12090 ad resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12091 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12092 Canonical form for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12093 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12094 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12095 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12096 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12097 <s xml:id="echoid-s1400" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12098 Resolutio, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12099 et eductio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12100 lateris minoris
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12101 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12102 Solution and extraction of the smaller root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12103 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12104 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12105 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12106 <s xml:id="echoid-s1401" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12107 Divisor
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12108 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12109 Divisor
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12110 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12111 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12112 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12113 <s xml:id="echoid-s1402" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12114 Ergo. 27. latus minus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12115 ergo: latus maius. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>7</mn><mn>0</mn><mo>-</mo><mn>2</mn><mn>7</mn><mo>=</mo><mn>3</mn><mn>4</mn><mn>3</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12116 vel: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>9</mn><mn>2</mn><mn>6</mn><mn>1</mn></mrow><mrow><mn>2</mn><mn>7</mn></mrow></mfrac><mo>=</mo><mn>3</mn><mn>4</mn><mn>3</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12117 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12118 Therefore 27 is the smaller root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12119 Therefore the larger root is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>7</mn><mn>0</mn><mo>-</mo><mn>2</mn><mn>7</mn><mo>=</mo><mn>3</mn><mn>4</mn><mn>3</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12120 or: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>9</mn><mn>2</mn><mn>6</mn><mn>1</mn></mrow><mrow><mn>2</mn><mn>7</mn></mrow></mfrac><mo>=</mo><mn>3</mn><mn>4</mn><mn>3</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12121 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12122 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12123 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12124 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12125 <s xml:id="echoid-s1403" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12126 Eductio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12127 lateris maioris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12128 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12129 Extraction of the larger root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12130 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12131 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12132 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12133 <s xml:id="echoid-s1404" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12134 Divisor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12135 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12136 Divisor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12137 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12138 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12139 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12140 <s xml:id="echoid-s1405" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12141 Divisor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12142 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12143 Divisor.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12144 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12145 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12146 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12147 <s xml:id="echoid-s1406" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12148 Ergo. latus maius. 343 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12149 ergo laus minor. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>7</mn><mn>0</mn><mo>-</mo><mn>3</mn><mn>4</mn><mn>3</mn><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12150 vel. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>9</mn><mn>2</mn><mn>6</mn><mn>1</mn></mrow><mrow><mn>3</mn><mn>4</mn><mn>3</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12151 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12152 Therefore the greater root is 343. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12153 therefore the smaller root is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>7</mn><mn>0</mn><mo>-</mo><mn>3</mn><mn>4</mn><mn>3</mn><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12154 or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>9</mn><mn>2</mn><mn>6</mn><mn>1</mn></mrow><mrow><mn>3</mn><mn>4</mn><mn>3</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12155 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12156 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12157 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12158 <pb file="add_6782_f416v" o="416v" n="833"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12159 <pb file="add_6782_f417" o="417" n="834"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12160 <div xml:id="echoid-div265" type="page_commentary" level="2" n="265">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12161 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12162 <s xml:id="echoid-s1407" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12163 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12164 <s xml:id="echoid-s1407" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12165 This is the first of a set of 18 pages on extracting roots of avulsed equations,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12166 that is, equations containing three terms, in which the term of highest degree is subtracted
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12167 (torn away, or 'avulsed') from the term of next higest degree.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12168 Such equations have two positive roots. It is therefore important to know the relative sizes of the roots
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12169 before beginning extraction by numerical methods. This is the problem Harriot investigates in this section. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12170 The work is closely based on Problems 16 to 20 in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12171 Viète, <emph style="it">De numerosa potestatum ad exegesin resolutione</emph>, 1600.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12172 Viète gave rules for finding the second positive root once the first is known, but without explanation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12173 In this section, Harriot fills in the missing details, showing how the two positive roots
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12174 are related to the coefficients of the original equation and to each other. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12175 For a general explanation of the method of extraction see Add MS 6782, f. 399.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12176 For further discussion see See Stedall 2003, 87–123 and 294, and Stedall 2011, 29–33. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12177 This first page of Section c is transcribed in full, but for subsequent pages,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12178 only phrases and sentences are transcribed, not the calculations or the single words used in them. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12179 For another version of the first page see Add MS 6783, f. 62v, f. 62. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12180 For Harriot's derivation of the canonical form for unequal roots, see Add MS 6783, f. 183.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12181 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12182 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12183 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12184 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12185 <head xml:id="echoid-head176" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12186 c.1.) De numerosa potestatum resolutione.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12187 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12188 On the numerical resolution of powers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12189 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12190 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12191 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12192 <s xml:id="echoid-s1409" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12193 prob. 16. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, duplex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12194 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12195 Problem 16. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12196 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12197 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12198 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12199 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12200 <s xml:id="echoid-s1410" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12201 Species canonica <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12202 ad radices inæquales.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12203 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12204 Canonical form for unequal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12205 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12206 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12207 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12208 <s xml:id="echoid-s1411" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12209 Nam: Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>. erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>b</mi></mstyle></math>. et ita est.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12210 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12211 For if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math> then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo>-</mo><mi>b</mi><mi>b</mi></mstyle></math>; and so it is.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12212 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12213 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12214 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12215 <s xml:id="echoid-s1412" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12216 Si, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>. erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>-</mo><mi>c</mi><mi>c</mi></mstyle></math>. est enim.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12217 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12218 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>=</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi><mo>-</mo><mi>c</mi><mi>c</mi></mstyle></math>; indeed it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12219 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12220 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12221 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12222 <s xml:id="echoid-s1413" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12223 est igitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12224 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12225 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12226 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12227 therefore it is so, that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12228 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12229 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12230 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12231 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12232 <s xml:id="echoid-s1414" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12233 Species ad radices <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12234 æquales. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>=</mo><mi>b</mi><mi>a</mi><mo>+</mo><mi>b</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12235 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12236 Canonical form for equal roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12237 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12238 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12239 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12240 <s xml:id="echoid-s1415" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12241 Vel: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>=</mo><mn>2</mn><mi>b</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12242 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12243 Or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>=</mo><mn>2</mn><mi>b</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12244 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12245 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12246 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12247 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12248 <s xml:id="echoid-s1416" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12249 si: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12250 erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12251 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12252 if: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12253 then: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi><mo>=</mo><mi>x</mi><mi>z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12254 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12255 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12256 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12257 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12258 <s xml:id="echoid-s1417" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12259 Sunt in ratione inæqualitatis: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12260 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12261 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12262 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, be in unequal ratio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12263 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12264 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12265 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12266 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12267 <s xml:id="echoid-s1418" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12268 sit, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> radix minor. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>, maior. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12269 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>b</mi><mo><</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo><</mo><mn>2</mn><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12270 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo><</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12271 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><mfrac><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo><</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12272 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12273 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> the larger. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12274 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mi>b</mi><mo><</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo><</mo><mn>2</mn><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12275 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo><</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12276 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><mfrac><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo><</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12277 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12278 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12279 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12280 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12281 <s xml:id="echoid-s1419" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12282 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo><</mo><mi>b</mi><mi>c</mi><mo><</mo><mi>c</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12283 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><msqrt><mrow><mi>b</mi><mi>c</mi></mrow></msqrt><mo><</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12284 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><msqrt><mrow><mi>x</mi><mi>z</mi></mrow></msqrt><mo><</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12285 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12286 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo><</mo><mi>b</mi><mi>c</mi><mo><</mo><mi>c</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12287 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><msqrt><mrow><mi>b</mi><mi>c</mi></mrow></msqrt><mo><</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12288 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><msqrt><mrow><mi>x</mi><mi>z</mi></mrow></msqrt><mo><</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12289 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12290 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12291 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12292 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12293 <s xml:id="echoid-s1420" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12294 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mn>2</mn><mo>,</mo><mi>x</mi><mi>z</mi><mo>:</mo><mn>1</mn><mo>,</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mi>z</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12295 Dico quod: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mi>z</mi></mrow><mrow><mi>d</mi></mrow></mfrac><mo><</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12296 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>d</mi><mo><</mo><mn>2</mn><mo>,</mo><mi>x</mi><mi>z</mi><mo><</mo><mi>c</mi><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12297 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo><</mo><mn>2</mn><mi>b</mi><mi>c</mi><mo><</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12298 est enim. est igitur
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12299 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12300 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>:</mo><mn>2</mn><mi>x</mi><mi>z</mi><mo>=</mo><mn>1</mn><mo>:</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mi>z</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12301 I say that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo><</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mi>z</mi></mrow><mrow><mi>d</mi></mrow></mfrac><mo><</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12302 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>d</mi><mo><</mo><mn>2</mn><mi>x</mi><mi>z</mi><mo><</mo><mi>c</mi><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12303 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo><</mo><mn>2</mn><mi>b</mi><mi>c</mi><mo><</mo><mi>b</mi><mi>c</mi><mo>+</mo><mi>c</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12304 indeed it is; therefore it is so.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12305 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12306 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12307 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12308 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12309 <s xml:id="echoid-s1421" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12310 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12311 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>a</mi><mo>></mo><mi>a</mi><mi>a</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12312 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>></mo><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12313 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12314 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>d</mi><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12315 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>a</mi><mo>></mo><mi>a</mi><mi>a</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12316 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>></mo><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12317 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12318 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12319 <s xml:id="echoid-s1422" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12320 Hoc est qualibet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12321 radice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12322 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12323 This is so whatever the root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12324 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12325 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12326 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12327 <s xml:id="echoid-s1423" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12328 Ergo [???] radix habet plures <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12329 figuras quam sunt in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12330 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12331 Therefore the [???] root has more figures than are in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12332 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12333 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12334 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12335 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12336 <s xml:id="echoid-s1424" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12337 Si una radix sit nota: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12338 altera erit cognita.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12339 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12340 If one root is known, the other will be known.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12341 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12342 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12343 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12344 <s xml:id="echoid-s1425" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12345 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> nota. quæratur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12346 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12347 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> is sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12348 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12349 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12350 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12351 <s xml:id="echoid-s1426" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12352 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12353 ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>b</mi><mo>=</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12354 vel: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12355 ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>x</mi><mi>z</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12356 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12357 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12358 therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>b</mi><mo>=</mo><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12359 or: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi><mo>=</mo><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12360 therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>x</mi><mi>z</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12361 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12362 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12363 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12364 <s xml:id="echoid-s1427" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12365 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> nota. quæratur, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12366 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>c</mi><mo>=</mo><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12367 et: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>x</mi><mi>z</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>=</mo><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12368 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12369 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> be known, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is sought. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12370 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>c</mi><mo>=</mo><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12371 and: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>x</mi><mi>z</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>=</mo><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12372 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12373 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12374 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12375 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12376 <s xml:id="echoid-s1428" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12377 Pro exemplo ad resolutionem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12378 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12379 According to this example for the solution.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12380 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12381 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12382 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12383 <s xml:id="echoid-s1429" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12384 In numeris sit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. 27. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> 343.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12385 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12386 In numbers, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>=</mo><mn>2</mn><mn>7</mn></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mo>=</mo><mn>3</mn><mn>4</mn><mn>3</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12387 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12388 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12389 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12390 <s xml:id="echoid-s1430" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12391 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>7</mn><mo>×</mo><mn>3</mn><mn>4</mn><mn>3</mn><mo>=</mo><mn>2</mn><mn>7</mn><mo>,</mo><mi>a</mi><mo>+</mo><mn>3</mn><mn>4</mn><mn>3</mn><mo>,</mo><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12392 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>9</mn><mn>2</mn><mn>6</mn><mn>1</mn><mo>=</mo><mn>3</mn><mn>7</mn><mn>0</mn><mo>,</mo><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12393 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12394 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mn>7</mn><mo>×</mo><mn>3</mn><mn>4</mn><mn>3</mn><mo>=</mo><mn>2</mn><mn>7</mn><mi>a</mi><mo>+</mo><mn>3</mn><mn>4</mn><mn>3</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12395 That is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>9</mn><mn>2</mn><mn>6</mn><mn>1</mn><mo>=</mo><mn>3</mn><mn>7</mn><mn>0</mn><mi>a</mi><mo>-</mo><mi>a</mi><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12396 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12397 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12398 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12399 <s xml:id="echoid-s1431" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12400 Limites radicum ex præcedentibus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12401 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12402 The limits of the roots from what has gone before.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12403 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12404 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12405 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12406 <pb file="add_6782_f417v" o="417v" n="835"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12407 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12408 <s xml:id="echoid-s1432" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12409 Johan Dycker <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12410 Johan
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12411 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12412 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12413 <pb file="add_6782_f418" o="418" n="836"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12414 <pb file="add_6782_f418v" o="418v" n="837"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12415 <pb file="add_6782_f419" o="419" n="838"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12416 <div xml:id="echoid-div266" type="page_commentary" level="2" n="266">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12417 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12418 <s xml:id="echoid-s1433" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12419 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12420 <s xml:id="echoid-s1433" xml:space="preserve">The referenceon this page is to Proposition 15 from Chapter 19 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12421 <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12422 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12423 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12424 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12425 XV. Datis tribus lateribus, dantur anguli.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12426 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12427 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12428 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12429 Given three sides, the angles are given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12430 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12431 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12432 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12433 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12434 <head xml:id="echoid-head177" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12435 Lemmata quædam <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12436 ad praxin prop. 15 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12437 Vieta lib. resp. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12438 pag. 35
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12439 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12440 Certain lemmas for carrying out Proposition 15, Viète, Responsorum liber VIII, page 35.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12441 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12442 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12443 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12444 <s xml:id="echoid-s1435" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12445 1. Duæ peripheriæ sigillatim minores quadranti, et earum complementa: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12446 æqualem habent differentiam. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12447 sint duæ peripheriæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, differentia <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12448 complementa earum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>o</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>o</mi></mstyle></math>, differentia etiam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12449 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12450 1. Two arcs each less than a quadrant, and their complements, have equal differences. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12451 Let the two arcs be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> abd <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, with difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12452 Their complements are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>o</mi></mstyle></math> adn <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>o</mi></mstyle></math>, also with difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12453 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12454 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12455 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12456 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12457 <s xml:id="echoid-s1436" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12458 2. Complementa aggregati duarum peripheriarum sigillatim minorum quadranti; et <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12459 aggregatum illarum complementorum: sunt æqualia. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12460 aggregatum ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math>. complementum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12461 complementum peripheriæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, est <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>o</mi></mstyle></math>, hoc est <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12462 complementum peripheriæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, est <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12463 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>o</mi><mo>+</mo><mi>o</mi><mi>c</mi></mstyle></math> est aggregatum complementorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12464 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>c</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>i</mi></mstyle></math> sunt æquales. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12465 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>o</mi><mi>d</mi></mstyle></math> est aggregatum complementorum et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>d</mi></mstyle></math> complementum aggregat.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12466 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12467 2. The complements of the sum of two arcs each less than a quadrant,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12468 and the sum of those complements, are equal. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12469 Therefore if the sum is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math> the complement is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12470 The complement of the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>o</mi></mstyle></math>, that is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12471 The complement of the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12472 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>o</mi><mo>+</mo><mi>o</mi><mi>c</mi></mstyle></math> is the sum of the complements. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12473 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>c</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>i</mi></mstyle></math> are equal. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12474 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>o</mi><mo>+</mo><mi>o</mi><mi>c</mi></mstyle></math> is the sum of the complements. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12475 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>c</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>i</mi></mstyle></math> are equal. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12476 Therfore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>o</mi><mi>d</mi></mstyle></math> is the sum of the coplements and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>d</mi></mstyle></math> is the complement of the sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12477 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12478 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12479 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12480 <pb file="add_6782_f419v" o="419v" n="839"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12481 <pb file="add_6782_f420" o="420" n="840"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12482 <div xml:id="echoid-div267" type="page_commentary" level="2" n="267">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12483 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12484 <s xml:id="echoid-s1437" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12485 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12486 <s xml:id="echoid-s1437" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12487 This page continues Harriot's work from Add MS 6787, f. 61, and Add MS 782, f. 422.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12488 on Viète's statement of 'Syntomon'. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12489 The third case is where one angle is greater than a right angle, the other less.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12490 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12491 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12492 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12493 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12494 <head xml:id="echoid-head178" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12495 <foreign xml:lang="gre">Syntomon</foreign> Secundo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12496 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12497 Syntomon, third case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12498 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12499 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12500 <pb file="add_6782_f420v" o="420v" n="841"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12501 <pb file="add_6782_f421" o="421" n="842"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12502 <div xml:id="echoid-div268" type="page_commentary" level="2" n="268">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12503 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12504 <s xml:id="echoid-s1439" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12505 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12506 <s xml:id="echoid-s1439" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12507 This page continues Harriot's work from Add MS 6787, f. 61,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12508 on Viète's statement of 'Syntomon'. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12509 The second case is where both angles are greater than a right angle.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12510 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12511 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12512 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12513 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12514 <head xml:id="echoid-head179" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12515 Vieta lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12516 pag. 39. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12517 <foreign xml:lang="gre">Syntomon</foreign> Secundo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12518 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12519 Viète, Responsorum liber VIII, page 39, Syntomon, second case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12520 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12521 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12522 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12523 <s xml:id="echoid-s1441" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12524 Interpretatio. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12525 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> una peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12526 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> altera <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12527 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>d</mi><mo>=</mo><mi>a</mi><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12528 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>d</mi></mstyle></math> differentia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12529 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12530 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12531 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12532 <s xml:id="echoid-s1442" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12533 1. Si duo rectangula fuerint sigillatim applicata ad <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12534 2. sinum totum; unum, <emph style="super">*</emph> <emph style="ul">duorum sinum</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12535 quorum utraque peripheriæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12536 sunt quadranti minores; alterum <emph style="super">+</emph> <emph style="ul">Maiorem periphe-</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12537 <emph style="ul">riæ sinum</emph> complementarum: Duæ latitudines <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12538 oriundæ component sinum complementi differentiæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12539 peripheriarum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12540 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12541 1, 2. If two rectangles are each applied to the whole sine,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12542 one <emph style="super">*</emph>of two sines, of which either arc is less than the quadrant,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12543 the other <emph style="super">+</emph> greater than the sine of the complement of the arc,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12544 then the two latitudes arising are composed of the sine of the complement of the differences of the arcs.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12545 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12546 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12547 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12548 <s xml:id="echoid-s1443" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12549 * sub duobus sinibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12550 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12551 * under two sines
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12552 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12553 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12554 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12555 <s xml:id="echoid-s1444" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12556 + sub illarum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12557 sinibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12558 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12559 under the sines of them
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12560 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12561 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12562 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12563 <s xml:id="echoid-s1445" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12564 3. Si duo rectangula fuerint sigillatimm applicata ad <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12565 4. sinum totum; unum, <emph style="super">*</emph> <emph style="ul">duorum sinum</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12566 quorum peripheriæ sunt <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12567 affectionis inter se diversæ; alterum, <emph style="ul">illarum peripheriæ</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12568 <emph style="ul">sinum</emph> complementarum: Duæ latitudines oriundæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12569 component sinum complementi aggregati peripheriæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12570 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12571 3, 4. If two rectangles are each applied to the whole sine,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12572 one <emph style="super">*</emph>of two sines, of which the relationship to the arc is different,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12573 the other the complements of the sines of those arcs,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12574 then the two latitudes arising are composed of the sine of the complement of the sum of the arcs.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12575 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12576 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12577 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12578 <pb file="add_6782_f421v" o="421v" n="843"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12579 <pb file="add_6782_f422" o="422" n="844"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12580 <div xml:id="echoid-div269" type="page_commentary" level="2" n="269">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12581 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12582 <s xml:id="echoid-s1446" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12583 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12584 <s xml:id="echoid-s1446" xml:space="preserve">The reference on this page is to Proposition 20 from Chapter 19 of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12585 <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12586 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12587 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12588 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12589 XX. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12590 Trianguli cujuslibet sphærici. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12591 Datis angulis duobus, & latere quod iis adjacent, datur angulus reliquus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12592 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12593 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12594 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12595 Given two angles and the side adjacent to them, the other angle is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12596 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12597 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12598 <s xml:id="echoid-s1447" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12599 Viète described four possible cases for this proposition; Harriot claims that he has missed some.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12600 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12601 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12602 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12603 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12604 <head xml:id="echoid-head180" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12605 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12606 pag. 38. b. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12607 Triangula ambigua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12608 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12609 Viète, Responsorum liber VIII, page 38v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12610 Ambiguous triangles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12611 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12612 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12613 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12614 <s xml:id="echoid-s1449" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12615 Iisdem positis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12616 Quadrati etiam: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12617 duo casus omissi a Vieta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12618 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12619 The same things being supposed, the quadrants are also: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12620 Two cases missed by Viète.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12621 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12622 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12623 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12624 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12625 <s xml:id="echoid-s1450" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12626 Inde <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12627 Habendis angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12628 [???] duorum reliquorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12629 angulorum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12630 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12631 Having the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, hence the other two angles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12632 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12633 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12634 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12635 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12636 <s xml:id="echoid-s1451" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12637 Quadranti etiam: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12638 duo casus omissi a Vieta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12639 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12640 The quadrants are also: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12641 Two cases missed by Viète.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12642 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12643 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12644 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12645 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12646 <s xml:id="echoid-s1452" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12647 Nota <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12648 Obliangulorum sphæricorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12649 duodecim sunt [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12650 quarum per perficuntu per <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12651 syntomon et [???] <emph style="st">operatione</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12652 [etc.]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12653 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12654 1. Two arcs each less tham a quadrant, and their complements, have equal differences. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12655 Let the two arcs be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, with difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12656 Their complements are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>o</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>o</mi></mstyle></math>, also with difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12657 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12658 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12659 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12660 <pb file="add_6782_f422v" o="422v" n="845"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12661 <pb file="add_6782_f423" o="423" n="846"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12662 <pb file="add_6782_f423v" o="423v" n="847"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12663 <pb file="add_6782_f424" o="424" n="848"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12664 <div xml:id="echoid-div270" type="page_commentary" level="2" n="270">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12665 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12666 <s xml:id="echoid-s1453" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12667 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12668 <s xml:id="echoid-s1453" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12669 Further work on the '<foreign xml:lang="gre">Eis procheiron scholia</foreign>, which follows Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12670 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12671 In the 1646 edition of Viete's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12672 the triangle referred to here is to be found on page 423.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12673 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12674 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12675 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12676 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12677 <head xml:id="echoid-head181" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12678 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12679 pag. 43. b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12680 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12681 Viète, Responsorum liber VIII, page 43v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12682 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12683 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12684 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12685 <s xml:id="echoid-s1455" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12686 Nota <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12687 Ergo datis 2<emph style="super">bus</emph> lateribuset angulo complemento <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12688 datur latus oppositum copendiose.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12689 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12690 Note <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12691 Therefore given the two sides and the complement of the angle, the opposite side is given more briefly.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12692 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12693 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12694 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12695 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12696 <s xml:id="echoid-s1456" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12697 See the papers of sines <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12698 proportionall.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12699 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12700 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12701 <pb file="add_6782_f424v" o="424v" n="849"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12702 <pb file="add_6782_f425" o="425" n="850"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12703 <pb file="add_6782_f425v" o="425v" n="851"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12704 <pb file="add_6782_f426" o="426" n="852"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12705 <div xml:id="echoid-div271" type="page_commentary" level="2" n="271">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12706 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12707 <s xml:id="echoid-s1457" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12708 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12709 <s xml:id="echoid-s1457" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12710 Further work on the '<foreign xml:lang="gre">Eis procheiron scholia</foreign>, which follows Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12711 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12712 In the 1646 edition of Viete's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12713 the triangle referred to here is to be found on page 423.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12714 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12715 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12716 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12717 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12718 <head xml:id="echoid-head182" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12719 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12720 pag. 43. b. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12721 1. Datis tribus lateribis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12722 quæritur angulus A.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12723 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12724 Viète, Responsorum liber VIII, page 43v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12725 Given three sides, there is sought angle A.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12726 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12727 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12728 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12729 <s xml:id="echoid-s1459" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12730 Analogia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12731 Vide syntomon 2<emph style="super">o</emph>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12732 Angulus quæsitis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12733 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12734 Ratio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12735 See syntomon 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12736 Angle sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12737 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12738 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12739 The second case of syntomon can be found on Add MS 6782, f. 421.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12740 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12741 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12742 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12743 <pb file="add_6782_f426v" o="426v" n="853"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12744 <pb file="add_6782_f427" o="427" n="854"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12745 <div xml:id="echoid-div272" type="page_commentary" level="2" n="272">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12746 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12747 <s xml:id="echoid-s1460" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12748 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12749 <s xml:id="echoid-s1460" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12750 Further work on the '<foreign xml:lang="gre">Eis procheiron scholia</foreign>, which follows Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12751 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12752 In the 1646 edition of Viete's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12753 the triangle referred to here is to be found on page 423.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12754 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12755 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12756 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12757 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12758 <head xml:id="echoid-head183" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12759 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12760 pag. 43. b. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12761 1. Datis tribus lateribis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12762 quæritur angulus D.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12763 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12764 Viète, Responsorum liber VIII, page 43v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12765 Given three sides, there is sought angle D.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12766 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12767 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12768 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12769 <s xml:id="echoid-s1462" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12770 Analogia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12771 Vide syntomon 2<emph style="super">o</emph>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12772 Angulus quæsitis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12773 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12774 Ratio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12775 See syntomon 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12776 Angle sought.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12777 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12778 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12779 The second case of syntomon can be found on Add MS 6782, f. 421.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12780 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12781 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12782 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12783 <pb file="add_6782_f427v" o="427v" n="855"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12784 <pb file="add_6782_f428" o="428" n="856"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12785 <div xml:id="echoid-div273" type="page_commentary" level="2" n="273">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12786 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12787 <s xml:id="echoid-s1463" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12788 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12789 <s xml:id="echoid-s1463" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12790 Further work on the '<foreign xml:lang="gre">Eis procheiron scholia</foreign>, which follows Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12791 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12792 In the 1646 edition of Viete's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12793 the triangle referred to here is to be found on page 423.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12794 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12795 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12796 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12797 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12798 <head xml:id="echoid-head184" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12799 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12800 pag. 43. b. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12801 1. Datis tribus lateribis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12802 quæritur angulus B.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12803 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12804 Viète, Responsorum liber VIII, page 43v. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12805 Given three sides, there is sought angle B.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12806 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12807 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12808 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12809 <s xml:id="echoid-s1465" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12810 Analogia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12811 numeratio in alia charta.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12812 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12813 Ratio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12814 Enumeration in the other sheet.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12815 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12816 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12817 The other sheet referred to here is probably Add MS 6782, f. 433.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12818 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12819 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12820 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12821 <pb file="add_6782_f428v" o="428v" n="857"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12822 <pb file="add_6782_f429" o="429" n="858"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12823 <div xml:id="echoid-div274" type="page_commentary" level="2" n="274">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12824 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12825 <s xml:id="echoid-s1466" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12826 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12827 <s xml:id="echoid-s1466" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12828 Further work on the '<foreign xml:lang="gre">Eis procheiron scholia</foreign>, which follows Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12829 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12830 In the 1646 edition of Viete's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12831 the triangle referred to here is to be found on page 423.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12832 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12833 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12834 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12835 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12836 <head xml:id="echoid-head185" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12837 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12838 pag. 43. b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12839 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12840 Viète, Responsorum liber VIII, page 43v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12841 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12842 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12843 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12844 <s xml:id="echoid-s1468" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12845 Menda in Vieta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12846 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12847 Wrong in Viète
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12848 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12849 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12850 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12851 <pb file="add_6782_f429v" o="429v" n="859"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12852 <pb file="add_6782_f430" o="430" n="860"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12853 <div xml:id="echoid-div275" type="page_commentary" level="2" n="275">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12854 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12855 <s xml:id="echoid-s1469" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12856 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12857 <s xml:id="echoid-s1469" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12858 The reference to Fink is to <emph style="it">Geometriae rotundi libri XIIII</emph> (1583), page 364.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12859 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12860 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12861 <s xml:id="echoid-s1470" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12862 The reference to Regiomontanus to <emph style="it">De triangulis omnimodis libri quinque</emph> ([1464], 1533, 1561),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12863 Book V, Proposition 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12864 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12865 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12866 <s xml:id="echoid-s1471" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12867 The reference to Viète is to the 'ALIUD' in Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12868 <emph style="it">Variorum resposorum liber VIII</emph>, Proposition 13.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12869 See Add MS 6787, f. 223.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12870 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12871 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12872 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12873 13 Vt rectangulum quod sit sub sinu toto & transsinuosa prima ad id quod sit
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12874 sub transsinuosa secunda & transsinuosa tertia, ita quod sit sub sinu complementi secundæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12875 & sinu complementi tertiæ ad id quod sit sub sinu toto & sinu complemnti primæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12876 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12877 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12878 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12879 As the product of the while sine and the secant of the first to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12880 that of the secant of the second and the secant of the third,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12881 so is that of the sine of the complement of the second and the sine of the complement of the third
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12882 to that of the whole sine and the sine of the complement of the first.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12883 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12884 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12885 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12886 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12887 <head xml:id="echoid-head186" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12888 Finkius in Geomet. rotundi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12889 lib. 14, 6. pag. 364. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12890 Regiom. lib.5.p.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12891 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12892 Fink in Geometria rotundi, Book XIV.6, page 364. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12893 Regiomontanus, Book V.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12894 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12895 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12896 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12897 <s xml:id="echoid-s1473" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12898 Utilis propositio: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12899 ad indagendum angulum inclinationis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12900 circuli alicuius planetæ vel cometæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12901 et ad alia.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12902 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12903 A useful proposition for delivering the angle of inclination of a circle of any planet or comet, and for other things.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12904 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12905 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12906 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12907 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12908 <s xml:id="echoid-s1474" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12909 In duobus triangulis rectangulis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12910 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>o</mi><mi>u</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>e</mi><mi>i</mi></mstyle></math>: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12911 Dantur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12912 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>o</mi></mstyle></math>. latitudo plaentæ una <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12913 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>e</mi></mstyle></math>. latitudo altera <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12914 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>e</mi></mstyle></math>. differentia longitudinum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12915 in duobus locis. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12916 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>i</mi></mstyle></math> datur ex consqequentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12917 et est arcus circuli <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12918 planetæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12919 Quæritur angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12920 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12921 In two right-angled triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>o</mi><mi>u</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>e</mi><mi>i</mi></mstyle></math>, there are given: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12922 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>o</mi></mstyle></math>, the latitude of one planet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12923 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>e</mi></mstyle></math>, the latitude of the other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12924 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>e</mi></mstyle></math>, the difference in longitude of the two locations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12925 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>i</mi></mstyle></math> is consequently given, and is the arc of a circle of a planet. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12926 There is sought angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>.</emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12927 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12928 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12929 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12930 <s xml:id="echoid-s1475" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12931 Inde per Finkium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12932 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12933 Quas Analogias deduxit ex superioribus ita: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12934 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12935 Sed ita nullum compendium oritur, igitur inutilis commutatio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12936 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12937 Thus by Fink. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12938 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12939 Whcih ratios one deduces from the above, thus: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12940 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12941 But in this way nothing shorter arises, therefore the change is not useful.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12942 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12943 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12944 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12945 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12946 <s xml:id="echoid-s1476" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12947 Utile compendium ita fit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12948 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12949 Latitudo, inventa <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12950 per syntomon.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12951 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12952 It may usefully be done more briefly thus: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12953 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12954 The latitude is found by syntomon.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12955 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12956 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12957 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12958 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12959 <s xml:id="echoid-s1477" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12960 vel per 13p. vieta lib. 8. resp. pag. 37. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12961 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12962 Hoc est:<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12963 latitudo inventa <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12964 + proportione <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12965 Hæc mutatio ergo inutilis: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12966 vel hæc melior quam <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12967 illa Finkij vel originis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12968 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12969 or by Proposition 13 of Viète, Responsorum liber VIII, page 37, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12970 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12971 That is:<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12972 the latitude found, and the proportion <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12973 This change is therefore not useful; or this is better than that of Fink or the original.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12974 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12975 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12976 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12977 <pb file="add_6782_f430v" o="430v" n="861"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12978 <pb file="add_6782_f431" o="431" n="862"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12979 <pb file="add_6782_f431v" o="431v" n="863"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12980 <pb file="add_6782_f432" o="432" n="864"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12981 <div xml:id="echoid-div276" type="page_commentary" level="2" n="276">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12982 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12983 <s xml:id="echoid-s1478" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12984 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12985 <s xml:id="echoid-s1478" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12986 Further work on the '<foreign xml:lang="gre">Eis procheiron scholia</foreign>, which follows Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12987 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12988 In the 1646 edition of Viete's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12989 a diagram realting to these figures is to be found on page 426.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12990 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12991 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12992 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12993 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12994 <head xml:id="echoid-head187" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12995 Vieta. pag. 45. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12996 resp. lib. 8.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12997 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12998 Viète, page 45, Responsorum liber VIII, page 43.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	12999 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13000 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13001 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13002 <s xml:id="echoid-s1480" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13003 Anguli obliquanguli <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13004 trianguli sphæricæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13005 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13006 Oblique-angled spherical triangles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13007 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13008 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13009 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13010 <pb file="add_6782_f432v" o="432v" n="865"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13011 <pb file="add_6782_f433" o="433" n="866"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13012 <div xml:id="echoid-div277" type="page_commentary" level="2" n="277">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13013 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13014 <s xml:id="echoid-s1481" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13015 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13016 <s xml:id="echoid-s1481" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13017 Further work on the '<foreign xml:lang="gre">Eis procheiron scholia</foreign>, which follows Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13018 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13019 In the 1646 edition of Viete's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13020 the triangles referred to here are to be found on pages 422 and 423.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13021 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13022 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13023 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13024 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13025 <head xml:id="echoid-head188" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13026 Vieta. rep. lib. 8 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13027 pag. 43. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13028 Anguli, rectanguli trianguli sphæricæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13029 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13030 Viète, Responsorum liber VIII, page 43. Angles, in right-angled spherical triangles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13031 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13032 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13033 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13034 <s xml:id="echoid-s1483" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13035 omnes combinationes faciunt trianguli. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13036 sunt quatuor tantum quia unus est 90.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13037 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13038 all combinatins make triangles; there are four such because one is 90.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13039 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13040 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13041 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13042 <head xml:id="echoid-head189" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13043 pag. 44. Anguli obliquianguli
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13044 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13045 page 44. Oblique angles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13046 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13047 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13048 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13049 <s xml:id="echoid-s1484" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13050 Nullam earum combinationium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13051 faciunt trainguli. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13052 Accipi igitur complementum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13053 ut facit Vieta. ita:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13054 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13055 None of these combinations makes a triangle. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13056 Therefore accept the complememnt of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> as Viète does, thus:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13057 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13058 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13059 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13060 <pb file="add_6782_f433v" o="433v" n="867"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13061 <pb file="add_6782_f434" o="434" n="868"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13062 <pb file="add_6782_f434v" o="434v" n="869"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13063 <pb file="add_6782_f435" o="435" n="870"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13064 <div xml:id="echoid-div278" type="page_commentary" level="2" n="278">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13065 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13066 <s xml:id="echoid-s1485" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13067 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13068 <s xml:id="echoid-s1485" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13069 The text referred to here is Johan Philip Lansberg,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13070 <emph style="it">Triangulorum geometriae libri quatuor</emph> (1591).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13071 Page 201 contains Lansberg's rule for finding a side of a spherical triangles, given its angles.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13072 See Add MS 6787, f. 197.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13073 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13074 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13075 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13076 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13077 <head xml:id="echoid-head190" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13078 Erallage pleuroniniche
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13079 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13080 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13081 <s xml:id="echoid-s1487" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13082 Lansberg. pag. 201. Demonstratio originis falsa est: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13083 Regularum aliquando
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13084 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13085 Lansberg, page 201. The original demonstration is false for some rules.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13086 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13087 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13088 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13089 <pb file="add_6782_f435v" o="435v" n="871"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13090 <pb file="add_6782_f436" o="436" n="872"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13091 <pb file="add_6782_f436v" o="436v" n="873"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13092 <pb file="add_6782_f437" o="437" n="874"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13093 <pb file="add_6782_f437v" o="437v" n="875"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13094 <pb file="add_6782_f438" o="438" n="876"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13095 <div xml:id="echoid-div279" type="page_commentary" level="2" n="279">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13096 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13097 <s xml:id="echoid-s1488" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13098 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13099 <s xml:id="echoid-s1488" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13100 A continuation of Harriot's work on the 'Dati sexti', from Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13101 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13102 Here he examines Proposition VI.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13103 The word 'parapompe' was originally used by Viète to describe each proposition. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13104 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13105 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13106 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13107 VII. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13108 Data summa vel differentia duarum perpheriarum, quarum prosinus datam habeant rationem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13109 dantur singulæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13110 1 Enimvero si utraque peripheria proponatur minor quadrante, vel utraque major. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13111 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13112 Vt adgregatum similium prosinuum ad differentiam eorundem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13113 ita sinus summæ peripheriarum ad sinuum differentiæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13114 Vel ita transsinuosa complementi differentiæ ad transsinuosam complementi summæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13115 2 Quod si una e peripheriis proponatur minor quadrante, altera maior, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13116 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13117 Vt adgregatum prosinuum ad differentiam eorundem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13118 ita sinus differentiæ peripheriarum ad sinum adgregati,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13119 Vel ita transsinuosa complementi summæ ad transsinuosam complementi differentiæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13120 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13121 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13122 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13123 VII. Given the sum or difference of two arcs, whose tangents are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13124 1. If both given arcs are less than a quadrant, or both greater,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13125 then as the sum of the tangents is to their difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13126 so is the sine of the sum of the arcs to the sine of their difference. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13127 Or as the secant of the complement of the difference to the secant of the complement of the sum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13128 2. But if one of the given arcs is less than a quadrant, the other greater,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13129 then as the sum of the tangents is to their difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13130 so is the sine of the difference of the arcs to the sine of the sum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13131 Or as the secant of the complement of the sum to the secant of the complement of the difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13132 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13133 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13134 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13135 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13136 <head xml:id="echoid-head191" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13137 Vieta. 37.b. lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13138 <foreign xml:lang="gre">parapompe</foreign> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13139 Dati Septimi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13140 Data summa vel differentia duarum peripheriarum, Â <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13141 et ratione O.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13142 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13143 Viète, page 37v, Responsorum liber VIII. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13144 Parapompe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13145 Seventh proposition. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13146 Given the sum or difference of two arcs and the ratio of their tangents.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13147 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13148 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13149 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13150 <s xml:id="echoid-s1490" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13151 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13152 utraque minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13153 quadrante
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13154 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13155 1. both less than a quadrant
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13156 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13157 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13158 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13159 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13160 <s xml:id="echoid-s1491" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13161 Interpetatio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13162 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, una peripheria, minor quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13163 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, altera peripheria minor quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13164 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi><mo>=</mo><mi>b</mi><mi>a</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13165 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>c</mi></mstyle></math>, differentia peripheriæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13166 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>d</mi></mstyle></math>, tangens <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13167 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math>, tangens <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13168 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>f</mi></mstyle></math>, differentia tangentium. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13169 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi></mstyle></math>, sinus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13170 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>l</mi></mstyle></math>, sinus differentiæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13171 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13172 Interpetation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13173 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, one arc, less than a quadrant. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13174 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, the other arc, less than a quadrant. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13175 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi><mo>=</mo><mi>b</mi><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13176 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>c</mi></mstyle></math>, the difference of the arcs. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13177 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>d</mi></mstyle></math>, tangent to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13178 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math>, tangento <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13179 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>f</mi></mstyle></math>, the difference of the tangents. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13180 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi></mstyle></math>, sine of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13181 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>l</mi></mstyle></math>, sine of the difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13182 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13183 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13184 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13185 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13186 <s xml:id="echoid-s1492" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13187 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13188 una maior
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13189 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13190 2. one greater
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13191 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13192 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13193 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13194 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13195 <s xml:id="echoid-s1493" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13196 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> peripheria maior quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13197 cætera ut supra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13198 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13199 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> is an arc greater than a quadrant; <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13200 the rest is as above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13201 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13202 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13203 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13204 <pb file="add_6782_f438v" o="438v" n="877"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13205 <pb file="add_6782_f439" o="439" n="878"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13206 <div xml:id="echoid-div280" type="page_commentary" level="2" n="280">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13207 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13208 <s xml:id="echoid-s1494" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13209 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13210 <s xml:id="echoid-s1494" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13211 A continuation of Harriot's work on the 'Dati sexti', from Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13212 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13213 Here he examines Proposition VI.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13214 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13215 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13216 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13217 VI. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13218 Data summa vel differentia duarum perpheriarum, quarum sinus datam habeant rationem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13219 dantur singulares peripheriæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13220 1 Enimvero si utraque peripheria proponitur minor quadrante, vel utraque major. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13221 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13222 Vt adgregatum similium sinuum ad differentiam eorundem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13223 ita prosinus dimidiæ summæ peripheriarum ad prosinum dimidiæ differentiæ earundem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13224 Vel ita prosinus complementi dimidiæ differentiæ peripheriarum ad prosinum complementi dimidiæ summæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13225 2 Quod si una e peripheriis proponatur minor quadrante, altera maior, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13226 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13227 Vt adgregatum sinuum ad differentiam eorundem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13228 ita prosinus dimidiæ differentiæ peripheriarum ad prosinum dimidiæ summæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13229 Vel ita prosinus complementi dimidiæ summæ ad prosinum complementi dimidiæ differentiæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13230 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13231 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13232 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13233 VI. Given the sum or difference of two arcs, whose sines are in a given ratio, each arc is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13234 1. If both given arcs are less than a quadrant of the circle, or both greater,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13235 then as the sum of those sines is to their difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13236 so is the tangent of half the sum of the arcs to the tangent of half their difference. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13237 Or as the tangent of the complement of half the difference of the arcs to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13238 the tangent of the complement of half the sum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13239 2. But if one of the given arcs is less than a quadrant, the other greater,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13240 then as the sum of the sines is to their difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13241 so is the tangent of half the difference of the arcs to the tangent of half their sum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13242 Or as the tangent of the complement of half the sum to the tangent of the complement of half the difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13243 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13244 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13245 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13246 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13247 <head xml:id="echoid-head192" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13248 Vieta. lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13249 pag. 37. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13250 VI. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13251 Data summa vel differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13252 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¥</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13253 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13254 Viète, Responsorum liber VIII, page 37, VI. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13255 Given the sum or difference and the ratio of their sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13256 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13257 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13258 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13259 <s xml:id="echoid-s1496" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13260 Interpetatio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13261 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, una peripheria minor quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13262 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, altera peripheria minor quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13263 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>g</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>c</mi></mstyle></math> ratio sinuum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13264 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>=</mo><mi>m</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13265 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>m</mi></mstyle></math> differentia inter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13266 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>h</mi></mstyle></math> differentia inter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>g</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13267 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13268 Interpetation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13269 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> one arc, less than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13270 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> the other arc, less than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13271 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>g</mi><mo>:</mo><mi>g</mi><mi>c</mi></mstyle></math> ratio of the sines <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13272 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>=</mo><mi>m</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13273 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>m</mi></mstyle></math> difference between <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13274 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>h</mi></mstyle></math> difference between <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>g</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13275 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13276 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13277 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13278 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13279 <s xml:id="echoid-s1497" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13280 Hic <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> est maior quadrante. non tamen variat casum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13281 Menda igitur in Vieta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13282 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13283 Here <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> is greater than a quadrant, nevertheless, the case does not change. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13284 Therefore wrong in Viète.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13285 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13286 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13287 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13288 <pb file="add_6782_f439v" o="439v" n="879"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13289 <pb file="add_6782_f440" o="440" n="880"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13290 <div xml:id="echoid-div281" type="page_commentary" level="2" n="281">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13291 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13292 <s xml:id="echoid-s1498" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13293 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13294 <s xml:id="echoid-s1498" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13295 A continuation of Harriot's work on the 'Dati sexti', from Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13296 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13297 Here he examines Propositions V.1 and V.2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13298 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13299 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13300 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13301 V. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13302 Data differentia duarum perpheriarum, quarum sinus datam habeant rationem, dantur singulæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13303 1 Enimvero si differentia sit maior quadrante circuli. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13304 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13305 Vt sinus componentium primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13306 ita transsinuosa complementi differentiæ ad prosinum complementi primæ minus prosinu complementi differentiæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13307 Cum autem prima sumetur maior quadrante, secunda sumetur minor, & contra. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13308 2 Et si differentia minor quadrante circuli, differentes autem peripheriæ diversæ sint speciei, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13309 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13310 Vt sinus primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13311 ita transsinuosa complementi differentiæ ad prosinum complementi differentiæ, plus prosinu complementi primæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13312 Cum autem prima sumetur maior quadrante, secunda sumetur minor, & contra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13313 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13314 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13315 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13316 V. Given the difference of two arcs, whose sines are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13317 1. If the difference is greater than a quadrant of the circle,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13318 then as the sine of the first component is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13319 so is the secant of the complement of the difference to the tangent of the complement of the first
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13320 minus the tangent of the complement of the difference. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13321 Moreover, when the first it taken greater than a quadrant, the second is taken less, and conversely. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13322 2. And if the difference is greater than a quadrant of the circle, but the different arcs have different signs,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13323 then as the sine of the first component is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13324 so is the secant of the complement of the difference to the tangent of the complement of the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13325 plus the tangent of the complement of the first.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13326 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13327 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13328 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13329 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13330 <head xml:id="echoid-head193" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13331 Vieta. lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13332 pag. 37. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13333 V. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13334 Data differentia duarum perpheriarum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13335 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¥</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13336 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13337 Viète, Responsorum liber VIII, page 37, V. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13338 Given the difference of two arcs and the ratio of their sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13339 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13340 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13341 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13342 <s xml:id="echoid-s1500" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13343 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13344 differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13345 maior quad.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13346 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13347 1. the difference greater than a quadrant
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13348 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13349 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13350 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13351 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13352 <s xml:id="echoid-s1501" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13353 Interpetatio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13354 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> una peripheria. cui æqualis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13355 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> altera <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13356 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>g</mi></mstyle></math> differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13357 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>h</mi></mstyle></math> angulus rectus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13358 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13359 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13360 Interpetation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13361 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> one arc, to which <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>c</mi></mstyle></math> is equal <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13362 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> the other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13363 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>g</mi></mstyle></math> the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13364 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>h</mi></mstyle></math>, a right angle <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13365 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13366 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13367 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13368 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13369 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13370 <s xml:id="echoid-s1502" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13371 Ut minor terminus sit primum proportionalium. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13372 Fiat angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>e</mi><mi>r</mi></mstyle></math>, æqualis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>k</mi></mstyle></math> angulo, qui est angulus complementi differentiæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13373 Tum triangula <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>r</mi><mi>g</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>l</mi><mi>k</mi><mi>e</mi></mstyle></math> sunt æquiangula. nam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>l</mi><mi>k</mi><mi>e</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>r</mi><mi>g</mi></mstyle></math> sunt anguli <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13374 residui æqualia <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>r</mi><mi>e</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>k</mi><mi>e</mi></mstyle></math>. et anguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi><mi>l</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>g</mi><mi>e</mi></mstyle></math> sunt æquales ab paralleles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>q</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>l</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13375 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13376 If the smaller term is the first proportional. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13377 Construct anlge <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>e</mi><mi>r</mi></mstyle></math> equal to angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>k</mi></mstyle></math>, which is the angle of the complement of the difference. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13378 Then triangles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>r</mi><mi>g</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>l</mi><mi>k</mi><mi>e</mi></mstyle></math> are equiangular, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>l</mi><mi>k</mi><mi>e</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>r</mi><mi>g</mi></mstyle></math> are residual angles from
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13379 the equal angles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>r</mi><mi>e</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>k</mi><mi>e</mi></mstyle></math>; and angles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi><mi>l</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>g</mi><mi>e</mi></mstyle></math> are equals by the parallels <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>q</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>l</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13380 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13381 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13382 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13383 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13384 <s xml:id="echoid-s1503" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13385 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13386 differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13387 minor quad: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13388 peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13389 una minor, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13390 altera maior <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13391 quadrante.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13392 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13393 2. the difference less than a quadrant; one arc less tha, the other greater than a quadrant.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13394 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13395 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13396 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13397 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13398 <s xml:id="echoid-s1504" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13399 Superiora verba et litteræ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13400 deservierunt etiam hinc diagram-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13401 mati; et concludant:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13402 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13403 The above words and letters serve also for this diagram; and end with:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13404 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13405 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13406 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13407 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13408 <s xml:id="echoid-s1505" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13409 Ut minor terminus sit primus proportionalium. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13410 Hic anguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>r</mi><mi>g</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>k</mi><mi>l</mi></mstyle></math>, sunt complemmentat <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13411 æqualium angulum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>e</mi><mi>n</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi><mi>h</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13412 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13413 As the lesser term is the first proportional. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13414 Here angles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>r</mi><mi>g</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>k</mi><mi>l</mi></mstyle></math> are complements of equal angles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>e</mi><mi>n</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi><mi>h</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13415 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13416 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13417 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13418 <pb file="add_6782_f440v" o="440v" n="881"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13419 <pb file="add_6782_f441" o="441" n="882"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13420 <div xml:id="echoid-div282" type="page_commentary" level="2" n="282">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13421 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13422 <s xml:id="echoid-s1506" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13423 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13424 <s xml:id="echoid-s1506" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13425 A continuation of Harriot's work on the 'Dati sexti', from Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13426 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13427 Here he examines Proposition V.3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13428 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13429 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13430 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13431 V. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13432 Data differentia duarum perpheriarum, quarum sinus datam habeant rationem, dantur singulæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13433 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13434 3 Et si denique differentia sit minor quadrante,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13435 utraque vero differentium vel quadrante minor vel utraque quadrante maior,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13436 ac prima quidem intelligatur ea cui debetur sinus major, secunda cui minor, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13437 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13438 Vt sinus primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13439 ita transsinuosa complementi differentiæ ad prosinum complementi differentiæ minus prosinu complementi primæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13440 Et, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13441 Vt sinus primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13442 ita transsinuosa complementi differentiæ ad prosinum complementi differentiæ plus prosinu complementi primæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13443 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13444 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13445 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13446 V. Given the difference of two arcs, whose sines are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13447 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13448 3. And if finally the difference is less than a quadrant,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13449 then as the sine of the first component is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13450 so is the secant of the complement of the difference to the tangent of the complement of the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13451 minus the tangent of the complement of the first.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13452 And as the sine of the first is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13453 so is the secant of the complement of the difference to the tangent of the complement of the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13454 plus the tangent of the complement of the first. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13455 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13456 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13457 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13458 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13459 <head xml:id="echoid-head194" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13460 Vieta. lib. 8. resp. pag. 37. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13461 V. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13462 Data differentia duarum perpheriarum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13463 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¥</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13464 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13465 Viète, Responsorum liber VIII, page 37, V. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13466 Given the difference of two arcs and the ratio of their sines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13467 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13468 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13469 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13470 <s xml:id="echoid-s1508" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13471 3. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13472 differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13473 minor quad. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13474 et <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13475 utraque <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13476 peripheriæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13477 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13478 3. the difference greater than a quadrant, and both the arcs.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13479 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13480 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13481 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13482 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13483 <s xml:id="echoid-s1509" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13484 Verba <emph style="super">et litteræ</emph> superiores <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13485 diagrammatis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13486 2, et 1, deservierunt <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13487 etiam huic.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13488 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13489 The words and letters for the above diagrams, 2 and 1, serve also for this,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13490 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13491 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13492 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13493 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13494 <s xml:id="echoid-s1510" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13495 Ut minor terminus sit primum proportinalium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13496 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13497 If the smaller term is the first proportional.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13498 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13499 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13500 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13501 <pb file="add_6782_f441v" o="441v" n="883"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13502 <pb file="add_6782_f442" o="442" n="884"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13503 <div xml:id="echoid-div283" type="page_commentary" level="2" n="283">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13504 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13505 <s xml:id="echoid-s1511" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13506 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13507 <s xml:id="echoid-s1511" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13508 A continuation of Harriot's work on the 'Dati sexti', from Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13509 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13510 Here he examines Proposition IV.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13511 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13512 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13513 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13514 IV. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13515 Data peripheria composita e duabus peripheriis, quarum sinus datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13516 1 Enimvero si composita minor est circuli quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13517 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13518 Vt sinus componentium primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13519 ita transsinuosa complementi compositæ ad prosinum complementi primæ minus prosinu complementi compositæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13520 2 Et si composita maior est quadrante, utraque vero componentium minor quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13521 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13522 Vt sinus primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13523 ita s complementi compositæ ad prosinum complementi compositæ plus prosinu complementi primæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13524 3 Et si denique componentium peripheriarum primæ sit minor quadrante, secunda maior, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13525 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13526 Vt sinus primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13527 ita transsinuosa complementi compositæ ad prosinum complementi compositæ minus prosinu complementi primæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13528 Et, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13529 Vt sinus primæ ad sinum secundæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13530 ita transsinuosa complementi compositæ ad prosinum complementi compositæ plus prosinu secundæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13531 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13532 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13533 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13534 IV. Given the sum of two arcs, whose sines are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13535 1. If the sum is less than a quadrant of the circle, then as the sine of the first component is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13536 so is the secant of the complement of the sum to the tangent of the complement of the first
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13537 minus the tangent of the complement of the sum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13538 2. And if the sum is greater than a quadrant, but both components are less than a quadrant,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13539 then as the sine of the first component is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13540 so is the secant of the complement of the sum to the tangent of the complement of the sum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13541 plus the tangent of the complement of the first. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13542 3. And if finally the first component of the sum is less than a quadrant, the second greater,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13543 then as the sine of the first component is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13544 so is the secant of the complement of the sum to the tangent of the complement of the sum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13545 minus the tangent of the complement of the first.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13546 And as the sine of the first is to the sine of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13547 so is the secant of the complement of the sum to the tangent of the complement of the sum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13548 plus the tangent of the second.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13549 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13550 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13551 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13552 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13553 <head xml:id="echoid-head195" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13554 Vieta. lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13555 pag. 38. b. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13556 IIII. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13557 Data peripheria composita <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13558 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¥</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13559 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13560 Viète, Responsorum liber VIII, page 38v, IV. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13561 Given a sum of arcs and the ratio of their sines, 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13562 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13563 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13564 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13565 <s xml:id="echoid-s1513" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13566 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13567 composita minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13568 quadrante
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13569 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13570 1. the sum less than a quadrant
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13571 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13572 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13573 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13574 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13575 <s xml:id="echoid-s1514" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13576 Interpetatio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13577 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> una peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13578 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> altera peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13579 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math>,<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>c</mi></mstyle></math>: ratio sinuum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13580 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13581 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13582 Interpetation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13583 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> one arc <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13584 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> the other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13585 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi><mo>:</mo><mi>d</mi><mi>c</mi></mstyle></math>, the ratio of sines <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13586 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13587 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13588 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13589 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13590 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13591 <s xml:id="echoid-s1515" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13592 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13593 composita maior; <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13594 utraque minor
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13595 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13596 2. the sum greater; both [arcs] less
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13597 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13598 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13599 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13600 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13601 <s xml:id="echoid-s1516" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13602 3. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13603 composita <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13604 maior: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13605 una minor, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13606 altera maior
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13607 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13608 3. the sum greater; one [arc] less, the other greater
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13609 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13610 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13611 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13612 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13613 <s xml:id="echoid-s1517" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13614 Inde cum 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13615 Menda in Vieta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13616 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13617 Hence like 2, wrong in Viète.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13618 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13619 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13620 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13621 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13622 <s xml:id="echoid-s1518" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13623 Aliter pro 3. Ut maior terminus sit primus proportionalium. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13624 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13625 Another way for 3, when the greater term is the first proportional.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13626 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13627 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13628 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13629 <pb file="add_6782_f442v" o="442v" n="885"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13630 <pb file="add_6782_f443" o="443" n="886"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13631 <div xml:id="echoid-div284" type="page_commentary" level="2" n="284">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13632 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13633 <s xml:id="echoid-s1519" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13634 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13635 <s xml:id="echoid-s1519" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13636 A continuation of Harriot's work on the 'Dati sexti', from Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13637 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13638 Here he examines Proposition III.2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13639 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13640 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13641 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13642 III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13643 Data summa vel differentia duarum peripheriarum, quarum transsinuosae datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13644 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13645 2 Quod si une e peripheriis proponitur minor quadrante, altera maior <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13646 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13647 Vt adgregatum similium transsinuousuarum ad differentiam earundem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13648 ita prosinus dimidia differentiæ peripheriarum ad prosinum complementi dimidæ summæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13649 Et ita prosinus dimidiæ summæ ad prosinum complementi dimidiæ differentiæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13650 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13651 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13652 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13653 III. Given the sum or difference of two arcs, whose secants are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13654 2. But if one of the arcs is less than a quadrant, the ohter greater, then as the sum of the similar secants is
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13655 to their difference, so is the tangent of half the difference of the arcs
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13656 to the tangent of the complement of half the sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13657 And so is the tangent of half the sum to the tangent of the complement of half the difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13658 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13659 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13660 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13661 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13662 <head xml:id="echoid-head196" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13663 Vieta. lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13664 pag. 38. b. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13665 III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13666 Data summa vel differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13667 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math>. 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13668 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13669 Viète, Responsorum liber VIII, page 38v, III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13670 Given the sum or difference of two arcs and the ratio of their secants, 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13671 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13672 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13673 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13674 <s xml:id="echoid-s1521" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13675 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13676 peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13677 una minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13678 quadrante; <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13679 altera maior.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13680 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13681 2. one arc is less than a quadrant, the other greater
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13682 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13683 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13684 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13685 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13686 <s xml:id="echoid-s1522" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13687 Interpetatio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13688 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> una peripheria, minor quadrante <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13689 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> altera, maior quadrante <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13690 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>-</mo><mi>a</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13691 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>, differentia inter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13692 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>c</mi></mstyle></math>, dimidia differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13693 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>g</mi></mstyle></math>, eius tangens <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13694 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>g</mi><mo>=</mo><mi>k</mi><mi>g</mi></mstyle></math>, et parallelæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13695 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math> secans peripheriæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13696 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math>, secans peripheriæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13697 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>t</mi><mo>=</mo><mi>e</mi><mi>d</mi><mo>=</mo><mi>e</mi><mi>f</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13698 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>t</mi><mi>h</mi></mstyle></math>, differentia secantium <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13699 fiat <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>y</mi><mo>=</mo><mi>e</mi><mi>t</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13700 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mi>k</mi></mstyle></math> dimidia summa compositæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13701 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>m</mi></mstyle></math>, complementum dimidiæ summæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13702 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13703 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13704 Interpetation <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13705 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> one arc, less than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13706 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> the other, greater than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13707 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>-</mo><mi>a</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13708 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>, the difference between <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13709 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>c</mi></mstyle></math>, half the difference <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13710 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>g</mi></mstyle></math>, its tangent <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13711 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>g</mi><mo>=</mo><mi>k</mi><mi>g</mi></mstyle></math>, and parallels <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13712 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math> secant of the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13713 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math>, secant of the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13714 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>t</mi><mo>=</mo><mi>e</mi><mi>d</mi><mo>=</mo><mi>e</mi><mi>f</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13715 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>t</mi><mi>h</mi></mstyle></math>, difference of the secants <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13716 fiat <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>y</mi><mo>=</mo><mi>e</mi><mi>t</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13717 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mi>k</mi></mstyle></math> half the sum of the composite arc <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13718 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>m</mi></mstyle></math>, complement of half the sum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13719 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13720 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13721 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13722 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13723 <pb file="add_6782_f443v" o="443v" n="887"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13724 <pb file="add_6782_f444" o="444" n="888"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13725 <div xml:id="echoid-div285" type="page_commentary" level="2" n="285">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13726 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13727 <s xml:id="echoid-s1523" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13728 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13729 <s xml:id="echoid-s1523" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13730 A continuation of Harriot's work on the 'Dati sexti', from Chapter XIX of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13731 Viète's <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13732 Here he examines Proposition III.1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13733 The word 'parapompe' was originally used by Viète to describe each proposition. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13734 The page number 36v given in the top left hand corner is incorrect; it should be 38v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13735 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13736 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13737 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13738 III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13739 Data summa vel differentia duarum peripheriarum, quarum transsinuosae datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13740 1 Enimvero si utraque peripheria proponatur minor quadrante vel utraque major. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13741 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13742 Vt adgregatum similium transsinuousuarum ad differentiam earundem,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13743 ita prosinus complementi dimidia summæ peripheriæ ad prosinum dimidæ differentiæ,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13744 Et ita prosinus complementi dimidiæ differentiæ ad prosinum dimidiæ summæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13745 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13746 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13747 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13748 III. Given the sum or difference of two arcs, whose secants are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13749 1. If both the given arcs are less than a quadrant or both greater, then as the sum of the similar secants is
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13750 to their difference, so is the tangent of the complement of half the sum of the arcs
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13751 to the tangent of half the difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13752 And so is the tangent of the complement of half the difference to the tangent of half the sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13753 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13754 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13755 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13756 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13757 <head xml:id="echoid-head197" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13758 Vieta. lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13759 pag. 36. b. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13760 III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13761 et pag. 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13762 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13763 data peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13764 composita. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13765 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¨</mo></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13766 <foreign xml:lang="gre">parapompe</foreign>. 3. Data summa vel differentia duarum peripheriarum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13767 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math>. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13768 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13769 Viète, Responsorum liber VIII, page 36v, III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13770 and page 38, 1, given the sum of arcs and the ratio of their secants <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13771 Parapompe III: Given the sum or difference of two arcs and the ratio of their secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13772 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13773 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13774 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13775 <s xml:id="echoid-s1525" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13776 I.1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13777 peripheria utraque <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13778 minor quadrante
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13779 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13780 I.1.either arc is less than a quadrant
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13781 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13782 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13783 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13784 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13785 <s xml:id="echoid-s1526" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13786 Arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. Tangens <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13787 Arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>. Tangens <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13788 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>=</mo><mi>b</mi><mi>i</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13789 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi><mo>,</mo><mi>d</mi><mi>i</mi><mi>f</mi><mi>f</mi><mi>e</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi></mstyle></math> ab <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>t</mi></mstyle></math> bc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>.</mo></mstyle></math><lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13790 Aggregatum tangentium <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi><mo>+</mo><mi>e</mi><mi>h</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13791 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>h</mi></mstyle></math>, est differentia tangentium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13792 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>k</mi></mstyle></math> est dimidium arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13793 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>r</mi></mstyle></math> est dimidium totius <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13794 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>s</mi></mstyle></math> est complementum arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>r</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13795 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>n</mi></mstyle></math> est tangens complementi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>k</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13796 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>l</mi></mstyle></math> est tangens arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>k</mi></mstyle></math>, secans <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13797 dimidij differentiæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13798 Lineæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>n</mi></mstyle></math> sit parallellæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13799 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13800 Arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, tangent <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13801 Arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, tangens <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13802 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>=</mo><mi>b</mi><mi>i</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13803 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi><mo>,</mo><mi>t</mi><mi>h</mi><mi>e</mi><mi>d</mi><mi>i</mi><mi>f</mi><mi>f</mi><mi>e</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>b</mi><mi>e</mi><mi>t</mi><mi>w</mi><mi>e</mi><mi>e</mi><mi>n</mi></mstyle></math> ab <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>n</mi><mi>d</mi></mstyle></math> bc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>.</mo></mstyle></math><lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13804 Sum of the tangents <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi><mo>+</mo><mi>e</mi><mi>h</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13805 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>h</mi></mstyle></math> is the difference between the tangents <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13806 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>k</mi></mstyle></math> is half the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13807 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>r</mi></mstyle></math> is half the total <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13808 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>s</mi></mstyle></math> is the complement of the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>r</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13809 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>n</mi></mstyle></math> is the tangent of the complement <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>k</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13810 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>l</mi></mstyle></math> is the tangent of the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>k</mi></mstyle></math>, cutting half the difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13811 The lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>n</mi></mstyle></math> are parallel.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13812 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13813 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13814 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13815 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13816 <s xml:id="echoid-s1527" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13817 <foreign xml:lang="gre">parapompe</foreign> pro pag. 38. Data peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13818 Triangles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>d</mi><mi>e</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>x</mi><mi>u</mi></mstyle></math> are equiangular <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13819 For angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>u</mi><mi>x</mi></mstyle></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math>, because either is the complement of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>e</mi><mi>u</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13820 and it is obvious that angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi><mi>h</mi></mstyle></math> is equal to angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>x</mi><mi>e</mi></mstyle></math>;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13821 therefore a third of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>u</mi><mi>x</mi></mstyle></math> is equal to angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13822 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13823 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>a</mi></mstyle></math>, is the tangent of the conplement of the sum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13824 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>x</mi></mstyle></math>, is the tangent of the second.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13825 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13826 <foreign xml:lang="gre">parapompe</foreign> for page 38. Given the sum of the arcs. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13827 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>=</mo><mi>b</mi><mi>i</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13828 Triangula <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>d</mi><mi>e</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>x</mi><mi>u</mi></mstyle></math> sunt æquiangula <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13829 Nam angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>u</mi><mi>x</mi></mstyle></math> est æqualis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> quia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13830 uterque est complementum anguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>e</mi><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13831 Et manifestum est angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi><mi>h</mi></mstyle></math> esse <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13832 æqualem angulo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>x</mi><mi>e</mi></mstyle></math>; Ergo tertius <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13833 angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>u</mi><mi>x</mi></mstyle></math> æqualis est angulo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13834 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13835 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>a</mi></mstyle></math>, est prosinus complementi compositæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13836 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>x</mi></mstyle></math>, est prosinus secundæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13837 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13838 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13839 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13840 <pb file="add_6782_f444v" o="444v" n="889"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13841 <pb file="add_6782_f445" o="445" n="890"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13842 <div xml:id="echoid-div286" type="page_commentary" level="2" n="286">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13843 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13844 <s xml:id="echoid-s1528" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13845 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13846 <s xml:id="echoid-s1528" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13847 At the end of Chapter XIX of <emph style="it">Variorum responsorum liber VIII</emph> (1593),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13848 under the heading 'DATI SEXTI', Viète listed six propositions for finding either of two arcs
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13849 given the sums of differences of the arcs and the ratio of their secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13850 In the 1646 edition of Viète's <emph style="it">Opera mathematica</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13851 the six propositions are to be found on page 413.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13852 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13853 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13854 <s xml:id="echoid-s1529" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13855 On this page Harriot examines Proposition I, part 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13856 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13857 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13858 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13859 I. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13860 Data peripheria composita e duabus peripheriis, quarum transsinuosae datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13861 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13862 2 Et si composita major est quadrante circuli, utraque vero componentium minor quadrante, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13863 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13864 Vt transsinuosa primæ ad transsinuousa secundæ, ita transsinuosa complementi composita ad prosinum secunda
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13865 minus prosinus complementa compositæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13866 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13867 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13868 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13869 I.Given an arc composed of two others, whose secants are in a given ratio, each is known individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13870 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13871 2. And if the sum is greater than a quarter of a circle, but each component is less than a quarter, then
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13872 as the secant of the first is to the secant of the second, so is the secant of the complement of the sum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13873 to the tangent of the second minus the tangent of the complement of the sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13874 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13875 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13876 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13877 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13878 <head xml:id="echoid-head198" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13879 Vieta. lib. 8. resp. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13880 pag. 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13881 Data peripheria composita duarum perpheriarum, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13882 et ratione <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ψ</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13883 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13884 Viète, Responsorum liber VIII, page 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13885 Given an arc composed of two arcs, and the ratio of their secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13886 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13887 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13888 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13889 <s xml:id="echoid-s1531" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13890 composita <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13891 maior <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13892 utrusque minor
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13893 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13894 the sum is greater or lesser than
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13895 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13896 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13897 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13898 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13899 <s xml:id="echoid-s1532" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13900 triangula <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>g</mi></mstyle></math> sunt equiangula. nam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi><mi>g</mi></mstyle></math> æqualis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math>, quia uterque <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13901 est complementum anguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>g</mi></mstyle></math>. et anguli ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> sunt æquales propter similia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13902 trianguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi><mi>i</mi></mstyle></math>, et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>g</mi><mi>i</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13903 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13904 Triangles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>g</mi></mstyle></math> are equiangular.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13905 For <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi><mi>g</mi></mstyle></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math>, because either is the complement of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>g</mi></mstyle></math>;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13906 and the angles at <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> and 4 d <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>r</mi><mi>e</mi><mi>e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi>b</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>u</mi><mi>s</mi><mi>e</mi><mi>o</mi><mi>f</mi><mi>s</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>a</mi><mi>n</mi><mi>g</mi><mi>l</mi><mi>e</mi><mi>s</mi></mstyle></math> adi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>n</mi><mi>d</mi></mstyle></math> bgi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>.</mo></mstyle></math></emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13907 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13908 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13909 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13910 <s xml:id="echoid-s1533" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13911 Non refert an <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> sit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13912 minor vel maior quam <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13913 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13914 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13915 It does not matter whether <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> is less than or greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13916 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13917 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13918 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13919 <pb file="add_6782_f445v" o="445v" n="891"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13920 <pb file="add_6782_f446" o="446" n="892"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13921 <div xml:id="echoid-div287" type="page_commentary" level="2" n="287">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13922 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13923 <s xml:id="echoid-s1534" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13924 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13925 <s xml:id="echoid-s1534" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13926 A continuation from Add MS 6782, f. 445, of Harriot's work on the 'Dati sexti' from Chapter XIX of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13927 <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13928 Here he examines Proposition I, part 3, which he has divided as 3 and 4,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13929 according to whether one takes the minus or plus sign in the final sentence of the statement.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13930 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13931 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13932 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13933 I. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13934 Data peripheria composita e duabus peripheriis, quarum transsinuosae datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13935 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13936 3 Et si denique componentium peripheriarum prima fit minor quadrante, secunda major, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13937 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13938 Vt transsinuosa primæ ad transsinuosam secundæ, ita transsinuosa complementi compositæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13939 ad prosinum complementi compositæ minus prosinu secundæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13940 Et, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13941 Vt transsinuosa secunda ad transsinuousam primæ, ita transsinuosa complementi compositæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13942 ad prosinum complementi compositæ plus prosinu secundæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13943 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13944 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13945 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13946 I.Given an arc composed of two others, whose secants are in a given ratio, each is known individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13947 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13948 3. And if further the first arc is less than a quadrant, the second greater, then
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13949 as the secant of the first is to the secant of the second, so is the secant of the complement of the sum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13950 to the sine of the complement of the sum minus the sine of the second, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13951 and <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13952 [4.] as the secant of the second to the secant of the first, so is the secant of the complement of the sum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13953 to the sine of the complement of the sum plus the sine of the second.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13954 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13955 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13956 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13957 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13958 <head xml:id="echoid-head199" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13959 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13960 pag. 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13961 3. et 4. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13962 Data peripheria composita e duabus peripheriis, quarum transsinuosæ <emph style="super"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¨</mo></mstyle></math></emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13963 datam habeant rationem, dantur singulæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13964 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13965 Viète, Responsorum liber VIII, page 38, Propositions 3 and 4. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13966 Given an arc composed of two arcs, whose secants are in a given ratio, each is given separately.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13967 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13968 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13969 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13970 <s xml:id="echoid-s1536" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13971 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math> peripheria composita <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13972 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> prima minor quadrante <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13973 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> secunda maior quadrante <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13974 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math> Transsinuosa <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, primæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13975 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>c</mi></mstyle></math> Transsinuosa <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, secundæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13976 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13977 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math> is the sum of the arcs <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13978 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> is the first, less than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13979 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> is the second, greater than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13980 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math> is the secant of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, the first <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13981 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>c</mi></mstyle></math> is the secant of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, the second
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13982 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13983 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13984 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13985 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13986 <s xml:id="echoid-s1537" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13987 1<emph style="super">o</emph>. Triangula <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi><mi>g</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>o</mi></mstyle></math> sunt æquiangula;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13988 propter parallelas <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13989 2<emph style="super">o</emph>. Triangula <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>m</mi></mstyle></math> sunt æquiangula.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13990 nam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math> est complementum anguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>h</mi></mstyle></math> inde æqualis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13991 angulo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>k</mi></mstyle></math>, cui æqualis fit per constructionem <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi><mi>m</mi></mstyle></math>. anguli igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi><mi>m</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math> sunt æquales <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13992 et anguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>m</mi></mstyle></math> sunt æquales propter parallelas <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>f</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math>. Tertius ergo angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi><mi>g</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13993 est æqualis tertio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>m</mi><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13994 3<emph style="super">o</emph>. Arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>k</mi></mstyle></math> sunt æquales. nam arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> est arcus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi><mo>-</mo><mi>b</mi><mi>k</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13995 hoc est <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi><mo>-</mo><mi>k</mi><mi>n</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13996 4<emph style="super">o</emph>. Triangula <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>h</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi><mi>o</mi></mstyle></math> sunt æqualia et æquiangula.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13997 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13998 1. Triangles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi><mi>g</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>o</mi></mstyle></math> are equiangular, because <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>o</mi></mstyle></math> are parallel. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	13999 2. Triangles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>m</mi></mstyle></math> are equiangular, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math> is the complement of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>h</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14000 thence equal to angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>k</mi></mstyle></math>, to which <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi><mi>m</mi></mstyle></math> is equal by construction;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14001 therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi><mi>m</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi><mi>d</mi></mstyle></math> are equal,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14002 and angles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi><mi>m</mi></mstyle></math> are equal because <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>f</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>h</mi></mstyle></math> are parallel.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14003 Therefore a third of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi><mi>g</mi></mstyle></math> is equal to a third of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>m</mi><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14004 3. Arcs <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>k</mi></mstyle></math> are equal, for arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> is arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi><mo>-</mo><mi>b</mi><mi>k</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14005 that is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi><mo>-</mo><mi>k</mi><mi>n</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14006 4. Triangles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi><mi>h</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi><mi>o</mi></mstyle></math> are equal and equiangular.<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14007 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14008 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14009 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14010 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14011 <s xml:id="echoid-s1538" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14012 peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14013 una minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14014 altera maior <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14015 quadrante
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14016 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14017 one of the arcs is less than, the other greater than a quadrant
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14018 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14019 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14020 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14021 <pb file="add_6782_f446v" o="446v" n="893"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14022 <pb file="add_6782_f447" o="447" n="894"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14023 <div xml:id="echoid-div288" type="page_commentary" level="2" n="288">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14024 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14025 <s xml:id="echoid-s1539" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14026 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14027 <s xml:id="echoid-s1539" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14028 A continuation from Add MS 6782, f. 445 and f. 446, of Harriot's work on the 'Dati sexti'
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14029 from Chapter XIX of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14030 <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14031 Here he examines Proposition II, part 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14032 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14033 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14034 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14035 II. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14036 Data differentia duarum perpheriarum, quarum transsinuosæ datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14037 1 Enimvero si differentia fit major circuli quadrante, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14038 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14039 Vt transsinuosa differentium primæ ad transsinuosum secundæ, ita transsinuosa complementi differentiæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14040 ad prosinum complementi differentiaæ plus prosinu secundæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14041 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14042 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14043 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14044 II.Given the difference of two arcs, whose secants are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14045 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14046 1. If the difference is greater than a quadrant, then
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14047 as the secant of the first is to the secant of the second, so is the secant of the complement of the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14048 to the sine of the complement of the difference plus the sine of the second.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14049 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14050 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14051 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14052 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14053 <head xml:id="echoid-head200" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14054 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14055 pag. 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14056 Data differentia duarum perpheriarum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14057 et ratione <emph style="super"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¨</mo></mstyle></math></emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14058 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14059 Viète, Responsorum liber VIII, page 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14060 Given the difference of two arcs, and the ratio of their secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14061 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14062 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14063 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14064 <s xml:id="echoid-s1541" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14065 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14066 differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14067 maior quadrante
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14068 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14069 1. difference greater than a quadrant.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14070 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14071 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14072 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14073 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14074 <s xml:id="echoid-s1542" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14075 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> una peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14076 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> altera <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14077 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>=</mo><mi>a</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14078 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>i</mi></mstyle></math> differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14079 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>k</mi></mstyle></math> compl. differentiæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14080 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14081 Triangula similia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14082 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14083 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> one arc <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14084 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> the other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14085 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>=</mo><mi>a</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14086 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>i</mi></mstyle></math> the difference <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14087 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>k</mi></mstyle></math> complement of the difference <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14088 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14089 Similar triangles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14090 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14091 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14092 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14093 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14094 <s xml:id="echoid-s1543" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14095 primus terminus minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14096 primus term maior
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14097 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14098 the first term less <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14099 the first term greater
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14100 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14101 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14102 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14103 <pb file="add_6782_f447v" o="447v" n="895"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14104 <pb file="add_6782_f448" o="448" n="896"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14105 <div xml:id="echoid-div289" type="page_commentary" level="2" n="289">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14106 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14107 <s xml:id="echoid-s1544" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14108 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14109 <s xml:id="echoid-s1544" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14110 A continuation of Harriot's work on the 'Dati sexti' from Chapter XIX of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14111 <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14112 Here he examines Proposition II, part 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14113 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14114 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14115 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14116 II. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14117 Data differentia duarum perpheriarum, quarum transsinuosæ datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14118 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14119 2 Et si differentia fit minor quadrante, differentes autem peripheriæ diversæ sint speciei. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14120 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14121 Vt transsinuosa primæ ad transsinuosum secundæ, ita transsinuosa complementi differentiæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14122 ad prosinum secundæ minus prosinu complementi differentiæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14123 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14124 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14125 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14126 II.Given the difference of two arcs, whose secants are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14127 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14128 2. And if the difference is less than a quadrant, and also the signs of each arc are different, then
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14129 as the secant of the first is to the secant of the second, so is the secant of the complement of the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14130 to the sine of the second minus the sine of the complement of the difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14131 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14132 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14133 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14134 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14135 <head xml:id="echoid-head201" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14136 Vieta. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14137 pag. 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14138 Data differentia duarum perpheriarum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14139 et ratione <emph style="super"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¨</mo></mstyle></math></emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14140 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14141 Viète, Responsorum liber VIII, page 38. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14142 Given the difference of two arcs, and the ratio of their secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14143 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14144 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14145 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14146 <s xml:id="echoid-s1546" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14147 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14148 Differentia minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14149 quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14150 peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14151 una minor, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14152 altera maior quadrante
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14153 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14154 2. Difference less than a quadrant; one arc greater than a quadrant, the other less.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14155 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14156 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14157 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14158 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14159 <s xml:id="echoid-s1547" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14160 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> una peripheria minor quadrante <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14161 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> altera peripheria maior quadrante <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14162 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>=</mo><mi>a</mi><mi>b</mi><mo>=</mo><mi>k</mi><mi>m</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14163 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>i</mi></mstyle></math> differentia, minor quadrante <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14164 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>n</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>f</mi></mstyle></math> parallelæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14165 Triangula similia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14166 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14167 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> one arc, less than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14168 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> the other arc, greater than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14169 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>=</mo><mi>a</mi><mi>b</mi><mo>=</mo><mi>k</mi><mi>m</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14170 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>i</mi></mstyle></math> the difference, less than a quadrant <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14171 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>n</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>f</mi></mstyle></math> parallels <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14172 Similar triangles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14173 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14174 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14175 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14176 <pb file="add_6782_f448v" o="448v" n="897"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14177 <pb file="add_6782_f449" o="449" n="898"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14178 <div xml:id="echoid-div290" type="page_commentary" level="2" n="290">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14179 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14180 <s xml:id="echoid-s1548" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14181 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14182 <s xml:id="echoid-s1548" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14183 A continuation of Harriot's work on the 'Dati sexti' from Chapter XIX of Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14184 <emph style="it">Variorum responsorum liber VIII</emph> (1593).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14185 Here he examines Proposition II, part 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14186 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14187 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14188 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14189 II. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14190 Data differentia duarum perpheriarum, quarum transsinuosæ datam habeant rationem, dantur singulæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14191 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14192 3 Et si denique differentia fit minor quadrante, utraque vero differentium vel minor quadrante,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14193 vel utraque major. Prima autem intelligatur ea ad quam pertinet transsiuosa major. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14194 Erit, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14195 Vt transsinuosa primæ ad transsinuosum secundæ, ita transsinuosa complementi differentiæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14196 ad prosinum secundæ minus prosinu complementi differentiæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14197 Et, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14198 Vt transsinuosa primæ ad transsinuosum secundæ, ita transsinuosa complementi differentiæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14199 ad prosinum primæ minus prosinu complementi differentiæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14200 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14201 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14202 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14203 II.Given the difference of two arcs, whose secants are in a given ratio, each is given individually. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14204 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14205 3. If the difference is less than a quadrant, and both arcs are less than a quadrant, or both greater, then
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14206 as the secant of the first is to the secant of the second, so is the secant of the complement of the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14207 to the sine of the second minus the sine of the complement of the difference; and
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14208 as the secant of the first is to the secant of the second, so is the secant of the complement of the difference
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14209 to the sine of the first minus the sine of the complement of the difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14210 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14211 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14212 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14213 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14214 <head xml:id="echoid-head202" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14215 Vieta. pag. 38.b. resp. lib. 8. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14216 Data differentia duarum perpheriarum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14217 et ratione <emph style="super"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>Î¨</mo></mstyle></math></emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14218 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14219 Viète, page 38v, Responsorum liber VIII. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14220 Given the difference of two arcs, and the ratio of their secants.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14221 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14222 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14223 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14224 <s xml:id="echoid-s1550" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14225 3. bis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14226 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14227 3. twofold.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14228 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14229 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14230 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14231 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14232 <s xml:id="echoid-s1551" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14233 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> una peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14234 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> altera <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14235 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>=</mo><mi>a</mi><mi>b</mi><mo>=</mo><mi>k</mi><mi>m</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14236 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14237 Ergo. anguli <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>o</mi><mi>g</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> æquales <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14238 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math> parallelæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14239 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi><mo>=</mo><mi>k</mi><mi>n</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14240 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>, differentia inter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14241 Triangula similia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14242 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14243 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> one arc <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14244 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> the other <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14245 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi><mo>=</mo><mi>a</mi><mi>b</mi><mo>=</mo><mi>k</mi><mi>m</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14246 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14247 Therefore angles <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>o</mi><mi>g</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>e</mi><mi>d</mi></mstyle></math> are equal <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14248 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math> are parallels <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14249 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi><mo>=</mo><mi>k</mi><mi>n</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14250 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>c</mi></mstyle></math>, the difference between <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14251 Similar triangles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14252 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14253 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14254 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14255 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14256 <s xml:id="echoid-s1552" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14257 Differentia minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14258 quadrante. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14259 Utraque peripheria <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14260 etiam minor,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14261 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14262 Difference less than a quadrant; each arc also less.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14263 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14264 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14265 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14266 <pb file="add_6782_f449v" o="449v" n="899"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14267 <pb file="add_6782_f450" o="450" n="900"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14268 <div xml:id="echoid-div291" type="page_commentary" level="2" n="291">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14269 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14270 <s xml:id="echoid-s1553" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14271 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14272 <s xml:id="echoid-s1553" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14273 The reference on this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14274 <emph style="it">Variorum responsorum liber VIII</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14275 Chapter 14, Proposition 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14276 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14277 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14278 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14279 Propositio I. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14280 Datis duabus inæqualibus lineis, una recta, altera circulari, invenire lineam rectam
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14281 minorem majore datarum, & majorem minore.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14282 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14283 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14284 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14285 Given two unequal lines, one straight, the other circular, to find a straight line
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14286 less than the greater of those given, and greater than the lesser.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14287 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14288 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14289 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14290 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14291 <head xml:id="echoid-head203" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14292 Resp. lib. 8. cap. 14. prop. 1. pag. 23
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14293 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14294 Responsorum liber VIII, Chapter 14, Proposition 1, page 23.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14295 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14296 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14297 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14298 <s xml:id="echoid-s1555" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14299 Datis duabus inæqualibus lineis: una recta, altera circulari: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14300 invenire lineam rectam, minorem majore datarum et majorem minore.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14301 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14302 Given two unequal lines, one straight, the other circular, to find a straight line
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14303 less than the greater of those given, and greater than the lesser.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14304 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14305 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14306 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14307 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14308 <s xml:id="echoid-s1556" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14309 Casus primus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14310 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14311 First case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14312 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14313 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14314 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14315 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14316 <s xml:id="echoid-s1557" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14317 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> recta. maior. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14318 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi></mstyle></math> circularis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14319 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math> Excessus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14320 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math> Circulari
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14321 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14322 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> be the straight line, greater. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14323 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi></mstyle></math> the circular line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14324 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math> the excess <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14325 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math> the circular line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14326 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14327 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14328 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14329 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14330 <s xml:id="echoid-s1558" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14331 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> maior circulari <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14332 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> quæcunque maior <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14333 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14334 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> is greater than the circular line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14335 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> is any quantity greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14336 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14337 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14338 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14339 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14340 <s xml:id="echoid-s1559" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14341 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>.</mo><mi>G</mi><mo>.</mo><mi>H</mi><mo>-</mo><mi>Z</mi><mo>.</mo><mi>A</mi></mstyle></math> quæsita linea <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14342 Nam subducendo ab <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>-</mo><mi>Z</mi></mstyle></math>. remanabit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14343 et a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>. remanabit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14344 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> igitur est minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14345 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14346 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>:</mo><mi>G</mi><mo>=</mo><mi>H</mi><mo>-</mo><mi>Z</mi><mo>:</mo><mi>A</mi></mstyle></math>, the line sought. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14347 For subtracting <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>-</mo><mi>Z</mi></mstyle></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math>, there remains <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>, there remains <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14348 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> is therefore less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14349 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14350 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14351 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14352 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14353 <s xml:id="echoid-s1560" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14354 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>.</mo><mi>G</mi><mo>.</mo><mi>Z</mi><mo>.</mo><mi>F</mi></mstyle></math> minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14355 et subducendo: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14356 Ergo collata ista proportione cum prima: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi><mo>=</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14357 Cum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> sit minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi></mstyle></math> est Maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14358 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> est Maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>. et minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14359 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14360 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>:</mo><mi>G</mi><mo>=</mo><mi>Z</mi><mo>:</mo><mi>F</mi></mstyle></math> less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14361 and subtracting: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14362 Therefore, combining this proportion with the first, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi><mo>=</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14363 Since <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14364 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math> and less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14365 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14366 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14367 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14368 <pb file="add_6782_f450v" o="450v" n="901"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14369 <pb file="add_6782_f451" o="451" n="902"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14370 <div xml:id="echoid-div292" type="page_commentary" level="2" n="292">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14371 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14372 <s xml:id="echoid-s1561" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14373 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14374 <s xml:id="echoid-s1561" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14375 This page is a continuation of Add MS 6782, f. 450, on Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14376 <emph style="it">Variorum responsorum liber VIII</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14377 Chapter 14, Proposition 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14378 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14379 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14380 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14381 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14382 <head xml:id="echoid-head204" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14383 Casus primus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14384 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14385 First case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14386 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14387 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14388 <pb file="add_6782_f451v" o="451v" n="903"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14389 <pb file="add_6782_f452" o="452" n="904"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14390 <div xml:id="echoid-div293" type="page_commentary" level="2" n="293">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14391 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14392 <s xml:id="echoid-s1563" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14393 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14394 <s xml:id="echoid-s1563" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14395 This page is a continuation of Add MS 6782, f. 450 and f. 451, on Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14396 <emph style="it">Variorum responsorum liber VIII</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14397 Chapter 14, Proposition 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14398 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14399 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14400 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14401 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14402 <head xml:id="echoid-head205" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14403 Resp. lib. 8. cap. 14. prop. 1. pag. 23
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14404 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14405 Responsorum liber VIII, Chapter 14, Proposition 1, page 23.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14406 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14407 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14408 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14409 <s xml:id="echoid-s1565" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14410 Casus secundus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14411 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14412 Second case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14413 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14414 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14415 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14416 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14417 <s xml:id="echoid-s1566" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14418 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> recta. minor. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14419 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi></mstyle></math> circularis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14420 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math> Excessus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14421 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14422 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> be the straight line, lesser. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14423 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi></mstyle></math> the circular line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14424 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math> the excess
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14425 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14426 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14427 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14428 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14429 <s xml:id="echoid-s1567" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14430 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> minor circulari
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14431 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14432 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> is less than the circular line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14433 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14434 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14435 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14436 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14437 <s xml:id="echoid-s1568" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14438 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>.</mo><mi>G</mi><mo>.</mo><mi>H</mi><mo>+</mo><mi>Z</mi><mo>.</mo><mi>E</mi></mstyle></math> quæsita linea <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14439 Et subducendo ab <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>+</mo><mi>Z</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math>: remanabit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14440 et ab <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. remanabit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi><mo>-</mo><mi>G</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14441 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> igitur maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14442 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14443 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>:</mo><mi>G</mi><mo>=</mo><mi>H</mi><mo>+</mo><mi>Z</mi><mo>:</mo><mi>E</mi></mstyle></math>, the line sought. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14444 For subtracting <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>+</mo><mi>Z</mi></mstyle></math>, there remains <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math>, there remains <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi><mo>-</mo><mi>G</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14445 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> is therefore greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14446 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14447 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14448 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14449 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14450 <s xml:id="echoid-s1569" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14451 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>.</mo><mi>G</mi><mo>.</mo><mi>Z</mi><mo>.</mo><mi>F</mi></mstyle></math> minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14452 Et per additione: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14453 Ergo, collata ista proportione cum prima: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>+</mo><mi>F</mi><mo>=</mo><mi>E</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14454 Cum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> sit minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>+</mo><mi>F</mi></mstyle></math> est minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>+</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14455 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> est minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>+</mo><mi>Z</mi></mstyle></math>. et Maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14456 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14457 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>:</mo><mi>G</mi><mo>=</mo><mi>Z</mi><mo>:</mo><mi>F</mi></mstyle></math> less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14458 And by addition: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14459 Therefore, combining this proportion with the first, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>+</mo><mi>F</mi><mo>=</mo><mi>E</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14460 Since <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>+</mo><mi>F</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>+</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14461 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math> and greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14462 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14463 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14464 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14465 <pb file="add_6782_f452v" o="452v" n="905"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14466 <pb file="add_6782_f453" o="453" n="906"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14467 <div xml:id="echoid-div294" type="page_commentary" level="2" n="294">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14468 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14469 <s xml:id="echoid-s1570" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14470 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14471 <s xml:id="echoid-s1570" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14472 This page appears to be a continuation of Harriot's work on Add MS 6782, f. 450 and f. 452,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14473 on Proposition 1 from Viète's <emph style="it">Variorum responsorum liber VIII</emph>, Chapter 14.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14474 Here he also refers to Euclid's <emph style="it">Elements</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14475 Book III, Proposition 16.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14476 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14477 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14478 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14479 III.16 The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14480 and into the space between the straight line and the circumference another straight line cannot be interposed;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14481 further the angle of the semicircle is greater, and the remaining angle less, than any acute rectilineal angle.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14482 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14483 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14484 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14485 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14486 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14487 <s xml:id="echoid-s1572" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14488 Si angulus semicirculi sit minor recto rectilineo: dabitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14489 angulus rectilineus maior angulo semicirculi et minor recto <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14490 rectilineo. Contra Eculidem lib. 3. prop. 16.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14491 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14492 If the angle in a semicircle is less than a right angle,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14493 there may be found an angle greater than the angle in the semicircle and less than a right angle.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14494 Against Euclid III.16.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14495 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14496 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14497 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14498 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14499 <s xml:id="echoid-s1573" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14500 Si angulus rectus et maior angulo semicirculi. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14501 Differentia inter angulum rectum et angulum semicurculi. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14502 Ergo angulus semicirculi. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14503 Et sit aliquis angulus rectilineus maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>H</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14504 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14505 Suppose a right angle is greater than the angle in a semicircle, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14506 The difference between the right angle and the angle in the semicircle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14507 Therefore the angle in the semicircle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14508 And let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> be any angle greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14509 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14510 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14511 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14512 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14513 <s xml:id="echoid-s1574" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14514 Tum ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> ita <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>-</mo><mi>Z</mi></mstyle></math> ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14515 aliquem <emph style="super">rectilineum</emph> angulum ... qui <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14516 minor est quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> et maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14517 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14518 Then as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> is to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> so <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>-</mo><mi>Z</mi></mstyle></math> is to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>, another angle which is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> and greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14519 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14520 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14521 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14522 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14523 <s xml:id="echoid-s1575" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14524 Nam subducendo ab <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>-</mo><mi>Z</mi></mstyle></math>: remanebit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14525 et ab <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>: remanebit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14526 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>.</mo><mi>G</mi><mo>.</mo><mi>Z</mi><mo>.</mo><mi>G</mi><mo>-</mo><mi>A</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> igitur minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14527 Et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>.</mo><mi>G</mi><mo>.</mo><mi>Z</mi><mo>.</mo><mi>F</mi></mstyle></math> minorem quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14528 Ergo subducendo erit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14529 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>.</mo><mi>G</mi><mo>.</mo><mi>H</mi><mo>-</mo><mi>Z</mi><mo>.</mo><mi>G</mi><mo>-</mo><mi>F</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14530 Ergo collata ista proportione cum prima: erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi><mo>=</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14531 Et: cum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> sit minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi></mstyle></math> est Maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14532 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> est Maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math> et minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14533 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14534 Now subtracting <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>-</mo><mi>Z</mi></mstyle></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> there remains <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>; and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>, there remains <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14535 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>:</mo><mi>G</mi><mo>=</mo><mi>Z</mi><mo>:</mo><mi>G</mi><mo>-</mo><mi>A</mi></mstyle></math>, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14536 And <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>:</mo><mi>G</mi><mo>=</mo><mi>Z</mi><mo>:</mo><mi>F</mi></mstyle></math> less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14537 Therefore, subtracting, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14538 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mo>:</mo><mi>G</mi><mo>=</mo><mi>H</mi><mo>-</mo><mi>Z</mi><mo>:</mo><mi>G</mi><mo>-</mo><mi>F</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14539 Therefore, combining this proportion with the first, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi><mo>=</mo><mi>A</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14540 And since <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>F</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14541 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi><mo>-</mo><mi>Z</mi></mstyle></math> and less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14542 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14543 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14544 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14545 <pb file="add_6782_f453v" o="453v" n="907"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14546 <pb file="add_6782_f454" o="454" n="908"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14547 <div xml:id="echoid-div295" type="page_commentary" level="2" n="295">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14548 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14549 <s xml:id="echoid-s1576" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14550 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14551 <s xml:id="echoid-s1576" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14552 The reference on this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14553 <emph style="it">Variorum responsorum liber VIII</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14554 Chapter 14, Proposition 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14555 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14556 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14557 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14558 Propositio III. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14559 Circulo dato, & linea recta in eo inscripta, quæ diametro minor existat,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14560 & alia insuper quæ circulum tangat in inscriptæ termino, educere lineam e centro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14561 ita secantem circulum & ipsam tangentem, ut pars educate e centro interjacens
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14562 inter cirumferentiam & inscriptam se habeat ad partem tangentis quæ est inter contactum & ipsam eductam,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14563 sicut dimidia inscripta ad majorem ea quæ ex centro inscriptam illam bisariam secat.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14564 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14565 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14566 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14567 Given a circle and a straight line inscribed in it, less than the diameter,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14568 and also a line that touches the circle at the end of the inscribed line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14569 to draw a line from the centre cutting the circle and the tangent, so that the part drawn from the centre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14570 lying between the circumference and the inscribed line is to the part of the tangent
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14571 between the contact and the drawn line as half the inscribed line to a line longer than that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14572 drawn from the centre bisecting the inscribed line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14573 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14574 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14575 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14576 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14577 <head xml:id="echoid-head206" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14578 In Caput 14. Responsorum vieta prop. 3. pa. 24
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14579 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14580 From Chapter 14 of Viète's Responsorum, Proposition 3, page 24.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14581 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14582 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14583 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14584 <s xml:id="echoid-s1578" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14585 et subducendo:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14586 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14587 and subtracting:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14588 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14589 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14590 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14591 <pb file="add_6782_f454v" o="454v" n="909"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14592 <pb file="add_6782_f455" o="455" n="910"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14593 <div xml:id="echoid-div296" type="page_commentary" level="2" n="296">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14594 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14595 <s xml:id="echoid-s1579" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14596 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14597 <s xml:id="echoid-s1579" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14598 The reference on this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14599 <emph style="it">Variorum responsorum liber VIII</emph>, Chapter 9, Proposition 13.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14600 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14601 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14602 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14603 Et si fuerint lineæ quotcunque sese excedentes, fit autem prima excessui aequalis,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14604 fiunt ab iis quatuor solida coninue proportionalia, qualia sequntur. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14605 Primum, Cubus minimæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14606 Secundum, Cubus compositæ ex maxima & minima, multaus adgregato cuborum minimæ & maximæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14607 Tertium, Adgregatum cuborume singulis ter duodecuplum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14608 Quartum, Cubus compositæ ex omnibus sextuplae.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14609 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14610 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14611 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14612 And if there are any number of lines exceeding each other, and moreover the first differences are equal,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14613 there arise from them four solids in continued proportion, which are as follows. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14614 First, the cube of the least. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14615 Second, the cube of the sum of the greatest and least, reduced by the sum of the cubes of the least and the greatest. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14616 Third, the sum of the cubes of each taken 36 times. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14617 Fourth, the cube of the sum of all, taken six times.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14618 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14619 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14620 <s xml:id="echoid-s1580" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14621 Note that in his initial calculations, expressed in terms of geometric solids,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14622 Harriot retains homogeneity by writing, for example, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>1</mn></mstyle></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14623 In the second column, where he moves from a geometric to arithmetic interpretation,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14624 he simplifies the notation by dropping the 1s.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14625 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14626 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14627 <s xml:id="echoid-s1581" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14628 For Harriot's teaching on progressions, see in particular Add MS 6782, f. 107 to f. 146v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14629 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14630 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14631 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14632 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14633 <head xml:id="echoid-head207" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14634 In propositione 13, cap.9. lib. 8. respons. pag. 14. b. Vietæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14635 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14636 From Proposition 13, Chapter 9, Liber VIII responsorum, page 14v, of Viète
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14637 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14638 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14639 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14640 <s xml:id="echoid-s1583" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14641 propositio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14642 Si fuerint lineæ quotcunque sese excedentes, fit autem prima excessui aequalis, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14643 fiunt ab iis quatuor solida coninue proportionalia, qualia sequntur. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14644 Primum, Cubus minimæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14645 Secundum, Cubus compositæ ex maxima et minima, multaus aggregato <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14646 cuborum minimæ et maximæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14647 Tertium, Adgregatum cuborume singulis ter duodecuplum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14648 Quartum, Cubus compositæ ex omnibus sextuplae.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14649 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14650 If there are any number of lines exceeding each other, and moreover the first differences are equal,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14651 there arise from them four solids in continued proportion, which are as follows. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14652 First, the cube of the least. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14653 Second, the cube of the sum of the greatest and least, reduced by the sum of the cubes of the least and the greatest. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14654 Third, the sum of the cubes of each taken 36 times. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14655 Fourth, the cube of the sum of all, taken six times.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14656 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14657 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14658 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14659 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14660 <s xml:id="echoid-s1584" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14661 Sit minima 1. maxima 4. Summa omnia sextupla sit 60. et sunt continuo <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14662 proportionalia solida. 1. 60. 360. 21600.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14663 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14664 Let the least quantity be 1, the greatest 4. Six times the sum of all of them is 60,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14665 and the proportional solids are 1, 60, 360, 21600.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14666 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14667 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14668 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14669 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14670 <s xml:id="echoid-s1585" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14671 Sit prima linea et excessus 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14672 et numerus linearum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14673 Summa <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>, sive triangulus numerus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14674 ipsius <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math> erit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi><mi>n</mi><mo>+</mo><mn>1</mn><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14675 cuius quadratum erit: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14676 atque hoc est per doctrina progressionum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14677 summa cuborum singulis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14678 Eis ter duodecuplum erit: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14679 Hoc est: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14680 pro 3<emph style="super">o</emph> solido
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14681 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14682 Let the first line and the excess be 1, and <lb/> the number of lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14683 Their sum, or triangular number, will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi><mi>n</mi><mo>+</mo><mn>1</mn><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>, whose square is: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14684 and by the doctrine of progressions, this is the sum of individual cubes. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14685 Three times their 12-tuple will be: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14686 That is: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14687 for the 3rd solid.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14688 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14689 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14690 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14691 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14692 <s xml:id="echoid-s1586" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14693 Composita ex maxima et minima <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>+</mo><mn>1</mn></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14694 Eius cubus erit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14695 Cubis multatis; erit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14696 pro 2<emph style="super">o</emph> solido
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14697 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14698 The sum of the greatest and least is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mo>+</mo><mn>1</mn></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14699 Its cube will be: </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14700 The cubes having been subtracted this will be: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14701 for the 2nd solid.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14702 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14703 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14704 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14705 <s xml:id="echoid-s1587" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14706 Composita ex omnibus ut supra <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi><mi>n</mi><mo>+</mo><mn>1</mn><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14707 Eius sextupla: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14708 Hoc est: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14709 Eius quadratum: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14710 Eius cubus: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14711 pro 4<emph style="super">o</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14712 solido <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14713 Quadratum si <emph style="st">dividatur</emph> <emph style="super">multiplicatur</emph> per 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14714 <emph style="st">[???]</emph> <emph style="super">primam lineam</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14715 faciet <emph style="st">secundum</emph> <emph style="super">tertium</emph> solidum ut supra.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14716 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14717 The sum of all, as above, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>n</mi><mi>n</mi><mo>+</mo><mn>1</mn><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14718 Six time this: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14719 That is: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14720 Its square: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14721 Its cube: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14722 for the 4th solid. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14723 The square, if the first line is multiplied by 1, makes the third solid, as above.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14724 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14725 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14726 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14727 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14728 <s xml:id="echoid-s1588" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14729 Solida continue proportionales
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14730 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14731 The continually proportional solids
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14732 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14733 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14734 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14735 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14736 <s xml:id="echoid-s1589" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14737 proportionalis operatio, dato primo <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14738 et secundo, inveniet 3<emph style="super">um</emph> et 4<emph style="super">tum</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14739 sub maiori formam notari sed <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14740 per reductionem; æqualia sunt illis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14741 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14742 The operation of proportion, given the first and second, will find the 3rd and 4th, under a greater form of notation,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14743 but by reduction, they are equal.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14744 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14745 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14746 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14747 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14748 <s xml:id="echoid-s1590" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14749 pro numeris vel numeris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14750 solidarum talis potest <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14751 esse notatio: et si fit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14752 in forma heterogenea. Vel: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14753 ennuntiari potest per lineas.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14754 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14755 for numbers, or solid numbers, the notation my be thus; and if done in heteregenous form.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14756 Or it may be expressed in lines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14757 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14758 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14759 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14760 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14761 <s xml:id="echoid-s1591" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14762 datis primo et secundo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14763 proportionalis operatio 3<emph style="super">um</emph> & 4<emph style="super">um</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14764 invenient ut sunt.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14765 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14766 given the first and second, by the operation of proportions, the 3rd and 4th may be found and are:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14767 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14768 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14769 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14770 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14771 <s xml:id="echoid-s1592" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14772 Nota, quod <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14773 etiam proportio potest <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14774 inveniri per plana <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14775 per lineas <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14776 per plano-plana &c. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14777 et eadem modi demonstrari. Etiam: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14778 proportionalia possunt fieri plano numero <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14779 ad libitum secundum nostram doctrinam de <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14780 progressionibus, quæ per traditiones veterum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14781 fieri non potuit.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14782 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14783 Note, that the proportion may also be found by planes, lines, plano-planes, etc.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14784 and demosntrated by the same method. Also, the proportionals may arise from plane numbers at will
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14785 according to my doctrine of progressions, which by old teachings could not be done.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14786 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14787 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14788 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14789 <pb file="add_6782_f455v" o="455v" n="911"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14790 <pb file="add_6782_f456" o="456" n="912"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14791 <div xml:id="echoid-div297" type="page_commentary" level="2" n="297">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14792 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14793 <s xml:id="echoid-s1593" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14794 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14795 <s xml:id="echoid-s1593" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14796 This page contains Harriot's working of Zetetic 10, the last from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14797 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14798 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14799 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14800 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14801 Zeteticum X <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14802 Invenire duo latera, quorum differentia fit ea quæ præscribitur,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14803 & præterea præfinitae unciæ primi, multatæ præfinitis unciis secundi,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14804 æquent differentiam quoque inter eas datam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14805 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14806 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14807 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14808 To find two lines, whose difference is prescribed,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14809 and also such that a fixed part of the first taken from a fixed part of the second
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14810 is likewise equal to a given difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14811 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14812 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14813 <s xml:id="echoid-s1594" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14814 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the difference between the two lines,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14815 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14816 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14817 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the gvien difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14818 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the parts of the first and second lines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14819 Harriot worked through the three cases given by Viète, using his own notation. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14820 The work is continued using numbers on Add MS 6782, f. 459.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14821 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14822 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14823 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14824 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14825 <head xml:id="echoid-head208" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14826 Zetet. lib. 1. Zet. 10. et primi lib. ultimum Sept. 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14827 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14828 Zetetica, Book I, Zetetic 10, and the last of the first book. September 6
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14829 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14830 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14831 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14832 <s xml:id="echoid-s1596" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14833 Invenire duo latera, quorum differentia sit ea quæ præscribitur, et præterea <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14834 præfinitæ unciæ lateris primi multatæ præfinitis unciis secundi, æquent <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14835 differentiam quoque inter eas datam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14836 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14837 To find two lines, whose difference is prescribed,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14838 and also such that a fixed part of the first subtracted from a fixed part of the second
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14839 is likewise equal to a given difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14840 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14841 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14842 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14843 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14844 <s xml:id="echoid-s1597" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14845 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. data differentia 2<emph style="super">orum</emph> laterum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14846 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. primum latus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14847 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. secundum latus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14848 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. portio primi lateri. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14849 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14850 hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>,</mo><mi>o</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14851 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. portio secundi lateris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14852 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14853 hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>e</mi><mo>,</mo><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14854 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>. differentia data <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>a</mi><mo>-</mo><mi>e</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14855 unde: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>+</mo><mi>e</mi><mo>=</mo><mi>a</mi></mstyle></math>. et: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>h</mi><mo>=</mo><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14856 Quæruntur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14857 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14858 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, the given difference between the two lines. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14859 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, the first line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14860 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, the second line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14861 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, the portion of the first line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14862 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math>, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14863 that is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>a</mi><mo>:</mo><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14864 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, the portion of the second line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14865 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math>, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14866 that is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>e</mi><mo>:</mo><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14867 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>, the given difference, equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14868 whence: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>+</mo><mi>e</mi><mo>=</mo><mi>a</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>h</mi><mo>=</mo><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14869 There are sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14870 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14871 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14872 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14873 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14874 <s xml:id="echoid-s1598" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14875 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. primum latus intelligitur maius duarum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14876 vel minus; sive ab eo exigantur unciæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14877 maioris vel minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14878 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14879 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, the first line can be understood to be the greater of the two, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14880 or the smaller; whether from it are taken greater fractions or smaller.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14881 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14882 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14883 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14884 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14885 <s xml:id="echoid-s1599" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14886 1. casus. sit primum latus maius: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14887 et exigantur ab eo maioris unciæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14888 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> portio primi lateris. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14889 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> portio secundi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14890 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14891 Case 1. Let the first line be greater, and from it are taken greater fractions. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14892 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the portion of the first line, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> the portion of the second line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14893 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14894 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14895 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14896 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14897 <s xml:id="echoid-s1600" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14898 PorrÃ², sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, portio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14899 secundi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14900 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14901 Further, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the portion of the second line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14902 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14903 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14904 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14905 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14906 <s xml:id="echoid-s1601" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14907 2. casus. sit primum latus maius <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14908 et exigantur ab eo minoris unciæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14909 hoc est ponatur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14910 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14911 Case 2. Let the first line be greater, and from it are taken smaller fractions,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14912 that is, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> is supposed less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14913 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14914 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14915 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14916 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14917 <s xml:id="echoid-s1602" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14918 PorrÃ², sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, portio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14919 secundi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14920 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14921 Further, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the portion of the second line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14922 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14923 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14924 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14925 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14926 <s xml:id="echoid-s1603" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14927 Nota. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14928 Hinc apparet quod <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> debet esse. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14929 In primo casu maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, ac etiam quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14930 In secundo casu minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, vel <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14931 In tertio maior vel minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> vel <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14932 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14933 Note. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14934 Here it is clear what <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> must be. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14935 In the first case, greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> and also than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14936 In the second case, less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14937 In the third, greater or less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14938 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14939 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14940 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14941 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14942 <s xml:id="echoid-s1604" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14943 3. casus. sit primum latus minus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14944 et exigantur ab eo maioris unciæ. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14945 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> portio primi lateris. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14946 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> portio secundi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14947 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14948 Case 3. Let the first line be smaller, and from it ar taken greater fractions. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14949 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> is the portion of the first line, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> the portion of the second line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14950 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14951 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14952 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14953 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14954 <s xml:id="echoid-s1605" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14955 PorrÃ², sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, portio secundi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14956 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14957 Further, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the portion of the second line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14958 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14959 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14960 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14961 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14962 <s xml:id="echoid-s1606" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14963 * Nota. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14964 Hinc facile apparet quod minores <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14965 unciæ non possunt exigi Ã primo latere <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14966 cum sit minus. Atque ideo non <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14967 datur quartus casus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14968 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14969 * Note. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14970 Here is is easily seen that smaller fractions cannot be taken from the first line since it is smaller.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14971 And therefore therefore no fourth case is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14972 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14973 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14974 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14975 <pb file="add_6782_f456v" o="456v" n="913"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14976 <pb file="add_6782_f457" o="457" n="914"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14977 <div xml:id="echoid-div298" type="page_commentary" level="2" n="298">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14978 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14979 <s xml:id="echoid-s1607" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14980 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14981 <s xml:id="echoid-s1607" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14982 This page contains the continuation of Harriot's working of Zetetic 7 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14983 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14984 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14985 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14986 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14987 Zeteticum VII <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14988 Datum latus ita secare, ut praefinitae unciae unius segmenti, adjunctae praefinitis unciis alterius:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14989 aequent summam praescriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14990 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14991 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14992 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14993 To cut a given line in such a way that a fixed part of one segment, added to a fixed part of the other,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14994 is equal to a prescribed sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14995 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14996 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14997 <s xml:id="echoid-s1608" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14998 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the whole line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	14999 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15000 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15001 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the prescribed sum,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15002 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the unknown parts of the first and second segments.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15003 Harriot followed Viète's method on Add MS 6782, f. 458.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15004 Here he works the same problem using numbers instead of lengths.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15005 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15006 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15007 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15008 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15009 <head xml:id="echoid-head209" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15010 Zet. lib. 1. Zet. 7.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15011 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15012 Zetetica, Book I, Zetetic 7
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15013 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15014 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15015 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15016 <s xml:id="echoid-s1610" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15017 Dividere numerum <emph style="super">datum</emph> in duas partes, ita ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15018 <emph style="super">unius</emph> primæ partis additæ, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>, secundæ: æquet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15019 summam præscriptam. oportuit ut summa præscripta sit
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15020 minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> numeri dati et maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15021 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15022 To divide a given number into two parts, so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of one, the first part,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15023 added to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> of the second equals a prescribed sum;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15024 the prescribed sum must be less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the given number and greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15025 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15026 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15027 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15028 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15029 <s xml:id="echoid-s1611" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15030 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. sit numerus datus. 60 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15031 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. igitur 15. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15032 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> erit 10. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15033 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> summa præscribenda debet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15034 esse maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, et minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15035 quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. sit ergo 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15036 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15037 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the given number, 60. Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> is 15 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> will be 10. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15038 The prescribed sum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> must be grater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> and less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, therefore let it be 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15039 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15040 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15041 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15042 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15043 <s xml:id="echoid-s1612" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15044 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. prima pars. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15045 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> primæ partis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15046 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15047 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> be the first part, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the first part.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15048 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15049 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15050 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15051 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15052 <s xml:id="echoid-s1613" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15053 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. secunda pars. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15054 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>: eius <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15055 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15056 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math> be the second part, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> of it.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15057 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15058 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15059 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15060 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15061 <s xml:id="echoid-s1614" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15062 hac analogia ita solvitur problema. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15063 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15064 Ergo. 36. erit secunda pars. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15065 6. erit eius <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15066 6. est <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi><mo>æ</mo></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15067 quæ æquat 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15068 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15069 The problem is thus solved by this ratio. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15070 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15071 Therefore 36 will be the second part. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15072 6 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> of it, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15073 6 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the first part <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15074 which makes 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15075 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15076 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15077 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15078 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15079 <s xml:id="echoid-s1615" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15080 aliter. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15081 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15082 Ergo. 24. erit prima pars. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15083 6. eius <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15084 6. est <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mi>s</mi><mi>e</mi><mi>c</mi><mi>u</mi><mi>n</mi><mi>d</mi><mo>æ</mo></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15085 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15086 Another way <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15087 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15088 Therefore 24 will be the first part. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15089 6 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of it, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15090 6 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> of the second part
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15091 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15092 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15093 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15094 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15095 <s xml:id="echoid-s1616" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15096 Aliud exemplum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15097 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15098 Another example
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15099 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15100 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15101 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15102 <pb file="add_6782_f457v" o="457v" n="915"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15103 <pb file="add_6782_f458" o="458" n="916"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15104 <div xml:id="echoid-div299" type="page_commentary" level="2" n="299">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15105 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15106 <s xml:id="echoid-s1617" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15107 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15108 <s xml:id="echoid-s1617" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15109 This is the first of several pages in which Harriot worked on Zetetica 7 to 10 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15110 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15111 Harriot at first treated the problems exactly as Viète had done, using the geometric language in which the word
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15112 <foreign xml:lang="lat">latus</foreign> represents an unknown line, side, or root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15113 However, in each case Harriot then switched from geometry to arithmetic,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15114 treating the known and unkown quantities as numbers rather than geometrical quantities.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15115 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15116 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15117 <s xml:id="echoid-s1618" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15118 This page contains Harriot's working of Zetetic 7.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15119 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15120 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15121 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15122 Zeteticum VII <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15123 Datum latus ita secare, ut præfinitæ unciæ unius segmenti, adjunctae præfinitis unciis alterius:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15124 æquent summam præscriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15125 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15126 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15127 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15128 To cut a given line in such a way that a fixed part of one segment, added to a fixed part of the other,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15129 is equal to a prescribed sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15130 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15131 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15132 <s xml:id="echoid-s1619" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15133 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the whole line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15134 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15135 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15136 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the prescribed sum,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15137 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the parts of the first and second segments.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15138 Harriot repeated Viète's working in his own notation, and also added some variants of his own.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15139 The numbers at the bottom of the page are taken from Viète.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15140 On Add MS 6782, f. 457, Harriot worked the same problem with further numerical examples.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15141 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15142 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15143 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15144 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15145 <head xml:id="echoid-head210" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15146 Lib. 1. Zetet. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15147 Zet. 7.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15148 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15149 Zetetica, Book I, Zetetic 7
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15150 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15151 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15152 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15153 <s xml:id="echoid-s1621" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15154 Datum latus ita secare, ut præfinitæ unciæ unius segmenti, adjunctae præfinitis unciis alterius:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15155 æquent summam præscriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15156 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15157 To cut a given line in such a way that a fixed part of one segment, added to a fixed part of the other,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15158 is equal to a prescribed sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15159 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15160 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15161 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15162 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15163 <s xml:id="echoid-s1622" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15164 sit datum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. latus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15165 et duo segmenta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15166 portio primæ segmenti <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15167 ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>: ita debet esse: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15168 summa præscripta sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15169 Ergo portio 2<emph style="super">i</emph> segmenti erit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15170 ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>: ita debet esse: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15171 Quæretur iam: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, et, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, segmenta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15172 et segmentorum portiones.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15173 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15174 Let the given line be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, and the two segments <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15175 The portion of the first segment is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>; as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> is to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, so must be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15176 The prescribed sum is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15177 Therefore the portion of the second segment will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15178 As <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> is to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, so must be % h - a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>t</mi><mi>o</mi></mstyle></math> u <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>.</mo></mstyle></math><lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15179 There are now sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, the segments, and the portions of the segments.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15180 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15181 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15182 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15183 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15184 <s xml:id="echoid-s1623" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15185 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> minor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> et maior <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15186 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15187 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> and greater then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15188 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15189 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15190 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15191 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15192 <s xml:id="echoid-s1624" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15193 Aliter. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15194 Sit portio secundæ segmenti, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15195 Ergo portio primæ segmenti <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15196 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15197 Another way. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15198 Let the portion of the second segment be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15199 Therefore the portion of the first segment is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15200 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15201 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15202 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15203 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15204 <s xml:id="echoid-s1625" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15205 Dantur etiam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, per superiores analogias.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15206 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15207 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math> are also given by the above ratios.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15208 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15209 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15210 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15211 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15212 <s xml:id="echoid-s1626" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15213 Additio nostra. Aliter.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15214 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15215 An addition of my own. Another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15216 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15217 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15218 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15219 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15220 <s xml:id="echoid-s1627" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15221 Aliter.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15222 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15223 Another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15224 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15225 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15226 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15227 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15228 <s xml:id="echoid-s1628" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15229 Nota. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15230 Etsi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, sit maior <emph style="super">quam</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>; est [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15231 minor <emph style="super">quam</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> per suppositione: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15232 Sed <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> est præscribenda ut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15233 sit minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, et maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15234 ut apparet per inventis analogijs.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15235 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15236 Note. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15237 Although <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, it is [???] less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> by supposition. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15238 But <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is prescribed so that it is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> and greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15239 as is clear from the ratios found.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15240 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15241 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15242 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15243 <pb file="add_6782_f458v" o="458v" n="917"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15244 <pb file="add_6782_f459" o="459" n="918"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15245 <div xml:id="echoid-div300" type="page_commentary" level="2" n="300">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15246 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15247 <s xml:id="echoid-s1629" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15248 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15249 <s xml:id="echoid-s1629" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15250 This page contains Harriot's working of Zetetic 10, the last from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15251 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15252 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15253 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15254 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15255 Zeteticum X <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15256 Invenire duo latera, quorum differentia fit ea quæ præscribitur,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15257 & præterea præfinitae unciæ primi, multatæ præfinitis unciis secundi,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15258 æquent differentiam quoque inter eas datam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15259 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15260 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15261 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15262 To find two lines, whose difference is prescribed,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15263 and also such that a fixed part of the first taken from a fixed part of the second
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15264 is likewise equal to a given difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15265 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15266 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15267 <s xml:id="echoid-s1630" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15268 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the difference between the two lines,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15269 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15270 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15271 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the gvien difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15272 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the parts of the first and second lines. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15273 Harriot followed Viète's method on Add MS 6782, f. 456.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15274 Here he works the same problem using numbers instead of lengths.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15275 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15276 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15277 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15278 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15279 <head xml:id="echoid-head211" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15280 Zetet. lib. 1. Zet. 10. et ultimum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15281 Exempla in numeris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15282 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15283 Zetetica, Book I, Zetetic 10, and the last. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15284 Examples in numbers.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15285 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15286 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15287 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15288 <s xml:id="echoid-s1632" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15289 1. Casus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15290 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15291 Case 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15292 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15293 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15294 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15295 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15296 <s xml:id="echoid-s1633" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15297 3. Casus. Ubi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> est maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15298 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15299 Case 3. Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15300 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15301 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15302 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15303 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15304 <s xml:id="echoid-s1634" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15305 3. Casus. Ubi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> est minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15306 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15307 Case 3. Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15308 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15309 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15310 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15311 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15312 <s xml:id="echoid-s1635" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15313 2. Casus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15314 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15315 Case 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15316 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15317 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15318 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15319 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15320 <s xml:id="echoid-s1636" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15321 Additio. 3. Casus. Ubi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> et minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15322 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15323 An addition. Case 3. Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> and less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15324 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15325 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15326 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15327 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15328 <s xml:id="echoid-s1637" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15329 Si <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> sit æqualis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> vel <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> non variat casum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15330 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15331 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> the case does not change.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15332 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15333 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15334 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15335 <pb file="add_6782_f459v" o="459v" n="919"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15336 <pb file="add_6782_f460" o="460" n="920"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15337 <div xml:id="echoid-div301" type="page_commentary" level="2" n="301">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15338 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15339 <s xml:id="echoid-s1638" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15340 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15341 <s xml:id="echoid-s1638" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15342 This page contains Harriot's working of Zetetic 9 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15343 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15344 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15345 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15346 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15347 Zeteticum IX <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15348 Invenire duo latera, quorum differentia sit ea quæ præscribitur,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15349 & præterea præfinitæ unciæ lateris unius, adjectæ præfinitis unciis alterius,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15350 æquabunt summam præscriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15351 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15352 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15353 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15354 To find two lines, whose difference is prescribed,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15355 and also such that a fixed part of one line added to a fixed part of the other is equal to a prescibed sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15356 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15357 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15358 <s xml:id="echoid-s1639" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15359 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the difference between the two lines,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15360 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15361 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15362 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the prescribed sum,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15363 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the parts of the first and second lines.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15364 Harriot repeated Viète's working in his own notation, and also added some variants of his own. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15365 The work is continued using numerical examples on Add MS 6782, f. 461.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15366 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15367 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15368 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15369 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15370 <head xml:id="echoid-head212" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15371 Zetet. Lib. 1. Zet. 9.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15372 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15373 Zetetica, Book I, Zetetic 9
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15374 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15375 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15376 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15377 <s xml:id="echoid-s1641" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15378 Invenire duo latera, quorum differentia sit ea quæ præscribitur, et præterea <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15379 præfinitæ unciæ lateris unius adjectæ præfinitis unciis alterius: æquabunt <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15380 summam præscriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15381 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15382 To find two lines, whose difference is prescribed,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15383 and also such that a fixed part of one line added to a fixed part of the other is equal to a prescribed sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15384 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15385 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15386 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15387 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15388 <s xml:id="echoid-s1642" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15389 Nota. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15390 Summa præscripta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15391 videlicet <emph style="st">debe</emph><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> debet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15392 esse maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, ut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15393 per postremis <emph style="st">notat</emph> infra <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15394 notatis analogijs appa-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15395 rebit <emph style="super">scilicet</emph> in primo casu. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15396 In secundo casu <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15397 primum latus ponitur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15398 minus, oportet ut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15399 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> fit maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15400 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15401 Note. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15402 The prescribed sum, namely <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>, must be grater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15403 as is apparent from the ratio written afterwards below in the first case. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15404 In the second case, where the first line is supposed smaller, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> must be greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15405 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15406 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15407 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15408 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15409 <s xml:id="echoid-s1643" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15410 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. data differentia 2<emph style="super">orum</emph> laterum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15411 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. primum latus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15412 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. secundum latus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15413 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. portio primi lateri. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15414 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15415 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>,</mo><mi>o</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15416 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. portio secundi lateris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15417 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15418 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>e</mi><mo>,</mo><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15419 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>. Summa præscripta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>a</mi><mo>+</mo><mi>e</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15420 Quæruntur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>: et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15421 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15422 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, the given difference between the two lines. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15423 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, the first line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15424 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, the second line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15425 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, the portion of the first line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15426 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15427 That is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>a</mi><mo>:</mo><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15428 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, the portion of the second line <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15429 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15430 That is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>e</mi><mo>:</mo><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15431 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>, the prescribed sum, equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>+</mo><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15432 There are sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15433 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15434 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15435 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15436 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15437 <s xml:id="echoid-s1644" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15438 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. primum latus intelligitur maius vel minus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15439 primo casu intelligitur maius.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15440 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15441 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, the first line can be understood to greater or smaller. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15442 In the first case it is understood to be greater.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15443 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15444 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15445 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15446 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15447 <s xml:id="echoid-s1645" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15448 Tum: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> portio primi lateris. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15449 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> portio secundi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15450 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15451 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> is the portion of the first line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15452 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> is the portion of the second line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15453 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15454 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15455 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15456 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15457 <s xml:id="echoid-s1646" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15458 PorrÃ², sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, portio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15459 secundi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15460 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15461 Further, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is the portion of the second line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15462 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15463 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15464 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15465 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15466 <s xml:id="echoid-s1647" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15467 Secundo casu primum segmentum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15468 intelligitur minus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15469 Ergo secundi segmenti erit maius. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15470 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> portio secundi lateris. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15471 ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>e</mi></mstyle></math> portio primi lateris, et minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15472 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15473 In the second case the first line is understood to be smaller. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15474 Therefore the second line will be greater. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15475 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the portion of the second line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15476 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>e</mi></mstyle></math> is the portion of the first line, and smaller.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15477 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15478 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15479 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15480 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15481 <s xml:id="echoid-s1648" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15482 PorrÃ², sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, portio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15483 primi lateris minoris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15484 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15485 Further, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the portion of the first, smaller line. </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15486 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15487 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15488 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15489 <s xml:id="echoid-s1649" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15490 Additio nostra pro <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15491 secundus casus aliter. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15492 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, portio primi lateris et minoris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15493 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> portio secundi lateris, et maioris. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15494 Quoniam: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>a</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math> latus minus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15495 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>h</mi><mo>-</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>h</mi><mo>-</mo><mi>b</mi><mi>a</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math> latus maius.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15496 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15497 An addition of my own for the second case another way. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15498 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the portion of the first and smaller line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15499 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math> is the portion of the second and greater line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15500 Since: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>a</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math> for the smaller line. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15501 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>h</mi><mo>-</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>h</mi><mo>-</mo><mi>b</mi><mi>a</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math> for the greater line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15502 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15503 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15504 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15505 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15506 <s xml:id="echoid-s1650" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15507 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> portio secundi lateris et maioris
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15508 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15509 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the portion of the second and greater line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15510 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15511 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15512 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15513 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15514 <s xml:id="echoid-s1651" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15515 Nota. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15516 Alia etiam est <emph style="st">[???]</emph> <emph style="ins ">zetesis supra</emph> ad <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15517 investigandum secundum portione in <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15518 primo casu, videlicet ea quæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15519 est primi lateris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15520 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15521 Note. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15522 The zetesis above is also another for investigating the second portion in the first case,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15523 namely that which is the first line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15524 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15525 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15526 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15527 <pb file="add_6782_f460v" o="460v" n="921"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15528 <pb file="add_6782_f461" o="461" n="922"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15529 <div xml:id="echoid-div302" type="page_commentary" level="2" n="302">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15530 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15531 <s xml:id="echoid-s1652" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15532 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15533 <s xml:id="echoid-s1652" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15534 This page continues Harriot's work on Zetetic 9 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15535 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15536 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15537 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15538 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15539 Zeteticum IX <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15540 Invenire duo latera, quorum differentia sit ea quæ præscribitur,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15541 & præterea præfinitæ unciæ lateris unius, adjectæ præfinitis unciis alterius,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15542 æquabunt summam præscriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15543 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15544 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15545 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15546 To find two lines, whose difference is prescribed,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15547 and also such that a fixed part of one line added to a fixed part of the other is equal to a prescibed sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15548 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15549 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15550 <s xml:id="echoid-s1653" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15551 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the difference between the two lines,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15552 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15553 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15554 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the prescribed sum,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15555 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the parts of the first and second lines. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15556 Harriot followed Viète's method on Add MS 6782, f. 462.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15557 Here he works the same problem using numbers instead of lengths.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15558 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15559 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15560 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15561 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15562 <head xml:id="echoid-head213" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15563 Zetet. Lib. 1. Zet. 9.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15564 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15565 Zetetica, Book I, Zetetic 9
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15566 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15567 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15568 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15569 <s xml:id="echoid-s1655" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15570 Invenire duas numerus quorum differentia sit 84, et præterea <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> <emph style="st">unius</emph> primi <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15571 numeri adjecta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> alterius æquabit summam præscriptam. oportet summam præscriptam <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15572 esse maiorem quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> dictæ differentiæ si primum latus sit maius: sed si minus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15573 esse maiorem quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15574 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15575 To find two numbers whose dfference is 84, and also such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> of the first number
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15576 added to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the other will be equal to a prescribed sum;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15577 the prescribed sum must be greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> of the said difference if the first root is the greater,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15578 but if it is the smaller, it must be greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15579 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15580 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15581 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15582 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15583 <s xml:id="echoid-s1656" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15584 vel: Invenire duas numerus quorum differentia sit 84, et pæterea <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> primi numeri <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15585 adjecta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> secunda æquabit summam præscriptam. oportet summam præscriptam <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15586 esse maiorem quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> dictæ differentiæ si primum latus sit maius: sed si minus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15587 esse maiorem quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15588 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15589 Or: To find two numbers whose dfference is 84, and also such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the first number
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15590 added to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> of the secon will be equal to a prescribed sum;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15591 the prescribed sum must be greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the said difference if the first root is the greater,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15592 but if it is the smaller, it must be greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15593 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15594 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15595 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15596 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15597 <s xml:id="echoid-s1657" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15598 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. differntia numerourm. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15599 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. primus numerus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15600 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. secundus numerus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15601 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. portio primi numeri. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15602 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15603 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. portio 2<emph style="super">i</emph> numeri <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15604 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15605 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> summa præscripta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>a</mi><mo>+</mo><mi>e</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15606 Quæruntur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15607 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15608 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, the difference between the numbers. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15609 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, the first number <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15610 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, the second number. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15611 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, the portion of the first number. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15612 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15613 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, the portion of the first number. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15614 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15615 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>, the prescribed sum, equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>+</mo><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15616 There are sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15617 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15618 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15619 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15620 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15621 <s xml:id="echoid-s1658" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15622 Primum latus maius. Portio maiorum uncium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15623 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15624 The first root greater. Portion greater than the fraction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15625 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15626 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15627 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15628 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15629 <s xml:id="echoid-s1659" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15630 Primum latus minus. Portio maiorum uncium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15631 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15632 The first root smaller. Portion greater than the fraction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15633 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15634 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15635 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15636 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15637 <s xml:id="echoid-s1660" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15638 Primum latus maius. Portio minorum uncium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15639 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15640 The first root greater. Portion less than the fraction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15641 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15642 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15643 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15644 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15645 <s xml:id="echoid-s1661" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15646 Primum latus minus. Portio minorum uncium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15647 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15648 The first root smaller. Portion less than the fraction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15649 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15650 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15651 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15652 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15653 <s xml:id="echoid-s1662" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15654 Primum latus minus. Ubi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> est maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> et minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15655 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15656 The first root smaller, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> but less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15657 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15658 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15659 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15660 <pb file="add_6782_f461v" o="461v" n="923"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15661 <pb file="add_6782_f462" o="462" n="924"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15662 <div xml:id="echoid-div303" type="page_commentary" level="2" n="303">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15663 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15664 <s xml:id="echoid-s1663" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15665 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15666 <s xml:id="echoid-s1663" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15667 This page continues Harriot's working of Zetetic 8 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15668 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15669 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15670 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15671 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15672 Zeteticum VIII <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15673 Datum latus ita secare, ut præfinitae unciae segmenti, multatæ præfinitis unciis secundi segmenti:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15674 æquent differentiam praescriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15675 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15676 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15677 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15678 To cut a given line in such a way that a fixed part of one segment, subtracted from a fixed part of the second segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15679 is equal to a prescribed difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15680 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15681 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15682 <s xml:id="echoid-s1664" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15683 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the whole line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15684 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15685 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15686 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the prescribed difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15687 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the unknown parts of the first and second segments.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15688 Harriot followed Viète's method on Add MS 6782, f. 464.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15689 Here he works the same problem using numbers instead of lengths.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15690 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15691 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15692 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15693 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15694 <head xml:id="echoid-head214" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15695 Zetet. Lib. 1. Zet. 8.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15696 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15697 Zetetica, Book I, Zetetic 8
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15698 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15699 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15700 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15701 <s xml:id="echoid-s1666" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15702 Datum numerum ita dividere in duas partes, ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> primæ partis, minus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> secundæ partis:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15703 sit æqualis numero pæscripto. oportuit numerum præscriptum esse minorum quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> totius.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15704 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15705 To divide a given number into two parts, so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> of the first part minus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the second part
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15706 is equal to a prescribed number; the prescribed number must be less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> of the whole.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15707 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15708 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15709 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15710 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15711 <s xml:id="echoid-s1667" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15712 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. numerus datus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15713 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. prima pars <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15714 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. secunda pars. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15715 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> primæ partis. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15716 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15717 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>. (minor quam 28) numerus præscriptus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15718 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>h</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>. secundæ partis. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15719 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>h</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15720 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15721 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, the given number. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15722 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, the first part <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15723 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, the second part. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15724 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> of the first part. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15725 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15726 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> (less than 28) is the prescribed number. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15727 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>h</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the second part <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15728 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>h</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15729 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15730 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15731 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15732 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15733 <s xml:id="echoid-s1668" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15734 SecundÃ²: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15735 Ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> primæ partis minus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> secundæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15736 sit æqualis numero præscripto. oportet <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15737 numerum præscriptum esse minorem quam <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15738 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> totius.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15739 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15740 Second. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15741 As <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the first part minus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> of the second is equal to the prescribed number,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15742 the prescribed number must be less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the total.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15743 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15744 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15745 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15746 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15747 <s xml:id="echoid-s1669" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15748 Analogia solvens problema.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15749 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15750 A ratio for solving the problem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15751 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15752 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15753 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15754 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15755 <s xml:id="echoid-s1670" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15756 Aliud exemplum. ubi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> sit 24. minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> et maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15757 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15758 Another example, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is 24, less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> and greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15759 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15760 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15761 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15762 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15763 <s xml:id="echoid-s1671" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15764 Exemplum 2<emph style="super">i</emph> casus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15765 sit iam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>. primæ partis. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15766 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15767 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>h</mi></mstyle></math> secundæ partis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15768 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>h</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15769 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15770 Example 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15771 Now let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the first part. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15772 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15773 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>h</mi></mstyle></math> is the second part.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15774 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>h</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15775 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15776 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15777 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15778 <pb file="add_6782_f462v" o="462v" n="925"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15779 <pb file="add_6782_f463" o="463" n="926"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15780 <div xml:id="echoid-div304" type="page_commentary" level="2" n="304">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15781 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15782 <s xml:id="echoid-s1672" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15783 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15784 <s xml:id="echoid-s1672" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15785 This page contains Harriot's working of Zetetic 1 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15786 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15787 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15788 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15789 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15790 Zeteticum I <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15791 Data differentia duorum laterum, & adgregato eorumdem, invenire latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15792 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15793 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15794 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15795 Given the difference of two roots, and their sum, find the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15796 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15797 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15798 <s xml:id="echoid-s1673" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15799 Viète used the letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the two roots, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for their difference, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> for their sum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15800 Harriot repeated Viète's working in his own symbolic notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15801 In the lower half of the page, he refers to a proposition in Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15802 <emph style="it">Effectionum geometricarum</emph>, Proposition 12,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15803 where a similar problem is solved geometrcially.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15804 In Harriot's diagrams, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> represent the two extremes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15805 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15806 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15807 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15808 Propositio XII <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15809 Data media trium proportionalium & differentia extremarum, invenire extremas.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15810 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15811 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15812 <s xml:id="echoid-s1674" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15813 Given the mean of three proportionals, and the difference of their extremes, find the extremes.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15814 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15815 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15816 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15817 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15818 <head xml:id="echoid-head215" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15819 Zet. 1. lib. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15820 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15821 Zetetic 1, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15822 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15823 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15824 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15825 <s xml:id="echoid-s1676" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15826 alia diagrapha. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15827 consule 12. p. effect.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15828 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15829 another diagram; see Effectionum, proposition 12.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15830 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15831 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15832 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15833 <pb file="add_6782_f463v" o="463v" n="927"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15834 <pb file="add_6782_f464" o="464" n="928"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15835 <div xml:id="echoid-div305" type="page_commentary" level="2" n="305">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15836 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15837 <s xml:id="echoid-s1677" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15838 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15839 <s xml:id="echoid-s1677" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15840 This page contains Harriot's working of Zetetic 8 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15841 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15842 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15843 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15844 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15845 Zeteticum VIII <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15846 Datum latus ita secare, ut præfinitae unciae segmenti, multatæ præfinitis unciis secundi segmenti:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15847 æquent differentiam praescriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15848 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15849 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15850 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15851 To cut a given line in such a way that a fixed part of one segment, subtracted from a fixed part of the second segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15852 is equal to a prescribed difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15853 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15854 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15855 <s xml:id="echoid-s1678" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15856 Viète used the letter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the whole line,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15857 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the first part to the first segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15858 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> for the ratio of the second part to the second segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15859 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi></mstyle></math> for the prescribed difference,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15860 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the parts of the first and second segments.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15861 Harriot repeated Viète's working in his own notation, and also added some variants of his own. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15862 The work is continued using numerical examples on Add MS 6782, f. 462.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15863 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15864 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15865 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15866 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15867 <head xml:id="echoid-head216" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15868 Zetet. Lib. 1. Zet. 8.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15869 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15870 Zetetica, Book I, Zetetic 8
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15871 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15872 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15873 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15874 <s xml:id="echoid-s1680" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15875 Datum latus ita secare, ut præfinitae unciæ segmenti, multatæ præfinitis unciis secundi segmenti:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15876 æquent differentiam præscriptam.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15877 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15878 To cut a given line in such a way that a fixed part of one segment, subtracted from a fixed part of the second segment,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15879 is equal to a prescribed difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15880 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15881 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15882 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15883 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15884 <s xml:id="echoid-s1681" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15885 Nota. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15886 Differentia præscripta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15887 videlicet <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> debet esse <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15888 minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15889 sive <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> sit maior vel <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15890 minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>, ut <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15891 infra patebit. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15892 Hic sequens argu-<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15893 mentatio <emph style="super">est</emph> firma ad <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15894 utraque casum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15895 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15896 Note. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15897 The prescribed difference, namely <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>, must be less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15898 whether <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> is greater or less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>, as is shown below.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15899 Here the following argument is sound in either case.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15900 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15901 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15902 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15903 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15904 <s xml:id="echoid-s1682" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15905 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. latus secandam. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15906 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. primum segmentum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15907 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>. secundum seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15908 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. portio primæ seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15909 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15910 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>,</mo><mi>o</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15911 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>. differentia præscripta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15912 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>h</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15913 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>-</mo><mi>h</mi><mo>,</mo><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15914 Quæruntur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, et segmentorum portiones. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15915 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>a</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>. primum seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15916 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>-</mo><mi>h</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>a</mi><mo>-</mo><mi>b</mi><mi>h</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>. secundum seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15917 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15918 Notum. Inde primum seg <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>b</mi><mi>a</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15919 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15920 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, the line to be cut. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15921 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>, the first segment <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15922 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, the second segment. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15923 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, the portion of the first segment. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15924 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>d</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>o</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15925 That is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>a</mi><mo>:</mo><mi>o</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15926 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>, the prescribed difference <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15927 The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>h</mi></mrow><mrow><mi>u</mi></mrow></mfrac></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15928 That is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>h</mi><mo>:</mo><mi>u</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15929 There are sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi></mstyle></math>, and the portions of the segments. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15930 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>a</mi><mo>:</mo><mfrac><mrow><mi>b</mi><mi>a</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>, the first segment <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15931 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>h</mi><mo>:</mo><mfrac><mrow><mi>b</mi><mi>a</mi><mo>-</mo><mi>b</mi><mi>h</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>, the second segement. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15932 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15933 Note. Thence the first segment, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>b</mi><mi>a</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15934 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15935 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15936 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15937 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15938 <s xml:id="echoid-s1683" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15939 PorrÃ², sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> portio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15940 secundi segmenti.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15941 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15942 Further, if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> is the portion of the second segment.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15943 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15944 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15945 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15946 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15947 <s xml:id="echoid-s1684" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15948 Additio nostra pro <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15949 portione secundi segmenti, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15950 aliter. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15951 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, portio secundi segmenti <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15952 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>+</mo><mi>h</mi></mstyle></math> portio primi segmenti. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15953 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>e</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>e</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>. secundum seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15954 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>,</mo><mi>b</mi><mo>:</mo><mi>e</mi><mo>+</mo><mi>h</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>e</mi><mo>+</mo><mi>b</mi><mi>h</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>. prim. seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15955 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15956 Notum inde sec. segmentum: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>b</mi><mi>e</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15957 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15958 An addition of my own for the portion of the second segment, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, another way. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15959 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the portion of the second segment, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>+</mo><mi>h</mi></mstyle></math> is the portion of the first segment. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15960 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>e</mi><mo>:</mo><mfrac><mrow><mi>b</mi><mi>e</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>, the second segment. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15961 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>h</mi><mo>:</mo><mfrac><mrow><mi>b</mi><mi>e</mi><mo>+</mo><mi>b</mi><mi>h</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>, the first segment. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15962 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15963 Note, thence the second segment: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>b</mi><mi>e</mi></mrow><mrow><mi>f</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15964 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15965 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15966 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15967 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15968 <s xml:id="echoid-s1685" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15969 Additio nostra. Aliter 1<emph style="super">o</emph>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15970 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>,</mo><mi>d</mi><mo>:</mo><mi>o</mi><mo>,</mo><mfrac><mrow><mi>b</mi><mi>o</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>. port. 1. seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15971 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>,</mo><mi>f</mi><mo>:</mo><mi>b</mi><mo>-</mo><mi>o</mi><mo>,</mo><mfrac><mrow><mi>f</mi><mi>b</mi><mo>-</mo><mi>f</mi><mi>o</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>. por. 2. seg.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15972 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15973 An addition of my own. Another way, 1. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15974 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>:</mo><mi>d</mi><mo>=</mo><mi>o</mi><mo>:</mo><mfrac><mrow><mi>b</mi><mi>o</mi></mrow><mrow><mi>d</mi></mrow></mfrac></mstyle></math>, the portion of the first segment. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15975 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>:</mo><mi>f</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>o</mi><mo>:</mo><mfrac><mrow><mi>f</mi><mi>b</mi><mo>-</mo><mi>f</mi><mi>o</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>, the portion of the second segment.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15976 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15977 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15978 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15979 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15980 <s xml:id="echoid-s1686" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15981 Aliter 2<emph style="super">o</emph>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15982 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>,</mo><mi>f</mi><mo>:</mo><mi>u</mi><mo>,</mo><mfrac><mrow><mi>f</mi><mi>u</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>. port. 2. seg. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15983 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>,</mo><mi>d</mi><mo>:</mo><mi>b</mi><mo>-</mo><mi>u</mi><mo>,</mo><mfrac><mrow><mi>d</mi><mi>b</mi><mo>-</mo><mi>d</mi><mi>u</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>. por. 1. seg.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15984 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15985 Another way, 2. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15986 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>:</mo><mi>f</mi><mo>=</mo><mi>u</mi><mo>:</mo><mfrac><mrow><mi>f</mi><mi>u</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>, the portion of the second segment. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15987 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>:</mo><mi>d</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>u</mi><mo>:</mo><mfrac><mrow><mi>d</mi><mi>b</mi><mo>-</mo><mi>d</mi><mi>u</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>, the portion of the first segment.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15988 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15989 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15990 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15991 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15992 <s xml:id="echoid-s1687" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15993 Nota. Hinc apparet quod <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> est minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15994 quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>; alias <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> esset minor <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15995 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>; totum [???] partem.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15996 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15997 Note. Here it is clear that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15998 otherwise <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> would be less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>; the whole [???] the part.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	15999 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16000 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16001 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16002 <pb file="add_6782_f464v" o="464v" n="929"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16003 <pb file="add_6782_f465" o="465" n="930"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16004 <div xml:id="echoid-div306" type="page_commentary" level="2" n="306">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16005 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16006 <s xml:id="echoid-s1688" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16007 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16008 <s xml:id="echoid-s1688" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16009 This page contains Harriot's working of Zetetic 6 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16010 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16011 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16012 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16013 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16014 Zeteticum VI <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16015 Datis duobus lateribs uno deficiente Ã justo, altero justum excedente, una cum ratione defectus ad excessum:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16016 invenire latus justum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16017 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16018 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16019 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16020 Given two roots, one less than the correct root, the other exceeding it,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16021 together with the ratio of the defect to the excess, find the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16022 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16023 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16024 <s xml:id="echoid-s1689" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16025 Viète used the letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> for the two roots, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>R</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math> for the ratio of the defect to the excess.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16026 Harriot repeated Viète's working, including his alternative method ('Aliter'), in his own symbolic notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16027 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16028 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16029 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16030 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16031 <head xml:id="echoid-head217" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16032 Zetet. lib. 1. Zet. 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16033 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16034 Zetetica, Book I, Zetetic 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16035 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16036 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16037 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16038 <s xml:id="echoid-s1691" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16039 Datis duobus lateribs uno deficiente Ã justo, altero justum excedente, una <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16040 cum ratione defectus ad excessum: invenire latus justum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16041 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16042 Given two roots, one less than the correct side, the other exceeding it,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16043 together with the ratio of the deficiency to the excess, find the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16044 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16045 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16046 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16047 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16048 <s xml:id="echoid-s1692" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16049 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. deficiens a justo. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16050 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. excedens justium. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16051 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math>. defectus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16052 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>. excessus ratione
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16053 primÃ². <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. esto defectus a justo. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16054 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>a</mi></mstyle></math>. latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16055 Quoniam: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>,</mo><mi>s</mi><mo>:</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>s</mi><mi>a</mi></mrow><mrow><mi>r</mi></mrow></mfrac></mstyle></math> excessus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16056 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16057 Ergo 80 latus iustum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16058 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16059 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the deficiency from the correct root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> the excess over the correct root,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16060 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> the ratio of the defect to the excess. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16061 First, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the defect from the correct side. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16062 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>a</mi></mstyle></math> is the correct root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16063 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>:</mo><mi>s</mi><mo>=</mo><mi>a</mi><mo>:</mo><mfrac><mrow><mi>s</mi><mi>a</mi></mrow><mrow><mi>r</mi></mrow></mfrac></mstyle></math>, the excess. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16064 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16065 Therefore 80 is the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16066 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16067 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16068 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16069 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16070 <s xml:id="echoid-s1693" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16071 SecundÃ² <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16072 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. esto excessus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16073 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>e</mi></mstyle></math>. latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16074 Tum: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mo>,</mo><mi>r</mi><mo>:</mo><mi>e</mi><mo>,</mo><mfrac><mrow><mi>r</mi><mi>e</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mstyle></math>. defectus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16075 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16076 Ergo 80 latus iustum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16077 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16078 Second. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16079 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the excess. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16080 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>e</mi></mstyle></math> is the correct root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16081 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mo>:</mo><mi>r</mi><mo>=</mo><mi>e</mi><mo>:</mo><mfrac><mrow><mi>r</mi><mi>e</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mstyle></math>, the defect. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16082 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16083 Therefore 80 is the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16084 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16085 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16086 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16087 <head xml:id="echoid-head218" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16088 Aliter
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16089 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16090 Another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16091 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16092 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16093 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16094 <s xml:id="echoid-s1694" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16095 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. esto latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16096 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>b</mi></mstyle></math>. defectus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16097 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>a</mi></mstyle></math>. excessus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16098 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16099 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the correct root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16100 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>a</mi></mstyle></math> is the defect, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>a</mi></mstyle></math> the excess.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16101 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16102 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16103 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16104 <pb file="add_6782_f465v" o="465v" n="931"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16105 <pb file="add_6782_f466" o="466" n="932"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16106 <div xml:id="echoid-div307" type="page_commentary" level="2" n="307">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16107 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16108 <s xml:id="echoid-s1695" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16109 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16110 <s xml:id="echoid-s1695" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16111 This page contains Harriot's working of Zetetic 5 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16112 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16113 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16114 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16115 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16116 Zeteticum V <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16117 Datis duobus lateribus excedentibus justum, una cum ratione excessuum: invenire latus justum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16118 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16119 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16120 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16121 Given two roots exceeding the correct one, and the ratio of the excesses, find the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16122 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16123 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16124 <s xml:id="echoid-s1696" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16125 Viète used the letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> for the two roots, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>R</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math> for the ratio of the excesses.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16126 Harriot repeated Viète's working, including his alternative method ('Aliter'), in his own symbolic notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16127 For Harriot's (and Viète's) use of the symbol that looks like a modern = sign,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16128 see the commentary to Add MS 6782, f. 467.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16129 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16130 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16131 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16132 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16133 <head xml:id="echoid-head219" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16134 Zetet. lib. 1. Zet. 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16135 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16136 Zetetica, Book I, Zetetic 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16137 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16138 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16139 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16140 <s xml:id="echoid-s1698" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16141 Datis duobus lateribus excedentibus iustum, una cum ratione excessum: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16142 invenire latus iustum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16143 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16144 Given two roots exceeding the correct root, and the ratio of the excesses, find the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16145 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16146 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16147 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16148 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16149 <s xml:id="echoid-s1699" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16150 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. latus primum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16151 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. latus secundum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16152 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math>. excessus primi <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16153 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>. excessus secundi ratione
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16154 primÃ². <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. esto excessus primi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16155 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>a</mi></mstyle></math>. latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16156 Tum: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>,</mo><mi>s</mi><mo>:</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>s</mi><mi>a</mi></mrow><mrow><mi>r</mi></mrow></mfrac></mstyle></math> Excessus 2<emph style="super">i</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16157 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16158 Ergo latus iustum 20.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16159 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16160 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the first side, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> the second, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> the ratio of the excesses. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16161 First, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the first excess. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16162 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>a</mi></mstyle></math> is the correct root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16163 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>:</mo><mi>s</mi><mo>=</mo><mi>a</mi><mo>:</mo><mfrac><mrow><mi>s</mi><mi>a</mi></mrow><mrow><mi>r</mi></mrow></mfrac></mstyle></math>, the second excess. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16164 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16165 Therefore the correct root is 20.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16166 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16167 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16168 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16169 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16170 <s xml:id="echoid-s1700" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16171 SecundÃ² <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16172 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. esto excessus secundi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16173 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>e</mi></mstyle></math>. latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16174 Tum: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mo>,</mo><mi>r</mi><mo>:</mo><mi>e</mi><mo>,</mo><mfrac><mrow><mi>r</mi><mi>e</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mstyle></math>. excessus primi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16175 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16176 Ergo latus iustum 30.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16177 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16178 Second. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16179 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the second excess. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16180 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>e</mi></mstyle></math> is the correct root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16181 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mo>:</mo><mi>r</mi><mo>=</mo><mi>e</mi><mo>:</mo><mfrac><mrow><mi>r</mi><mi>e</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mstyle></math>, the first excess. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16182 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16183 Therefore the correct root is 30.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16184 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16185 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16186 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16187 <head xml:id="echoid-head220" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16188 Aliter
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16189 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16190 Another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16191 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16192 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16193 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16194 <s xml:id="echoid-s1701" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16195 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. esto latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16196 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>a</mi></mstyle></math>. excessus primi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16197 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>a</mi></mstyle></math>. excessus secundi.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16198 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16199 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the correct root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16200 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>a</mi></mstyle></math> is the first excess, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>-</mo><mi>a</mi></mstyle></math> the second excess.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16201 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16202 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16203 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16204 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16205 <s xml:id="echoid-s1702" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16206 20. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. latus iustum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16207 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16208 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mn>2</mn><mn>0</mn></mstyle></math>, the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16209 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16210 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16211 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16212 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16213 <s xml:id="echoid-s1703" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16214 Nota. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16215 Si notatio ita fiat. sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. latus minus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16216 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. latus maius <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16217 &c. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16218 Tunc non opus esset isto <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16219 signo =.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16220 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16221 Note. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16222 Of the notation is thus: let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the smaller side, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> the larger, etc. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16223 Then there would be no need for this sign =.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16224 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16225 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16226 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16227 <pb file="add_6782_f466v" o="466v" n="933"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16228 <pb file="add_6782_f467" o="467" n="934"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16229 <div xml:id="echoid-div308" type="page_commentary" level="2" n="308">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16230 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16231 <s xml:id="echoid-s1704" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16232 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16233 <s xml:id="echoid-s1704" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16234 This page contains Harriot's working of Zetetic 4 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16235 <emph style="it">Zeteticorum libri quinque</emph>, Book I.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16236 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16237 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16238 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16239 Zeteticum IV <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16240 Datis duobus lateribus deficientibus Ã justo, una cum ratione defectum: invenire latus justum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16241 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16242 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16243 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16244 Given two roots less than the correct one, and the ratio of the defects, find the correct root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16245 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16246 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16247 <s xml:id="echoid-s1705" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16248 Viète used the letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> for the two roots, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>R</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math> for the ratio of the defects.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16249 Harriot repeated Viète's working, including his alternative method ('Aliter'),in his own symbolic notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16250 The symbol that looks like a modern = sign is to be read as a minus sign,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16251 used by Harriot (following Viète) in cases where it was not known which quantity was greater.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16252 Thus, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mi>b</mi></mstyle></math> is to be read as '<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>b</mi></mstyle></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>-</mo><mi>a</mi></mstyle></math>, whichever is positive'.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16253 In modern notation the same result is represented by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo lspace="0em" rspace="0em" maxsize="1">\|</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo lspace="0em" rspace="0em" maxsize="1">\|</mo></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16254 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16255 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16256 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16257 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16258 <head xml:id="echoid-head221" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16259 Zetet. lib. 1. Zet. 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16260 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16261 Zetetica, Book I, Zetetic 4
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16262 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16263 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16264 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16265 <s xml:id="echoid-s1707" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16266 Datis duobus lateribus deficientibus a iusto, una cum ratione defectum: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16267 invenire latus iustum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16268 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16269 Given two roots less than the true one, together with the ratio of the defects, find the true root.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16270 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16271 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16272 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16273 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16274 <s xml:id="echoid-s1708" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16275 primÃ². <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16276 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. latus primum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16277 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. latus secundum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16278 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math>. defectus primum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16279 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>. defectus secundi ratione
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16280 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. esto defectus primi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16281 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>a</mi></mstyle></math>. latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16282 Tum: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>,</mo><mi>s</mi><mo>:</mo><mi>a</mi><mo>,</mo><mfrac><mrow><mi>s</mi><mi>a</mi></mrow><mrow><mi>r</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16283 defect. 2<emph style="super">i</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16284 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16285 Ergo latus iustum: 60.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16286 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16287 First. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16288 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the first root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> the second, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> the ratio of the first defect to the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16289 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> the first defect. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16290 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>a</mi></mstyle></math> is the true root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16291 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mo>:</mo><mi>s</mi><mo>=</mo><mi>a</mi><mo>:</mo><mfrac><mrow><mi>s</mi><mi>a</mi></mrow><mrow><mi>r</mi></mrow></mfrac></mstyle></math>, the second defect. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16292 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16293 Therefore the correct root is 60.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16294 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16295 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16296 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16297 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16298 <s xml:id="echoid-s1709" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16299 secundÃ² <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16300 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. esto defectus secundi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16301 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>+</mo><mi>e</mi></mstyle></math>. latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16302 Tum: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mo>,</mo><mi>r</mi><mo>:</mo><mi>e</mi><mo>,</mo><mfrac><mrow><mi>r</mi><mi>e</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16303 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16304 Ergo latus iustum: 60.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16305 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16306 Second <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16307 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the second defect. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16308 Therefore the true root is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>+</mo><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16309 Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mo>:</mo><mi>r</mi><mo>=</mo><mi>e</mi><mo>:</mo><mfrac><mrow><mi>r</mi><mi>e</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16310 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16311 Therefore the correct root is 60.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16312 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16313 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16314 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16315 <head xml:id="echoid-head222" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16316 Aliter
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16317 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16318 Another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16319 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16320 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16321 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16322 <s xml:id="echoid-s1710" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16323 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. esto latus iustum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16324 Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>b</mi></mstyle></math>. defectus primi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16325 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>d</mi></mstyle></math>. defectus secundi. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16326 Quære: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>b</mi><mo>,</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo>:</mo><mi>r</mi><mo>,</mo><mi>s</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16327 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>a</mi><mo>-</mo><mi>r</mi><mi>d</mi><mo>=</mo><mi>s</mi><mi>a</mi><mo>-</mo><mi>s</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16328 Hoc est: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mi>b</mi><mo>=</mo><mo>=</mo><mi>r</mi><mi>d</mi><mo>=</mo><mi>s</mi><mi>a</mi><mo>=</mo><mo>=</mo><mi>r</mi><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16329 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>s</mi><mi>b</mi><mo>=</mo><mo>=</mo><mi>r</mi><mi>d</mi></mrow><mrow><mi>s</mi><mo>=</mo><mo>=</mo><mi>r</mi></mrow></mfrac><mo>=</mo><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16330 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16331 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the correct root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16332 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>b</mi></mstyle></math> is the first defect, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>d</mi></mstyle></math> the second. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16333 Obtain: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>-</mo><mi>b</mi><mo>:</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo>=</mo><mi>r</mi><mo>:</mo><mi>s</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16334 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo lspace="0em" rspace="0em" maxsize="1">\|</mo><mi>r</mi><mi>a</mi><mo>-</mo><mi>r</mi><mi>d</mi><mo lspace="0em" rspace="0em" maxsize="1">\|</mo><mo>=</mo><mo lspace="0em" rspace="0em" maxsize="1">\|</mo><mi>s</mi><mi>a</mi><mo>-</mo><mi>s</mi><mi>b</mi><mo lspace="0em" rspace="0em" maxsize="1">\|</mo></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16335 That is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mo lspace="0em" rspace="0em" maxsize="1">\|</mo><mi>s</mi><mi>b</mi><mo>-</mo><mi>r</mi><mi>d</mi><mo lspace="0em" rspace="0em" maxsize="1">\|</mo></mrow><mrow><mo lspace="0em" rspace="0em" maxsize="1">\|</mo><mi>s</mi><mo>-</mo><mi>r</mi><mo lspace="0em" rspace="0em" maxsize="1">\|</mo></mrow></mfrac><mo>=</mo><mi>a</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16336 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16337 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16338 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16339 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16340 <s xml:id="echoid-s1711" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16341 <emph style="st">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16342 Emendata Vieta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16343 si <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> sit minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. vel <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>, minor quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16344 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>a</mi><mo>-</mo><mi>r</mi><mi>d</mi><mo>=</mo><mi>s</mi><mi>a</mi><mo>-</mo><mi>s</mi><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16345 Tum si <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> sit maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>: vel <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> maior quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16346 Inde: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>a</mi><mo>-</mo><mi>s</mi><mi>a</mi><mo>=</mo><mi>r</mi><mi>d</mi><mo>-</mo><mi>s</mi><mi>b</mi></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16347 Vel: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>e</mi><mo>+</mo><mi>s</mi><mi>e</mi><mo>=</mo><mi>s</mi><mi>g</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16348 Unde: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mfrac><mrow><mi>r</mi><mi>d</mi><mo>-</mo><mi>s</mi><mi>b</mi></mrow><mrow><mi>r</mi><mo>-</mo><mi>s</mi></mrow></mfrac></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16349 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16350 A correction to Viète. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16351 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> is smaller than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> is smaller than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>a</mi><mo>-</mo><mi>r</mi><mi>d</mi><mo>-</mo><mi>s</mi><mi>a</mi><mo>-</mo><mi>s</mi><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16352 Then if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16353 thence <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>a</mi><mo>-</mo><mi>s</mi><mi>a</mi><mo>-</mo><mi>r</mi><mi>d</mi><mo>-</mo><mi>s</mi><mi>b</mi></mstyle></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>e</mi><mo>+</mo><mi>s</mi><mi>e</mi><mo>=</mo><mi>s</mi><mi>g</mi></mstyle></math>. Whence <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>=</mo><mfrac><mrow><mi>r</mi><mi>d</mi><mo>-</mo><mi>s</mi><mi>b</mi></mrow><mrow><mi>r</mi><mo>-</mo><mi>s</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16354 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16355 </emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16356 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16357 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16358 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16359 <s xml:id="echoid-s1712" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16360 Nota <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16361 Si notatis ita fiat: sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>. latus minus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16362 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> latus maius. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16363 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> defectus minus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16364 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> defectus maius ratione <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16365 Tunc non opus est isto signo =
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16366 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16367 Note <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16368 If the notation is thus: let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> the larger root,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16369 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> the ratio of the smaller defect to the larger, then there is no need for this sign ==
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16370 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16371 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16372 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16373 <pb file="add_6782_f467v" o="467v" n="935"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16374 <div xml:id="echoid-div309" type="page_commentary" level="2" n="309">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16375 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16376 <s xml:id="echoid-s1713" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16377 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16378 <s xml:id="echoid-s1713" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16379 This page contains some of Harriot's rough working on Zetetic 9 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16380 <emph style="it">Zeteticorum libri quinque</emph>, Book I. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16381 For fuller treatments of the material see Add MS 6782, f. 460 adn f. 461.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16382 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16383 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16384 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16385 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16386 <head xml:id="echoid-head223" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16387 Zet. 9. Cas. 2
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16388 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16389 Zetetic 9, case 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16390 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16391 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16392 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16393 <s xml:id="echoid-s1715" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16394 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. portio primi lateris et <emph style="st">maioris</emph> minimis. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16395 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math>. portio secundi et maioris <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16396 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16397 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, the portion of the first line, the lesser. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16398 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mo>-</mo><mi>a</mi></mstyle></math>, the portion of the second and greater line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16399 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16400 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16401 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16402 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16403 <s xml:id="echoid-s1716" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16404 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. portio secundi lateris et maioris.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16405 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16406 et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the portion of the second and greater line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16407 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16408 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16409 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16410 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16411 <s xml:id="echoid-s1717" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16412 Primum latus minus. Portio minorum uncium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16413 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16414 The first line smaller. Portion less than the fraction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16415 </emph>]<lb/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16417 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16418 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16419 <s xml:id="echoid-s1718" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16420 Primum latus maius. Portio minorum uncium.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16421 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16422 The first line greater. Portion less than the fraction.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16423 </emph>]<lb/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16425 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16426 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16427 <s xml:id="echoid-s1719" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16428 Primum latus minus.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16429 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16430 The first line smaller.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16431 </emph>]<lb/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16433 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16434 <pb file="add_6782_f468" o="468" n="936"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16435 <div xml:id="echoid-div310" type="page_commentary" level="2" n="310">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16436 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16437 <s xml:id="echoid-s1720" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16438 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16439 <s xml:id="echoid-s1720" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16440 The reference here is to Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16441 <emph style="it">Ad problema, quod ... proposuit Adrianus Romanus, responsum</emph> (1595),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16442 pages 5, 7, and 13.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16443 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16444 </p>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16447 <head xml:id="echoid-head224" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16448 ad pag: 5.7. & 13. Vietæ ad Adrianum. videlicet responsi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16449 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16450 On pages 5, 7, and 13 of Viète, Adrianus, that is, his responses.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16451 </emph>]<lb/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16455 Aliter.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16456 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16457 Another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16458 </emph>]<lb/>
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22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16460 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16461 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16462 <s xml:id="echoid-s1723" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16463 Excedit semicirculum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16464 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16465 Exceeds a semicircle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16466 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16467 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16468 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16469 <pb file="add_6782_f468v" o="468v" n="937"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16470 <pb file="add_6782_f469" o="469" n="938"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16471 <div xml:id="echoid-div311" type="page_commentary" level="2" n="311">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16472 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16473 <s xml:id="echoid-s1724" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16474 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16475 <s xml:id="echoid-s1724" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16476 The positions of this page amongst other pages referring to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16477 <emph style="it">Adrianus Romanus responsum</emph>, and its subject matter,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16478 trisection and quinquisection of an angle, suggests that it relates to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16479 <emph style="it">Adrianus Romanus responsum</emph>, Chapter V.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16480 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16481 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16482 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16483 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16484 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16485 <s xml:id="echoid-s1726" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16486 Pentachotomia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16487 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16488 Quinquisection of an angle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16489 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16490 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16491 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16492 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16493 <s xml:id="echoid-s1727" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16494 Trichotomia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16495 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16496 Trisection of an angle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16497 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16498 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16499 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16500 <pb file="add_6782_f469v" o="469v" n="939"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16501 <div xml:id="echoid-div312" type="page_commentary" level="2" n="312">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16502 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16503 <s xml:id="echoid-s1728" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16504 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16505 <s xml:id="echoid-s1728" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16506 The positions of this page amongst other pages referring to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16507 <emph style="it">Adrianus Romanus responsum</emph>, and its subject matter,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16508 trisection and quinquisection of an angle, suggests that it relates to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16509 <emph style="it">Adrianus Romanus responsum</emph>, Chapter V.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16510 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16511 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16512 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16513 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16514 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16515 <s xml:id="echoid-s1730" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16516 Pentachotomia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16517 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16518 Quinquisection of an angle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16519 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16520 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16521 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16522 <pb file="add_6782_f470" o="470" n="940"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16523 <div xml:id="echoid-div313" type="page_commentary" level="2" n="313">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16524 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16525 <s xml:id="echoid-s1731" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16526 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16527 <s xml:id="echoid-s1731" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16528 The references on this page are to Viète,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16529 <emph style="it">Ad problema, quod ... proposuit Adrianus Romanus, responsum</emph> (1595),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16530 pages 7v and 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16531 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16532 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16533 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16534 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16535 <head xml:id="echoid-head225" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16536 ad: pag: 7.b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16537 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16538 On page 7v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16539 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16540 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16541 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16542 <s xml:id="echoid-s1733" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16543 omisit Vieta radices negativas <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16544 ut in omnibus alijs aequationibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16545 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16546 Viète omits negative roots, as in all other equations.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16547 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16548 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16549 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16550 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16551 <s xml:id="echoid-s1734" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16552 Exemplum pag: 5. pono sub meliori forma <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16553 quam Vieta, ut sequitur: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16554 et est generalis ad omnes sectiones anguli <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16555 imparis numeri.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16556 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16557 Example from page 5, I put in a better form than Viète, as follows;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16558 and it is general for all angular sections of odd number.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16559 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16560 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16561 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16562 <pb file="add_6782_f470v" o="470v" n="941"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16563 <div xml:id="echoid-div314" type="page_commentary" level="2" n="314">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16564 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16565 <s xml:id="echoid-s1735" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16566 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16567 <s xml:id="echoid-s1735" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16568 A continuation from Add MS 6782, f. 470, of work on Viète's,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16569 <emph style="it">Ad problema, quod ... proposuit Adrianus Romanus, responsum</emph> (1595).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16570 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16571 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16572 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16573 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16574 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16575 <s xml:id="echoid-s1737" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16576 aliter: sed melius in alia charta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16577 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16578 another way, but better in the other sheet
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16579 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16580 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16581 The other sheet referred to here is the reverse of this one, Add MS 6782, f. 470.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16582 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16583 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16584 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16585 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16586 <s xml:id="echoid-s1738" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16587 Trichotomia. sic brevie
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16588 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16589 Trisection, thus briefly
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16590 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16591 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16592 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16593 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16594 <s xml:id="echoid-s1739" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16595 hinc sequitur:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16596 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16597 this follows:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16598 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16599 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16600 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16601 <pb file="add_6782_f471" o="471" n="942"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16602 <div xml:id="echoid-div315" type="page_commentary" level="2" n="315">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16603 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16604 <s xml:id="echoid-s1740" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16605 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16606 <s xml:id="echoid-s1740" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16607 The positions of this page amongst other pages referring to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16608 <emph style="it">Adrianus Romanus responsum</emph>, and its subject matter,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16609 trisection of an angle, suggests that it relates to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16610 <emph style="it">Adrianus Romanus responsum</emph>, Chapter V.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16611 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16612 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16613 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16614 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16615 <head xml:id="echoid-head226" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16616 Trichotomia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16617 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16618 Trisection
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16619 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16620 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16621 <pb file="add_6782_f471v" o="471v" n="943"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16622 <pb file="add_6782_f472" o="472" n="944"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16623 <div xml:id="echoid-div316" type="page_commentary" level="2" n="316">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16624 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16625 <s xml:id="echoid-s1742" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16626 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16627 <s xml:id="echoid-s1742" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16628 This page contains further work on Zetetic 2 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16629 <emph style="it">Zeteticorum libri quinque</emph>, Book II.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16630 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16631 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16632 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16633 Zeteticum II <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16634 Dato rectangulo sub lateribus, & adgregato quadratorum, inveniuntur latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16635 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16636 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16637 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16638 Given the product of two sides, and the sum of their squares, the sides may be found.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16639 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16640 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16641 <s xml:id="echoid-s1743" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16642 Harriot began the problem on Add MS 6782, f. 472, but he described the treatment on this page as better.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16643 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16644 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16645 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16646 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16647 <head xml:id="echoid-head227" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16648 lib. 2. Zetet. Zet. 2. secundo et melius.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16649 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16650 Zetetica, Book II, Zetetic 2. Second way, and better.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16651 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16652 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16653 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16654 <s xml:id="echoid-s1745" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16655 Dato rectangulo sub lateribus et adgregato quadratorum, inveniuntur latera. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16656 Enimvero duplum planum sub lateribus adiectum quidem <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16657 adgregatum quadratorum, æquatur quadrato summa laterum:] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16658 sit planum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>, cui æquale <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>θ</mi></mstyle></math>. et adgregatum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16659 quadratorum laterum sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>γ</mi><mi>H</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>λ</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16660 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16661 Ergo datur summa latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16662 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16663 Given a rectangle from its sides, and the sum of their squares, there may be found the sides. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16664 Certainly, twic the rectangle from the sides added to the sum of the squares
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16665 is equal to the square of the sum of the sides. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16666 Let the plane be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>, which is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>θ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16667 and the sum of the squares of the sides is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>γ</mi><mi>H</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>λ</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16668 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16669 Therefore the sum of the sides is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16670 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16671 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16672 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16673 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16674 <s xml:id="echoid-s1746" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16675 Ablatum uno, quadrato differentiæ.] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16676 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16677 ergo, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>\</mo><mi>a</mi><mi>l</mi><mi>p</mi><mi>h</mi><mi>μ</mi></mstyle></math> est differentia laterum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16678 et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ρ</mi><mi>o</mi></mstyle></math> est quadratum differenti
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16679 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16680 Subtracting from one, the square of the difference, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16681 <lb/>[...]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16682 therefore, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>μ</mi></mstyle></math> is the difference of the sides, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ρ</mi><mi>o</mi></mstyle></math> is the square of the difference.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16683 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16684 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16685 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16686 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16687 <s xml:id="echoid-s1747" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16688 In notis: sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math> planum æquale <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math> . <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16689 Ergo, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>a</mi><mi>a</mi></mstyle></math>. adgregati <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16690 Et. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>e</mi><mi>e</mi></mstyle></math>. differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16691 Ergo per 1.z et primi lib. dantur latera <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>β</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16692 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16693 In letters, let the plane <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math> be equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16694 Therefore, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>a</mi><mi>a</mi></mstyle></math>, the sum. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16695 And <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>b</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>c</mi><mi>c</mi><mo>=</mo><mi>e</mi><mi>e</mi></mstyle></math>, the difference <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16696 Therefore, by Zetetic 1 from the first book, there are given the sides <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>β</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16697 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16698 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16699 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16700 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16701 <s xml:id="echoid-s1748" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16702 Aliter. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16703 Sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. et sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16704 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16705 Another way. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16706 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math> be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> and let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math> be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16707 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16708 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16709 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16710 <pb file="add_6782_f472v" o="472v" n="945"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16711 <pb file="add_6782_f473" o="473" n="946"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16712 <div xml:id="echoid-div317" type="page_commentary" level="2" n="317">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16713 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16714 <s xml:id="echoid-s1749" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16715 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16716 <s xml:id="echoid-s1749" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16717 This page contains some very brief observations on Zetetic 3 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16718 <emph style="it">Zeteticorum libri quinque</emph>, Book II.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16719 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16720 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16721 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16722 Zeteticum III <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16723 Dato rectangulo sub lateribus, & differentia laterum: inveniuntur latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16724 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16725 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16726 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16727 Given the product of two sides and their difference, the sides may be found.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16728 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16729 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16730 <s xml:id="echoid-s1750" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16731 This is Proposition I.30 from the <emph style="it">Arithmetica</emph> of Diophantus,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16732 but Harriot refers only to Viète's version of it.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16733 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16734 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16735 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16736 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16737 <head xml:id="echoid-head228" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16738 lib. 2. Zet. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16739 Zet. 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16740 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16741 Zetetica, Book II, Zetetic 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16742 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16743 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16744 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16745 <s xml:id="echoid-s1752" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16746 Dato rectangulo sub lateribus, et differentia laterum inveniuntur latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16747 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16748 Given the product of two sides and their difference, the sides may be found.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16749 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16750 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16751 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16752 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16753 <s xml:id="echoid-s1753" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16754 Enimvero:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16755 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16756 Certainly:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16757 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16758 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16759 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16760 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16761 <s xml:id="echoid-s1754" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16762 Sint notæ et in 2, zetetico.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16763 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16764 This is noted also in Zetetic 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16765 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16766 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16767 For Harriot's treatment of Zetetic 2, see Add MS 6782, f. 474 and f. 472.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16768 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16769 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16770 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16771 <pb file="add_6782_f473v" o="473v" n="947"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16772 <pb file="add_6782_f474" o="474" n="948"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16773 <div xml:id="echoid-div318" type="page_commentary" level="2" n="318">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16774 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16775 <s xml:id="echoid-s1755" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16776 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16777 <s xml:id="echoid-s1755" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16778 This page contains Harriot's working of Zetetic 2 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16779 <emph style="it">Zeteticorum libri quinque</emph>, Book II.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16780 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16781 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16782 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16783 Zeteticum II <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16784 Dato rectangulo sub lateribus, & adgregato quadratorum, inveniuntur latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16785 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16786 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16787 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16788 Given the product of two sides, and the sum of their squares, the sides may be found.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16789 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16790 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16791 <s xml:id="echoid-s1756" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16792 Harriot's treatment of the problem is continued on Add MS 6782, f. 472.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16793 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16794 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16795 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16796 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16797 <head xml:id="echoid-head229" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16798 lib. 2. Zeteticorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16799 Zet. 2. primo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16800 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16801 Zetetica, Book II <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16802 Zetetic 2. First way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16803 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16804 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16805 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16806 <s xml:id="echoid-s1758" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16807 Dato rectangulo sub lateribus et adgregato quadratorum, inveniuntur latera. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16808 Hoc est: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16809 Data recta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>γ</mi></mstyle></math> et plano <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>; invenientur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16810 latera <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>γ</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16811 vel: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16812 Data recta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math> et quadrato <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ε</mi></mstyle></math>: invenientur <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16813 duæ <emph style="super">rectæ</emph> lineæ quæ cum data <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>γ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16814 efficiunt triangulum rectangulum æquale dimidio <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16815 dati quadrati <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ε</mi></mstyle></math>, ita ut linea data sit Hyponetusu. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16816 sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>: Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>γ</mi><mi>δ</mi></mstyle></math> erit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16817 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16818 Given a rectangle from its sides, and the sum of their squares, there may be found the sides. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16819 That is: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16820 Given the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>γ</mi></mstyle></math> and the surface <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16821 there may be found the sides <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>γ</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16822 or: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16823 Given the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>γ</mi></mstyle></math> and the square <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ε</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16824 there may be found two straight lines which, with the given line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>γ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16825 form a right-angled triangle equal to half the given square <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>ε</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16826 in such a way that the given line is the hypotenuse.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16827 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16828 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16829 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16830 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16831 <s xml:id="echoid-s1759" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16832 Aliter. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16833 Sit rectangulum datum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>. cui æquale <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>θ</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16834 et adgregatum quadratorum sit: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16835 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16836 data igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16837 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16838 Another way. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16839 Let the given rectangle be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>, which is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>θ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16840 and the sum of the squares is: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16841 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16842 therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16843 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16844 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16845 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16846 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16847 <s xml:id="echoid-s1760" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16848 Itaque in notis: sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> . <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16849 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16850 Inveniatur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, et dicatur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16851 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16852 Thus in symbols: let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math> be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16853 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16854 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> is found, and is said to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16855 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16856 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16857 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16858 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16859 <s xml:id="echoid-s1761" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16860 Et <emph style="super">quia</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>, est minor <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16861 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16862 And because <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16863 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16864 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16865 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16866 <pb file="add_6782_f474v" o="474v" n="949"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16867 <pb file="add_6782_f475" o="475" n="950"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16868 <div xml:id="echoid-div319" type="page_commentary" level="2" n="319">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16869 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16870 <s xml:id="echoid-s1762" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16871 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16872 <s xml:id="echoid-s1762" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16873 The reference at the top of this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16874 <emph style="it">Zeteticorum libri quinque</emph>, Book V, Zetetic 14.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16875 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16876 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16877 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16878 Zeteticum XIV <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16879 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> quadratum minus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> plano adaequare uni quadrato, quod fit minus quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16880 sed majus quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16881 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16882 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16883 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16884 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>-squared minus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math> is equal to a square, which is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi><mi>A</mi></mstyle></math> but greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi><mi>A</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16885 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16886 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16887 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16888 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16889 <head xml:id="echoid-head230" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16890 Zeteticorum. lib. 5. Zet: 14.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16891 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16892 Zetetica, Book V, Zetetic 14.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16893 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16894 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16895 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16896 <s xml:id="echoid-s1764" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16897 minus quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16898 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16899 less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16900 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16901 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16902 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16903 <s xml:id="echoid-s1765" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16904 maius quam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16905 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16906 greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16907 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16908 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16909 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16910 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16911 <s xml:id="echoid-s1766" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16912 Quæritur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, ponatur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16913 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16914 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math> is sought, suppose it is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16915 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16916 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16917 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16918 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16919 <s xml:id="echoid-s1767" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16920 solutio problematis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16921 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16922 solution to the problem
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16923 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16924 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16925 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16926 <pb file="add_6782_f475v" o="475v" n="951"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16927 <pb file="add_6782_f476" o="476" n="952"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16928 <div xml:id="echoid-div320" type="page_commentary" level="2" n="320">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16929 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16930 <s xml:id="echoid-s1768" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16931 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16932 <s xml:id="echoid-s1768" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16933 The reference at the top of this page appears to be to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16934 <emph style="it">Zeteticorum libri quinque</emph>, Book V, Zetetic 14,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16935 as on Add MS 6782, f. 475.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16936 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16937 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16938 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16939 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16940 <head xml:id="echoid-head231" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16941 Zet. lib. Zet: 14.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16942 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16943 Zetetica, Book [V], Zetetic 14.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16944 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16945 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16946 <pb file="add_6782_f476v" o="476v" n="953"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16947 <pb file="add_6782_f477" o="477" n="954"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16948 <div xml:id="echoid-div321" type="page_commentary" level="2" n="321">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16949 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16950 <s xml:id="echoid-s1770" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16951 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16952 <s xml:id="echoid-s1770" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16953 This page contains a lemma needed for Zetetic 10 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16954 <emph style="it">Zeteticorum libri quinque</emph>, Book II.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16955 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16956 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16957 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16958 Zeteticum X <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16959 Dato plano, quod constat tum rectangulo sub lateribus, tum quadratis singulorum laterum,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16960 datoque è lateribus uno, invenire latus reliquum.</quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16961 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16962 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16963 Given a plane, consisting of a rectangle from two sides together with the individual squares of the sides,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16964 and given also one of the sides, find the remaining side.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16965 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16966 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16967 <s xml:id="echoid-s1771" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16968 Viète called the given side <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, and the side to be found <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>D</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16969 and arrived at the following conclusion:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16970 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16971 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16972 <quote xml:lang="">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16973 Planum constans rectangulo sub lateribus, & quadratis singulorum laterum,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16974 multatum dodrante quadrati lateris dati, æquale est quadrato lateris compositi, ex quæsito latere & dimido dati.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16975 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16976 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16977 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16978 The plane consisting of a rectangle from the sides and the square of the individual sides,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16979 minus three-quarters of the square of the given root,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16980 is equal to the square of the line composed of the sought line and half the given line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16981 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16982 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16983 <s xml:id="echoid-s1772" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16984 Borrowing Viète's notation, his statement may be written as the identity
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16985 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>A</mi><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>D</mi><mrow><msup><mo maxsize="1">)</mo><mn>2</mn></msup></mrow><mo>+</mo><mrow><msup><mi>D</mi><mn>2</mn></msup></mrow><mo>+</mo><mo maxsize="1">(</mo><mi>D</mi><mi>A</mi><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mrow><msup><mi>D</mi><mn>2</mn></msup></mrow><mo maxsize="1">)</mo><mo>=</mo><mrow><msup><mi>A</mi><mn>2</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16986 On this page Harriot investigated the problem geometrically.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16987 On Add MS 6782, f. 479v, he treated it algebraically.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16988 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16989 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16990 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16991 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16992 <head xml:id="echoid-head232" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16993 Lemma. ad Zet. 2, 10.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16994 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16995 Lemma to Zetetic II.10
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16996 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16997 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16998 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	16999 <s xml:id="echoid-s1774" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17000 Si recta linea <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>β</mi></mstyle></math> dividatur bisariam in puncto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>γ</mi></mstyle></math>: et ei adjiciatur altera <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17001 linea <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math>: dico quod:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17002 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17003 If the straight line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>β</mi></mstyle></math> is divided in two at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>γ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17004 and to it is added another line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>δ</mi></mstyle></math>, I say that:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17005 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17006 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17007 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17008 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17009 <s xml:id="echoid-s1775" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17010 Aliter. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17011 Sit rectangulum datum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>. cui æquale <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>θ</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17012 et adgregatum quadratorum sit: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17013 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17014 data igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17015 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17016 Another way. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17017 Let the given rectangle be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>δ</mi></mstyle></math>, which is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>δ</mi><mi>θ</mi></mstyle></math>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17018 and the sum of the squares is: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17019 <lb/>[...]<lb/> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17020 therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>α</mi><mi>x</mi></mstyle></math> is given.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17021 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17022 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17023 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17024 <pb file="add_6782_f477v" o="477v" n="955"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17025 <pb file="add_6782_f478" o="478" n="956"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17026 <pb file="add_6782_f478v" o="478v" n="957"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17027 <pb file="add_6782_f479" o="479" n="958"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17028 <pb file="add_6782_f479v" o="479v" n="959"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17029 <div xml:id="echoid-div322" type="page_commentary" level="2" n="322">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17030 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17031 <s xml:id="echoid-s1776" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17032 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17033 <s xml:id="echoid-s1776" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17034 There are margin notes on this page referring to Zetetica 9 and 10 from Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17035 <emph style="it">Zeteticorum libri quinque</emph>, Book II.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17036 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17037 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17038 <quote xml:lang="">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17039 Zeteticum IX <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17040 Dato rectangulo sub lateribus, & differentia quadratorum, invenire latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17041 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17042 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17043 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17044 Given a rectangle from two sides and the difference of their squares, find the sides.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17045 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17046 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17047 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17048 Zeteticum X <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17049 Dato plano, quod constat tum rectangulo sub lateribus, tum quadratis singulorum laterum,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17050 datoque è lateribus uno, invenire latus reliquum.</quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17051 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17052 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17053 Given a plane, consisting of a rectangle from two sides together with the individual squares of the sides,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17054 and given also one of the sides, find the remaining side.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17055 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17056 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17057 <s xml:id="echoid-s1777" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17058 For a fuller investigation of Zetetic X, see Add MS 6782, f. 477.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17059 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17060 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17061 <s xml:id="echoid-s1778" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17062 At the bottom of the page there is what appears to be a list of books.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17063 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17064 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17065 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17066 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17067 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17068 <s xml:id="echoid-s1780" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17069 Zet.2,9
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17070 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17071 Zetetic II.9
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17072 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17073 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17074 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17075 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17076 <s xml:id="echoid-s1781" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17077 cubuc rectanguli sub <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17078 lateribus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17079 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17080 cube of the rectangle from the sides
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17081 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17082 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17083 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17084 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17085 <s xml:id="echoid-s1782" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17086 Zet.2,10
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17087 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17088 Zetetic II.10
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17089 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17090 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17091 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17092 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17093 <s xml:id="echoid-s1783" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17094 [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17095 [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17096 [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17097 [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17098 A bagg of books [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17099 Vitello <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17100 Euclid. 2. vol. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17101 physica Arist. [???] <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17102 Ethica Piccolomini
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17103 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17104 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17105 <pb file="add_6782_f480" o="480" n="960"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17106 <div xml:id="echoid-div323" type="page_commentary" level="2" n="323">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17107 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17108 <s xml:id="echoid-s1784" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17109 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17110 <s xml:id="echoid-s1784" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17111 The reference at the top of this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17112 <emph style="it">Zeteticorum libri quinque</emph>, Book V, Zetetic 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17113 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17114 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17115 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17116 Zeteticum IV <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17117 Invenire numero tria plana, quae bina juncta, ac etiam ipsa trium summa adscito dato plano,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17118 quadratum constituant.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17119 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17120 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17121 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17122 To find three plane numbers, of which the sum of any two, as also the sum of all three,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17123 added to a given plane, constitutes a square.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17124 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17125 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17126 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17127 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17128 <head xml:id="echoid-head233" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17129 Zet. 4: lib. 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17130 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17131 Zetetic 4, Book V.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17132 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17133 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17134 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17135 <s xml:id="echoid-s1786" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17136 Invenire numero tria plana quæ bina juncta ac etiam ipsa trium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17137 summa adscito dato plano Quadratum constituant.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17138 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17139 To find three plane numbers, of which the sum of any two, as also the sum of all three,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17140 added to a given plane, constitutes a square.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17141 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17142 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17143 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17144 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17145 <s xml:id="echoid-s1787" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17146 Sit datum planum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17147 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17148 Let the given plane be
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17149 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17150 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17151 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17152 <s xml:id="echoid-s1788" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17153 Aggregatum primi quæsiti <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17154 plani et secundi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17155 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17156 The sum of the first plane sought and the second
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17157 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17158 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17159 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17160 <s xml:id="echoid-s1789" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17161 Aggregatum secundi <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17162 et tertij
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17163 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17164 The sum of the second and the third
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17165 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17166 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17167 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17168 <s xml:id="echoid-s1790" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17169 Summa trium
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17170 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17171 The sum of the three
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17172 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17173 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17174 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17175 <s xml:id="echoid-s1791" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17176 Inde: summa <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math> aggregato <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17177 primi et secundi <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17178 erit tertium planum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17179 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17180 Whence: the sum, minus the sum of the first and the second, will be the first plane.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17181 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17182 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17183 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17184 <s xml:id="echoid-s1792" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17185 etiam: summa <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>-</mo></mstyle></math> aggregato <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17186 secundi et tertij <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17187 erit primum planum <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17188 also: the sum, minus the sum of the second and third, will be the first plane
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17189 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17190 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17191 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17192 <s xml:id="echoid-s1793" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17193 Inde: Aggregatum primi et <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17194 tertij adscito plani <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mn>1</mn></mstyle></math> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17195 æquale <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>f</mi></mstyle></math> quadrato
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17196 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17197 Whence: the sum of the first and third added to the plane <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mn>1</mn></mstyle></math> will equal the square <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>f</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17198 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17199 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17200 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17201 <pb file="add_6782_f480v" o="480v" n="961"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17202 <pb file="add_6782_f481" o="481" n="962"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17203 <div xml:id="echoid-div324" type="page_commentary" level="2" n="324">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17204 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17205 <s xml:id="echoid-s1794" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17206 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17207 <s xml:id="echoid-s1794" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17208 This page is one of the few that contains a date: 29 August 1600.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17209 The date is consistent with the suggestion that Harriot's friend Nathaniel Torporley met Viète in person
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17210 in Paris in the late 1590s, and brought Viète's books back to England (see Stedall 2003). <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17211 This appears to be the first of several pages in which Harriot worked systematically through Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17212 <emph style="it">Zeteticorum libri quinque</emph> (1591 or 1593),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17213 re-writing the propositions and proofs in his own notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17214 He began here with Zetetics 2 and 3 from Book 1; Zetetic 1 is sketched in outline on Add MS 6782, f. 463.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17215 He reached the end of Book I nine days later on 6 September (see Add MS 6782, f. 456.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17216 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17217 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17218 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17219 Zeteticum II <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17220 Data differentia duorum laterum, & ratione eorumdem, invenire latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17221 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17222 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17223 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17224 Given the difference of two roots, and their ratio, find the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17225 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17226 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17227 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17228 Zeteticum III <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17229 Data summa laterum, & ratione eorumdem: invenire latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17230 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17231 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17232 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17233 Given the sum of two sides, and their ratio, find the sides.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17234 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17235 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17236 <s xml:id="echoid-s1795" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17237 Viète used the letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>E</mi></mstyle></math> for the two roots, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>R</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math> for their ratio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17238 Harriot repeated Viète's working in his own symbolic notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17239 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17240 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17241 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17242 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17243 <head xml:id="echoid-head234" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17244 Zetet. lib. 1. Zet. 2. 1600. August. 29.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17245 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17246 Zetetica, Book I, Zetetic 2. 1600, August 29.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17247 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17248 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17249 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17250 <s xml:id="echoid-s1797" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17251 Datur differentia duorum laterum et ratione eorundem invenire latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17252 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17253 Given the difference of two roots and their ratio, find the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17254 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17255 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17256 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17257 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17258 <s xml:id="echoid-s1798" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17259 PrimÃ². <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17260 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> differentia <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17261 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> minus latus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17262 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> maius latus <emph style="st">in</emph> ratione
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17263 latus minus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17264 ergo latus maius <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>+</mo><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17265 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>,</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>:</mo><mi>r</mi><mo>,</mo><mi>s</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17266 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17267 First. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17268 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> be the difference, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17269 and let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> be the ratio of the smaller root to the larger root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17270 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the smaller root, therefore the larger root is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>+</mo><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17271 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>:</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mi>r</mi><mo>:</mo><mi>s</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17272 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17273 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17274 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17275 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17276 <s xml:id="echoid-s1799" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17277 SecundÃ² <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17278 latus maius. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17279 Ergo latus minus. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>-</mo><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17280 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>,</mo><mi>e</mi><mo>-</mo><mi>b</mi><mo>:</mo><mi>s</mi><mo>,</mo><mi>r</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17281 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17282 Second. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17283 Let the larger root be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>, therefore the smaller root is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>-</mo><mi>b</mi></mstyle></math>. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17284 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>:</mo><mi>e</mi><mo>-</mo><mi>b</mi><mo>=</mo><mi>s</mi><mo>:</mo><mi>r</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17285 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17286 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17287 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17288 <head xml:id="echoid-head235" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17289 Zet. 3. Data summa laterum, et ratione eorundem invenire latera.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17290 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17291 Zetetic 3. Given the sum of the roots and their ratio, find the roots.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17292 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17293 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17294 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17295 <s xml:id="echoid-s1800" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17296 primÃ². <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17297 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>G</mi></mstyle></math>. summa laterum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17298 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math>. minus latus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17299 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>. maius latus <emph style="st">in</emph> ratione <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17300 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. esto maius latus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17301 ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mo>-</mo><mi>a</mi></mstyle></math> latus minus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17302 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>,</mo><mi>g</mi><mo>-</mo><mi>a</mi><mo>:</mo><mi>r</mi><mo>,</mo><mi>s</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17303 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17304 First. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17305 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math> be the sum of the roots, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17306 and let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math> be the ratio of the smaller root to the larger root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17307 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> be the larger root, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mo>-</mo><mi>a</mi></mstyle></math> is the smaller root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17308 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mo>:</mo><mi>g</mi><mo>-</mo><mi>a</mi><mo>=</mo><mi>r</mi><mo>:</mo><mi>s</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17309 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17310 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17311 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17312 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17313 <s xml:id="echoid-s1801" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17314 secundÃ² <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17315 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. esto minus latus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17316 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>-</mo><mi>g</mi></mstyle></math>. maius latus. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17317 Ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>,</mo><mi>g</mi><mo>-</mo><mi>e</mi><mo>:</mo><mi>s</mi><mo>,</mo><mi>r</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17318 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17319 Second. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17320 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> be the smaller root, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>-</mo><mi>g</mi></mstyle></math> the larger root. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17321 Therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>:</mo><mi>g</mi><mo>-</mo><mi>e</mi><mo>=</mo><mi>s</mi><mo>:</mo><mi>r</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17322 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17323 [<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17324 Here <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mo>-</mo><mi>g</mi></mstyle></math> in the third line is clearly a writing or copying error for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mo>-</mo><mi>e</mi></mstyle></math>;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17325 Harriot has proceeded correctly with <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mo>-</mo><mi>e</mi></mstyle></math> in the fourth line.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17326 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17327 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17328 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17329 <pb file="add_6782_f481v" o="481v" n="963"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17330 <pb file="add_6782_f482" o="482" n="964"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17331 <pb file="add_6782_f482v" o="482v" n="965"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17332 <pb file="add_6782_f483" o="483" n="966"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17333 <pb file="add_6782_f483v" o="483v" n="967"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17334 <pb file="add_6782_f484" o="484" n="968"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17335 <pb file="add_6782_f484v" o="484v" n="969"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17336 <pb file="add_6782_f485" o="485" n="970"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17337 <pb file="add_6782_f485v" o="485v" n="971"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17338 <pb file="add_6782_f486" o="486" n="972"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17339 <pb file="add_6782_f486v" o="486v" n="973"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17340 <pb file="add_6782_f487" o="487" n="974"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17341 <pb file="add_6782_f487v" o="487v" n="975"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17342 <pb file="add_6782_f488" o="488" n="976"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17343 <pb file="add_6782_f488v" o="488v" n="977"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17344 <pb file="add_6782_f489" o="489" n="978"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17345 <pb file="add_6782_f489v" o="489v" n="979"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17346 <pb file="add_6782_f490" o="490" n="980"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17347 <div xml:id="echoid-div325" type="page_commentary" level="2" n="325">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17348 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17349 <s xml:id="echoid-s1802" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17350 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17351 <s xml:id="echoid-s1802" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17352 This page contains work on one of the ratios given by Viète under the heading 'Syntomon'
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17353 in Chapter XIX, Proposition 21 of <emph style="it">Variorum responsorum liber VIII</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17354 For other pages based on the same (36, 45, 70)-degree spherical triangle see Add MS 6787, f. 36 to 39.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17355 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17356 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17357 <s xml:id="echoid-s1803" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17358 The reference to Regiomontanus is to his <emph style="it">De triangulis omnimodis</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17359 Book 5, Proposition 2. For the same proposition, see also Add MS 6787, f. 51.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17360 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17361 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17362 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17363 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17364 <head xml:id="echoid-head236" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17365 Investigatio analogiæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17366 Vietanæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17367 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17368 An investigation of one of Viète's ratios
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17369 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17370 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17371 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17372 <s xml:id="echoid-s1805" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17373 (Investigavit Vieta <emph style="super">(ut putamus)</emph> per <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17374 diagramma Regiomontani <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17375 lib. 5. pr. de triangulis <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17376 cum quibusdam additamentis,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17377 ut nos <emph style="st">alibi</emph> etiam alibi.)
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17378 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17379 Viète investigated this (as I believe) from a diagram of Regiomontanus in Book 5 of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17380 <emph style="it">De triangulis</emph> with certain additions, as I have also done elsewhere.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17381 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17382 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17383 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17384 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17385 <s xml:id="echoid-s1806" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17386 ut Vieta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17387 pag: 47.b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17388 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17389 As Viète, page 47v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17390 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17391 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17392 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17393 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17394 <s xml:id="echoid-s1807" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17395 ut Vieta <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17396 pag: 35.b.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17397 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17398 As Viète, page 35v.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17399 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17400 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17401 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17402 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17403 <s xml:id="echoid-s1808" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17404 conditiones <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17405 alteri Δ<emph style="super">i</emph> <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17406 contrariæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17407 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17408 conditions in other, opposite triangles
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17409 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17410 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17411 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17412 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17413 <s xml:id="echoid-s1809" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17414 Nota. Et si signum (<) ponatur sub <emph style="st">ab</emph>, intelligetur quod ab < 90. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17415 Ita signum (>) sub <emph style="st">d</emph>, denotat d > 90. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17416 Istud signum, (< >), denotat unum latus maius alterum minus 90. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17417 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17418 Note. If this sign (<) is placed under <emph style="st">ab</emph>, it is to be understood that ab < 90. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17419 This sign (>) under <emph style="st">d</emph>, indicates that d > 90. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17420 These signs, (< >), indicate that one side is greater than, the other less than 90. &c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17421 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17422 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17423 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17424 <pb file="add_6782_f490v" o="490v" n="981"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17425 <pb file="add_6782_f491" o="491" n="982"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17426 <div xml:id="echoid-div326" type="page_commentary" level="2" n="326">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17427 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17428 <s xml:id="echoid-s1810" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17429 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17430 <s xml:id="echoid-s1810" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17431 This page contains work on one of the ratios given by Viète under the heading 'Syntomon'
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17432 in Chapter XIX, Proposition 21 of <emph style="it">Variorum responsorum liber VIII</emph>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17433 For other pages based on the same (36, 45, 70)-degree spherical triangle see Add MS 6787, f. 36 to 39.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17434 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17435 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17436 <s xml:id="echoid-s1811" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17437 The reference to Regiomontanus is to his <emph style="it">De triangulis omnimodis</emph>,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17438 Book 5, Proposition 2. For the same proposition, see also Add MS 6787, f. 51.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17439 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17440 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17441 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17442 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17443 <head xml:id="echoid-head237" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17444 Investigatio omnium <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17445 analogiarum et casuum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17446 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17447 An investigation of all the ratios and cases.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17448 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17449 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17450 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17451 <s xml:id="echoid-s1813" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17452 Æquationes conjugatæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17453 sunt eadem: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17454 et una est <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17455 impossibilis: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17456 sunt igiture <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17457 tres tantum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17458 diversæ <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17459 æquationes. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17460 et <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17461 illæ, tres <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17462 primæ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17463 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17464 The conjugate equations are the same, and one is impossible;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17465 there are therefore as many as three different equations, and of these, the first three.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17466 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17467 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17468 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17469 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17470 <s xml:id="echoid-s1814" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17471 Ergo sunt tres analogiæ diversæ, et casus 6.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17472 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17473 Therefore there are three different ratios, and 6 cases.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17474 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17475 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17476 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17477 <pb file="add_6782_f491v" o="491v" n="983"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17478 <pb file="add_6782_f492" o="492" n="984"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17479 <pb file="add_6782_f492v" o="492v" n="985"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17480 <pb file="add_6782_f493" o="493" n="986"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17481 <pb file="add_6782_f493v" o="493v" n="987"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17482 <pb file="add_6782_f494" o="494" n="988"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17483 <pb file="add_6782_f494v" o="494v" n="989"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17484 <pb file="add_6782_f495" o="495" n="990"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17485 <pb file="add_6782_f495v" o="495v" n="991"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17486 <pb file="add_6782_f496" o="496" n="992"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17487 <pb file="add_6782_f496v" o="496v" n="993"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17488 <pb file="add_6782_f497" o="497" n="994"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17489 <pb file="add_6782_f497v" o="497v" n="995"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17490 <pb file="add_6782_f498" o="498" n="996"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17491 <pb file="add_6782_f498v" o="498v" n="997"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17492 <pb file="add_6782_f499" o="499" n="998"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17493 <pb file="add_6782_f499v" o="499v" n="999"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17494 <pb file="add_6782_f500" o="500" n="1000"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17495 <pb file="add_6782_f500v" o="500v" n="1001"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17496 <pb file="add_6782_f501" o="501" n="1002"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17497 <div xml:id="echoid-div327" type="page_commentary" level="2" n="327">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17498 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17499 <s xml:id="echoid-s1815" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17500 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17501 <s xml:id="echoid-s1815" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17502 The reference at the top of this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17503 <emph style="it">Zeteticorum libri quinque</emph>, Book IV, Zetetic 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17504 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17505 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17506 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17507 Zeteticum IV <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17508 Invenire duo triangula rectangula simili datas habentes hypotenusas,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17509 & diducti ab iis tertii trianguli basis, composita ex perpendiculo primi & base secundi,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17510 erit ea quæ præfinitur. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17511 Oportebit autem basim illam præfinitam præstare hypotenusæ primi.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17512 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17513 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17514 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17515 To find two similar right-angled triangles having given hypotenuses,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17516 and subtracting the base of a third triangle,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17517 composed of the perpendicular of the first and the base of the second,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17518 will give a predefined quantity.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17519 The predefined base, moreover, must be greater than the hypotenuse of the first triangle.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17520 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17521 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17522 <s xml:id="echoid-s1816" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17523 Viète used the letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math> for the hypotenuses of the first and second triangles,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17524 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>M</mi></mstyle></math> for the perpendicular of the third.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17525 Harriot followed Viète's working but in his own lower-case notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17526 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17527 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17528 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17529 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17530 <head xml:id="echoid-head238" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17531 Zet. 4. 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17532 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17533 Zetetica, Book IV, Zetetic 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17534 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17535 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17536 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17537 <s xml:id="echoid-s1818" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17538 operatio fit <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17539 per. 3am
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17540 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17541 the operation may be done by the third
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17542 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17543 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17544 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17545 <pb file="add_6782_f501v" o="501v" n="1003"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17546 <pb file="add_6782_f502" o="502" n="1004"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17547 <div xml:id="echoid-div328" type="page_commentary" level="2" n="328">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17548 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17549 <s xml:id="echoid-s1819" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17550 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17551 <s xml:id="echoid-s1819" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17552 The reference at the top of this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17553 <emph style="it">Zeteticorum libri quinque</emph>, Book IV, Zetetic 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17554 This is also Proposition II.9 from the <emph style="it">Arithmetica</emph> of Diophantus,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17555 but Harriot refers only to Viète's version of it.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17556 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17557 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17558 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17559 Zeteticum II <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17560 Invenire numero duo quadrata, aequalia duobus aliis datis quadratis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17561 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17562 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17563 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17564 To find in numbers two squares equal to two other given squares.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17565 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17566 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17567 <s xml:id="echoid-s1820" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17568 One may interpret the problem as asking for two sets of Pythagorean triples with the same third side,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17569 or two rational right-angled triangles with the same hypotenuse.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17570 Viète called the sides of the first two squares <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, and the hypotenuse <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Z</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17571 The words 'synæreseos' and 'diæreseos' were used by Viète and are typical of the Greek terms
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17572 he frequently introduced into his writing.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17573 Harriot followed Viète's working but in his own lower-case notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17574 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17575 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17576 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17577 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17578 <head xml:id="echoid-head239" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17579 Zet. lib. 4. 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17580 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17581 Zetetica, Book IV, Zetetic 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17582 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17583 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17584 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17585 <s xml:id="echoid-s1822" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17586 prop. 2.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17587 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17588 Proposition 2
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17589 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17590 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17591 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17592 <s xml:id="echoid-s1823" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17593 via synæreseos
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17594 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17595 by expansion
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17596 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17597 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17598 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17599 <s xml:id="echoid-s1824" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17600 via diæreseos
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17601 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17602 by contraction
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17603 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17604 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17605 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17606 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17607 <s xml:id="echoid-s1825" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17608 prop. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17609 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17610 Proposition 1
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17611 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17612 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17613 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17614 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17615 <s xml:id="echoid-s1826" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17616 prop. 3. eadem ac secunda aliter
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17617 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17618 Proposition 3. the same and the second another way.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17619 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17620 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17621 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17622 <pb file="add_6782_f502v" o="502v" n="1005"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17623 <pb file="add_6782_f503" o="503" n="1006"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17624 <div xml:id="echoid-div329" type="page_commentary" level="2" n="329">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17625 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17626 <s xml:id="echoid-s1827" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17627 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17628 <s xml:id="echoid-s1827" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17629 The reference at the top of this page is to Viète's
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17630 <emph style="it">Zeteticorum libri quinque</emph>, Book IV, Proposition 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17631 This is also Proposition II.9 from the <emph style="it">Arithemtica</emph> of Diophantus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17632 (see also Add MS 6782, f. 502).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17633 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17634 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17635 <quote xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17636 Zeteticum II <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17637 Rursus, invenire numero duo quadrata, aequalia duobus aliis datis quadratis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17638 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17639 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17640 <quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17641 Again, to find in numbers two squares equal to two other given squares.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17642 </quote>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17643 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17644 <s xml:id="echoid-s1828" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17645 One may interpret the problem as asking for two sets of Pythagorean triples with the same third side,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17646 or two rational right-angled triangles with the same hypotenuse.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17647 Viète called the sides of the first two squares <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17648 Harriot followed Viète's working but in his own lower-case notation.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17649 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17650 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17651 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17652 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17653 <head xml:id="echoid-head240" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17654 Zet. lib. 4. 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17655 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17656 Zetetica, Book IV, Zetetic 3.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17657 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17658 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17659 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17660 <s xml:id="echoid-s1830" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17661 1. triang.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17662 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17663 triangle 1
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17664 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17665 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17666 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17667 <s xml:id="echoid-s1831" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17668 2. Δ. simili.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17669 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17670 triangle 2, similar
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17671 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17672 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17673 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17674 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17675 <s xml:id="echoid-s1832" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17676 3. Δ.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17677 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17678 triangle 3
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17679 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17680 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17681 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17682 <s xml:id="echoid-s1833" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17683 3. Δ. alterum.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17684 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17685 triangle 3, alternative
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17686 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17687 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17688 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17689 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17690 <s xml:id="echoid-s1834" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17691 3. Δ. aliter.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17692 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17693 triangle 3 another way
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17694 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17695 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17696 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17697 <pb file="add_6782_f503v" o="503v" n="1007"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17698 <pb file="add_6782_f504" o="504" n="1008"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17699 <pb file="add_6782_f504v" o="504v" n="1009"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17700 <pb file="add_6782_f505" o="505" n="1010"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17701 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17702 <s xml:id="echoid-s1835" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17703 Talia problemata hic
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17704 <emph style="super">schemata explicantur</emph>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17705 <emph style="st">apponuntur</emph> quæ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17706 <emph style="st">conducunt</emph> ad Magisteriorum <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17707 formas conducunt intelligendas. <emph style="st">[???]</emph> similis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17708 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17709 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17710 <pb file="add_6782_f505v" o="505v" n="1011"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17711 </div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17712 </text>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/ casties parents: diff changeset	17713 </echo>

Mercurial > hg > mpdl-xml-content

annotate texts/XML/echo/en/Harriot_Add_MS_6782_HSPGZ0AE.xml @ 6:22d6a63640c6