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  <metadata>
    <dcterms:identifier>ECHO:AYB35Z4D.xml</dcterms:identifier>
    <dcterms:creator>Harriot, Thomas</dcterms:creator>
    <dcterms:title xml:lang="en">Mss. 6788</dcterms:title>
    <dcterms:date xsi:type="dcterms:W3CDTF">null</dcterms:date>
    <dcterms:language xsi:type="dcterms:ISO639-3">eng</dcterms:language>
    <dcterms:rights>CC-BY-SA</dcterms:rights>
    <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license>
    <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder>
    <echodir>/permanent/library/AYB35Z4D</echodir>
    <log>Automatically generated by BareEchoXml.java on 13-Mar-2012 17:47</log>
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  <text xml:lang="eng" type="free">
 <div xml:id="echoid-div1" type="section" level="1" n="1">
 <pb file="0001.jpg" o="1r" n="1"/>
 <pb file="0002.jpg" o="1v" n="2"/>
 <pb file="0003.jpg" o="2r" n="3"/>
 <head xml:id="echoid-head1" xml:space="preserve">
 [b].) Length of mastes by calculation
 in feet, &amp; tenths of a foote.
 </head>
 <p>
 <s xml:id="echoid-s1" xml:space="preserve">
 The ships: <lb/>
 depth: breadth: length:
 </s>
 <lb/>
 <s xml:id="echoid-s2" xml:space="preserve">
 Tonnes <lb/>
 of <lb/>
 burden.
 </s>
 <lb/>
 <s xml:id="echoid-s3" xml:space="preserve">
 bredth of <lb/>
 the ship.
 </s>
 <lb/>
 <s xml:id="echoid-s4" xml:space="preserve">
 lengths of the <lb/>
 mayne mast.
 </s>
 <lb/>
 <s xml:id="echoid-s5" xml:space="preserve">
 Differences
 </s>
 </p>
 <p>
 <s xml:id="echoid-s6" xml:space="preserve">
 The tonnes here were <lb/>
 found by cubicall proportion. <lb/>
 The which Mr Bakers rule <lb/>
 doth <emph style="super">also</emph> bring forth <reg norm="instantly" type="abbr">instly</reg>.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s7" xml:space="preserve">
 The caracte taken by Sr John Burrows 1592. voyadger 2. <emph style="super">p.</emph> 198. <lb/>
 depth. bredth. lengthe. lengthe of the maste. circuit at the parteners. mayne yard. <lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s8" xml:space="preserve">
 Tonnage by judgement &amp; report. 1600. tonne. <lb/>
 by the former rule of Baker. 1457. tonne.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s9" xml:space="preserve">
 The Prince <lb/>
 1610. <lb/>
 [???]. <lb/>
 Sept. 25.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s10" xml:space="preserve">
 length. 132f. by the keele (21f rake of the poste, 45f rake of the stern) <lb/>
 beake end <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn><mn>3</mn><mn>2</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mn>2</mn></mstyle></math> <lb/>
 summe: 220f <lb/>
 bredth. 44f <lb/>
 width. 18f. maide. likely to draw 19f laden.
 </s>
 </p>
 <pb file="0004.jpg" o="2v" n="4"/>
 <p xml:lang="lat">
 <s xml:id="echoid-s11" xml:space="preserve">
 Nota pro pagina (a)
 <lb/>[<emph style="it">tr:
 Note for page a.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0005.jpg" o="3r" n="5"/>
 <head xml:id="echoid-head2" xml:space="preserve">
 [a].) for the mastes of ships (mayne mast)
 </head>
 <p>
 <s xml:id="echoid-s12" xml:space="preserve">
 By experience: as the bredth <lb/>
 the maste:
 </s>
 </p>
 <p>
 <s xml:id="echoid-s13" xml:space="preserve">
 Data: Mastes <lb/>
 bredth
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s14" xml:space="preserve">
 1<emph style="super">o</emph> Quæritur: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> diameter hyperboles? <lb/>
 per, 21, p: lib. 1. <lb/>
 Appol. <lb/>
 hoc est: <lb/>
 dantur omnes præter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, sit igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <lb/>
 unde per æquationem habetur
 <lb/>[<emph style="it">tr:
 1. There is sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, the diameter of a hyperbola? <lb/>
 By Proposition I.21 of Apollonius, <lb/>
 that is: <lb/>
 There are given all besides <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>, therefore let there be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, <lb/>
 whence by the equation are had:
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s15" xml:space="preserve">
 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> etiam dicitur <lb/>
 latus transversum)
 <lb/>[<emph style="it">tr:
 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> is also said to be the latus transversum)
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s16" xml:space="preserve">
 2<emph style="super">o</emph> Quæritur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, latus rectum. (figuræ <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>) <lb/>
 vel linea iuxta quam possunt ordinatim applicatæ. <lb/>
 per eandem <lb/>
 21, p: lib. 1. <lb/>
 Appol. <lb/>
 hoc est: <lb/>
 datur igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, latus rectum.
 <lb/>[<emph style="it">tr:
 2. There is sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, the latus rectum (<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> in the figure),
 or adjacent lines which can be applied ordinates. <lb/>
 By the same Proposition I.21 of Apollonius, <lb/>
 that is: <lb/>
 Therefore there is given <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math>, the latus rectum.
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s17" xml:space="preserve">
 lineæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>f</mi></mstyle></math> &amp;c. <lb/>
 dicuntur lineæ <lb/>
 ordinatim applicatæ.
 <lb/>[<emph style="it">tr:
 the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>f</mi></mstyle></math> etc. are said to be the applied ordinates.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s18" xml:space="preserve">
 3<emph style="super">o</emph> Quæritur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>q</mi></mstyle></math>, linea cuius quadratum æquatur <lb/>
 quartæ parti figuræ. <lb/>
 per 1,p: 2<emph style="super">i</emph> lib. <lb/>
 Appol. <lb/>
 <lb/>[...]<lb/> <lb/>
 unde habetur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>q</mi></mstyle></math>. et inde ducuntur <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>q</mi></mstyle></math>, et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>r</mi></mstyle></math> asymptoti (per centrum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>) <lb/>
 Et inde hyperbole describitur.
 <lb/>[<emph style="it">tr:
 3. There is sought <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>q</mi><mn>4</mn><mo>,</mo><mi>t</mi><mi>h</mi><mi>e</mi><mi>l</mi><mi>i</mi><mi>n</mi><mi>e</mi><mi>w</mi><mi>h</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>s</mi><mi>q</mi><mi>u</mi><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>s</mi><mi>a</mi><mi>f</mi><mi>o</mi><mi>u</mi><mi>r</mi><mi>t</mi><mi>h</mi><mi>p</mi><mi>r</mi><mi>t</mi><mi>o</mi><mi>f</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>f</mi><mi>i</mi><mi>g</mi><mi>u</mi><mi>r</mi><mi>e</mi><mo>.</mo></mstyle></math><lb/>
 By Proposition II.1 of Apollonius, <lb/>
 <lb/>[...]<lb/> <lb/>
 Whence is had <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>q</mi></mstyle></math>, and hence there may be drawn <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>q</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>r</mi></mstyle></math>, the asympototes,
 and hence the hyperbola is described.
 </emph>]<lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s19" xml:space="preserve">
 To find the lengths of other mastes by numbers. <lb/>
 Let the bredth: (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi><mi>a</mi></mstyle></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>a</mi></mstyle></math>) be <lb/>
 taken in tenths of a foote &amp; then <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mo>=</mo><mn>5</mn><mn>2</mn><mn>4</mn><mfrac><mrow><mn>2</mn></mrow><mrow><mn>7</mn></mrow></mfrac></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi><mo>=</mo><mn>1</mn><mn>2</mn><mn>9</mn><mn>6</mn></mstyle></math> <lb/>
 &amp; so for any others. <lb/>
 Invented this: Feb: 28th 1607/1608. <lb/>
 &amp; gave it to E. Marlow <lb/>
 for Mr Baker the shipwrite.
 </s>
 </p>
 <pb file="0006.jpg" o="3v" n="6"/>
 <pb file="0007.jpg" o="4r" n="7"/>
 <p>
 <s xml:id="echoid-s20" xml:space="preserve">
 This way therefore the calculation may <lb/>
 be also made.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s21" xml:space="preserve">
 I am of opinion that depth is to be <lb/>
 regarded with the bredth for the length of <lb/>
 the mastes: for put the case I have the <lb/>
 mast length for 20 foot broad &amp; 10 foote <lb/>
 deep, which is 60 foot as in the table.
 </s>
 <lb/>
 <s xml:id="echoid-s22" xml:space="preserve">
 And then I keeping the bredth <lb/>
 wold have my ship of <emph style="st">[???]</emph> <lb/>
 lesser depth as 7 foot; the maste is <lb/>
 also to be shorter. &amp; then consider <emph style="st">whether</emph> <lb/>
 whether the shortening of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi></mstyle></math> the latus rectum in proportion to the depth <lb/>
 will bring forthe the length of the second maste or not.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s23" xml:space="preserve">
 The length of the ship in this reckoning I thinkw also to be like <lb/>
 regarded because, when the mast is fitted for bredth &amp; <lb/>
 depth, it cannot be amisse for the longest dimension. <lb/>
 Therefore I make the rule thus:
 </s>
 </p>
 <pb file="0008.jpg" o="4v" n="8"/>
 <pb file="0009.jpg" o="5r" n="9"/>
 <pb file="0010.jpg" o="5v" n="10"/>
 <pb file="0011.jpg" o="6r" n="11"/>
 <pb file="0012.jpg" o="6v" n="12"/>
 <pb file="0013.jpg" o="7r" n="13"/>
 <pb file="0014.jpg" o="7v" n="14"/>
 <pb file="0015.jpg" o="8r" n="15"/>
 <div xml:id="echoid-div1" type="page_commentary" level="2" n="1">
<p>
<s xml:id="echoid-s24" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s24" xml:space="preserve">
 The problem of finding a circle touching two given points and a given line is here called the
 'Problema naupegicum', though is not clear from these pages exactly how this problem is relevant to ship-building.
 Harriot notes that he has met the problem elsewhere, in the pages of Pappus, Book 7,
 where it is attributed to Apollonius.
 It seems that at this time Harriot was not yet as familiar with the work of Apollonius
 as he later became. For much more work on this and related problems,
 see his notes on Viète's <emph style="it">Apollonius Gallus</emph> (1600). <lb/>
 Observe that where Harriot moves into formal mathematics he also begins to write in Latin.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head3" xml:space="preserve" xml:lang="lat">
 Problema Naupegicum
 </head>
 <p xml:lang="lat">
 <s xml:id="echoid-s26" xml:space="preserve">
 Hinc problema unum Appoloniacum <emph style="super">solvitur</emph>, <lb/>
 de quo mentionem facit Pappus lib. 7. <lb/>
 ex. lib. Appol. <lb/>[...]<lb/> <lb/>
 pa. 159.
 <lb/>[<emph style="it">tr:
 This problem is an Apollonian one, solved, of which mention is made in
 Pappus, Book 7, on the Book of Apollonius, page 159. <lb/>
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s27" xml:space="preserve">
 Datis duobus punctis et linea: <lb/>
 circulum, illa tria contingentem, describere.
 <lb/>[<emph style="it">tr:
 Given two points and line, to draw a circle touching those three.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s28" xml:space="preserve">
 Puncta data: <lb/>
 <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>e</mi></mstyle></math> <lb/>
 linea data <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>d</mi></mstyle></math> <lb/>
 interminata.
 <lb/>[<emph style="it">tr:
 The given points, <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>e</mi></mstyle></math>; the given line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>d</mi></mstyle></math>, continued indefinitely.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s29" xml:space="preserve">
 Quæritur: <lb/>
 punctum contactus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>.
 <lb/>[<emph style="it">tr:
 Sought is the point of contact, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s30" xml:space="preserve">
 cæteri casus <lb/>
 possibiles et <lb/>
 impossibiles facile <lb/>
 intelligantur <lb/>
 vide alteram paginam.
 <lb/>[<emph style="it">tr:
 Other cases, possible and impossible, are easily understood, see the other page.
 </emph>]<lb/>
 [<emph style="it">Note:
 The other sheet referred to here is the reverse of this one, Add MS 6788, f. 8v,
 which lists some possible and impossible cases.
  </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s31" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>e</mi></mstyle></math> datis, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi></mstyle></math> nota erit. <lb/>
 <lb/>[...]<lb/> <lb/>
 Igitur <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>s</mi></mstyle></math> est media proportionalis inter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>s</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>s</mi></mstyle></math>, et nota <lb/>
 centrum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math> erit in concursum perpendicularium <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>A</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>A</mi></mstyle></math>. <lb/>
 Dabuntur etiam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>h</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>d</mi></mstyle></math>. vel <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>l</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>l</mi><mi>e</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>l</mi><mo>=</mo><mi>l</mi><mi>e</mi></mstyle></math>. quia <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>l</mi><mi>e</mi></mstyle></math> rectus. <lb/>
 In triangulo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>t</mi><mi>b</mi></mstyle></math> dantur duo latera et angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>t</mi><mi>e</mi><mi>b</mi></mstyle></math>; ergo omnia latera <lb/>
 et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>h</mi></mstyle></math> semidiameter peripheriæ circumscribentis dabuntur in numeris <lb/>
 canonis per doctrinam triangulorum, et etiam in partibus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> primo datis.
 <lb/>[<emph style="it">tr:
 If <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>i</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>e</mi></mstyle></math> are given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>e</mi></mstyle></math> will be known. <lb/>
 <lb/>[...]<lb/> <lb/>
 Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>s</mi></mstyle></math> is the mean proportional between <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>s</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>s</mi></mstyle></math>, and the known centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi></mstyle></math>
 will be at the metting point of the perpendicular <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>A</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>A</mi></mstyle></math>. <lb/>
 Also <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>h</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>d</mi></mstyle></math> are given, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>l</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>l</mi><mi>e</mi></mstyle></math>; and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>l</mi><mo>=</mo><mi>l</mi><mi>e</mi></mstyle></math> because <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>l</mi><mi>e</mi></mstyle></math> is a right angle. <lb/>
 In the triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>t</mi><mi>b</mi></mstyle></math> there are given two lines and the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>t</mi><mi>e</mi><mi>b</mi></mstyle></math>; therefore all the sides and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>A</mi><mi>h</mi></mstyle></math>,
 the semidiameter of the circumscribed circumference are given in tabulated numbers by the doctrine of triangles,
 and also in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, given at the beginning.
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s32" xml:space="preserve">
 Et sine doctrina triangulorum in hinc modum quæsita inveninuntur:
 <lb/>[<emph style="it">tr:
 And without the doctrine of traingles, what is sought may be found by this method:
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s33" xml:space="preserve">
 Facillima <lb/>
 operatio <emph style="st">notatur</emph> <lb/>
 notatur *
 <lb/>[<emph style="it">tr:
 Most easily the working may be denoted as at *
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0016.jpg" o="8v" n="16"/>
 <p xml:lang="lat">
 <s xml:id="echoid-s34" xml:space="preserve">
 Sit recta linea inter duo puncta data:
 <lb/>[<emph style="it">tr:
 Let the straight line be between the two given points:
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0017.jpg" o="9r" n="17"/>
 <p>
 <s xml:id="echoid-s35" xml:space="preserve">
 Mr. Fr: Godolphin
 </s>
 </p>
 <pb file="0018.jpg" o="9v" n="18"/>
 <pb file="0019.jpg" o="10r" n="19"/>
 <head xml:id="echoid-head4" xml:space="preserve" xml:lang="lat">
 Problema Appolonicum aliud. vide Pappum. lib. 7. pag. 159.
 <lb/>[<emph style="it">tr:
 Another problem of Apollonius, see Pappus, Book 7, page 159.
 </emph>]<lb/>
 </head>
 <p xml:lang="lat">
 <s xml:id="echoid-s36" xml:space="preserve">
 Datis duobus punctis intra peripheriam circuli: per illa puncta <lb/>
 et terminos Diametri circuli dati, peripheriam circuli ducere.
 <lb/>[<emph style="it">tr:
 Given two points inside the circumference of a circle,
 through those points and the ends of the diameter of the given circle,
 draw the circumference of a circle.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s37" xml:space="preserve">
 Data. <lb/>
 <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>. puncta.
 <lb/>[<emph style="it">tr:
 Given, the points <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>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s38" xml:space="preserve">
 Ex ista constructione <lb/>
 cæteri casus facile <lb/>
 intelligantur.
 <lb/>[<emph style="it">tr:
 From this construction, other cases are easily understood.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s39" xml:space="preserve">
 Usus in planisphæ-<lb/>
 rio ptolomaico.
 <lb/>[<emph style="it">tr:
 Used in the planisphere of Ptolemy.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s40" xml:space="preserve">
 Sit iam factum. Et peripheria circuli transiens per data puncta sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>h</mi></mstyle></math> <lb/>
 cuius centrum <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>c</mi><mi>f</mi><mi>e</mi></mstyle></math> diameter circuli dati. a punctis <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>b</mi></mstyle></math> datis ducuntur <lb/>
 per centrum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, <emph style="super">lineæ</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi><mi>h</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi><mi>m</mi></mstyle></math>.
 Rectangulum ex <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>f</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi></mstyle></math>; hoc est quadratum <lb/>
 ex <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi></mstyle></math>, æquantur rectangulo ex <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>h</mi></mstyle></math>; vel <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>m</mi></mstyle></math>. Ergo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi></mstyle></math> est media <lb/>
 proportionalis inter <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>h</mi></mstyle></math>.
 <lb/>[<emph style="it">tr:
 Suppose it already done. And let the circumference of the circle passing through the given points be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>h</mi></mstyle></math>,
 whose centre is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>. And <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>f</mi><mi>e</mi></mstyle></math> is the diameter of the given circle. From the given points <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>b</mi></mstyle></math>
 there are drawn through the centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi><mi>h</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi><mi>m</mi></mstyle></math>.
 The product of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>f</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi></mstyle></math>, that is, the square of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi></mstyle></math>, is equal to the product of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>h</mi></mstyle></math>,
 or of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>m</mi></mstyle></math>. Therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>e</mi></mstyle></math> is the mean proportional between <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>h</mi></mstyle></math>.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s41" xml:space="preserve">
 Problema igitur perficitur ad hunc modum. A punctis datis <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>b</mi></mstyle></math> ducantur rectæ <lb/>
 ad centrum <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>a</mi><mi>f</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math>. ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> et a puncto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>d</mi></mstyle></math> perpendicularis, ut <lb/>
 ducatur recta <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math>. et a puncto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> erigatur perpendicularis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>o</mi></mstyle></math>. producatur <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> et concurret cum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>o</mi></mstyle></math> in puncto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>. a medio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>h</mi></mstyle></math> fit perpendicularis <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>g</mi></mstyle></math> <lb/>
 et a mdeio <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> sit perpendicularsi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>r</mi></mstyle></math>. secabit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>q</mi></mstyle></math> in puncto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>. quod est centrum <lb/>
 peripheriæ quæsitæ. demonstratio manifesta ex propertate superius allata. &amp;c.
 <lb/>[<emph style="it">tr:
 The problem is therefore brought about in this way. From the given points <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>b</mi></mstyle></math>
 there are drawn the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math> to the centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>.
 Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>d</mi></mstyle></math> be perpendicular to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, so that there is drawn the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi></mstyle></math>.
 And form the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> there is erected the perpendicular <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>o</mi></mstyle></math>.
 The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>f</mi></mstyle></math> is extended and meets <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>o</mi></mstyle></math> in the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi></mstyle></math>.
 From the middle of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>h</mi></mstyle></math> there is constructed the perpendicular <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>g</mi></mstyle></math>,
 and from the middle of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> the perpendicular <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>r</mi></mstyle></math> will cut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>q</mi></mstyle></math> in the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>g</mi></mstyle></math>,
 which is the centre of the sought circumference.
 The demonstration is clear from the property reported above. etc.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s42" xml:space="preserve">
 Si dentur <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>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math>, et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>e</mi></mstyle></math> in numeris; Dabuntur etiam in iisdem <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>g</mi></mstyle></math> et <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>g</mi></mstyle></math> <lb/>
 nam angulus <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi><mi>h</mi></mstyle></math> cogitus est ex data triangulo <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>f</mi></mstyle></math>. Dantur <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>h</mi></mstyle></math>. notum igitur <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math>. et diameter circumscribentis peripheriæ per doctrinam triangulorum. &amp;c.
 <lb/>[<emph style="it">tr:
 If there are given <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>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>f</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>e</mi></mstyle></math> in numbers,
 there will be given also in the same way <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>i</mi><mi>g</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>g</mi></mstyle></math>, for the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>a</mi><mi>h</mi></mstyle></math>
 is known from the given triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>f</mi></mstyle></math>. The lines <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>h</mi></mstyle></math> are given, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>h</mi></mstyle></math> is known,
 and the diameter of the circumference of the circumscribing circle from the doctrine of triangles. etc.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0020.jpg" o="10v" n="20"/>
 <pb file="0021.jpg" o="11r" n="21"/>
 <pb file="0022.jpg" o="11v" n="22"/>
 <pb file="0023.jpg" o="12r" n="23"/>
 <pb file="0024.jpg" o="12v" n="24"/>
 <pb file="0025.jpg" o="13r" n="25"/>
 <pb file="0026.jpg" o="13v" n="26"/>
 <pb file="0027.jpg" o="14r" n="27"/>
 <pb file="0028.jpg" o="14v" n="28"/>
 <pb file="0029.jpg" o="15r" n="29"/>
 <div xml:id="echoid-div2" type="page_commentary" level="2" n="2">
<p>
<s xml:id="echoid-s43" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s43" xml:space="preserve">
 This folio provides a canon, or rule, for finding the square root of a quantity <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>+</mo><mi>f</mi></mstyle></math>. <lb/>
 Using the fundamental property established in the first line,
 the first term in the canon can be rewritten as the square root of <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mi>b</mi><mi>b</mi><mo>+</mo><mi>c</mi><mi>c</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><msqrt><mrow><mfrac><mrow><mo maxsize="1">(</mo><mi>b</mi><mi>b</mi><mo>+</mo><mi>c</mi><mi>c</mi><mrow><msup><mo maxsize="1">)</mo><mn>2</mn></msup></mrow></mrow><mrow><mn>4</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>4</mn><mi>b</mi><mi>c</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msqrt></mstyle></math> <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mi>b</mi><mi>b</mi></mstyle></math>. <lb/>
 Similarly, the second term yields <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>c</mi></mstyle></math>.
 Thus the sum of the square roots yields <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>+</mo><mi>c</mi></mstyle></math>, as required. <lb/>
 A numerical example is worked at the bottom of the page.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head5" xml:space="preserve" xml:lang="lat">
 De extractione radicis quadratæ <lb/>
 e binomio plano.
 <lb/>[<emph style="it">tr:
 On the extraction of cube roots of plane binomes
 </emph>]<lb/>
 </head>
 <p xml:lang="lat">
 <s xml:id="echoid-s45" xml:space="preserve">
 Fundamentum
 <lb/>[<emph style="it">tr:
 Fundamental property
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s46" xml:space="preserve">
 Sit: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>&gt;</mo><mi>c</mi></mstyle></math>.
 <lb/>[<emph style="it">tr:
 Suppose: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mo>&gt;</mo><mi>c</mi></mstyle></math>.
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s47" xml:space="preserve">
 ergo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>&gt;</mo><mi>f</mi></mstyle></math>.
 <lb/>[<emph style="it">tr:
 therefore: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mo>&gt;</mo><mi>f</mi></mstyle></math>.
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s48" xml:space="preserve">
 per lemma.
 <lb/>[<emph style="it">tr:
 by the lemma
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s49" xml:space="preserve">
 Canon.
 <lb/>[<emph style="it">tr:
 Rule.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s50" xml:space="preserve">
 Illustratio Canonis per numeros.
 <lb/>[<emph style="it">tr:
 An illustration of the rule in numbers.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0030.jpg" o="15v" n="30"/>
 <pb file="0031.jpg" o="16r" n="31"/>
 <pb file="0032.jpg" o="16v" n="32"/>
 <pb file="0033.jpg" o="17r" n="33"/>
 <p>
 <s xml:id="echoid-s51" xml:space="preserve">
 ships <lb/>
 bredth <lb/>
 in <lb/>
 feet
 </s>
 </p>
 <p>
 <s xml:id="echoid-s52" xml:space="preserve">
 lengths of <lb/>
 the mayne <lb/>
 maste in <lb/>
 feet. yards.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s53" xml:space="preserve">
 Diameter at <lb/>
 the parteners <lb/>
 in: <lb/>
 yards. feet.
 </s>
 </p>
 <pb file="0034.jpg" o="17v" n="34"/>
 <pb file="0035.jpg" o="18r" n="35"/>
 <head xml:id="echoid-head6" xml:space="preserve">
 Diameter of the mayne maste <lb/>
 at the parteners.
 </head>
 <p>
 <s xml:id="echoid-s54" xml:space="preserve">
 Yardes. Denaryes.
 </s>
 </p>
 <pb file="0036.jpg" o="18v" n="36"/>
 <pb file="0037.jpg" o="19r" n="37"/>
 <p>
 <s xml:id="echoid-s55" xml:space="preserve">
 Ships <lb/>
 bredth: <lb/>
 feet.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s56" xml:space="preserve">
 Timber <lb/>
 and space
 </s>
 </p>
 <p>
 <s xml:id="echoid-s57" xml:space="preserve">
 Tymbers <lb/>
 in bredth
 </s>
 </p>
 <p>
 <s xml:id="echoid-s58" xml:space="preserve">
 The number of <lb/>
 bendes in the whole <lb/>
 length from stern <lb/>
 to post.
 </s>
 </p>
 <pb file="0038.jpg" o="19v" n="38"/>
 <pb file="0039.jpg" o="20r" n="39"/>
 <p>
 <s xml:id="echoid-s59" xml:space="preserve">
 The Hollanders have 3900 fishing ships and vessels. <lb/>
 100 doggerboates <lb/>
 700 pinkes &amp; welboates <lb/>
 700 strandboates <lb/>
 400 Euars <lb/>
 400 Galligates, Drivers &amp; Todboates. <lb/>
 1600 Busses.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s60" xml:space="preserve">
 The Hollanders set on nomber 200000 [???] by those fishing. <lb/>
 &amp; 7200 sayle of shippes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s61" xml:space="preserve">
 A busse of 180 tonnes imployeth of mariners <lb/>
 &amp;a fishermen in her selfe about 40. <lb/>
 &amp; besides 3 shippes, one to fetch her salt <lb/>
 an other to carry forth barrelles &amp; salt <lb/>
 into her at sea &amp; to bring her heavinges <lb/>
 backe to her owne country. The third to <lb/>
 transport her heavinges beyond seas. - those 3, 60 men.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s62" xml:space="preserve">
 Huyes <lb/>
 Hulkes <lb/>
 Lurdens of 3. 4. 5. 6oo tonnes <lb/>
 for the Begene. <lb/>
 Maseskips the like for the <lb/>
 Mase. <lb/>
 They are of a long &amp; <lb/>
 shallow building.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s63" xml:space="preserve">
 English fishing vessels. <lb/>
 Crayers <lb/>
 &amp; Cobles <lb/>
 from 5 to 20 tonnes
 </s>
 </p>
 <p>
 <s xml:id="echoid-s64" xml:space="preserve">
 Seen at land spinners &amp; hemp winders <lb/>
 to make canbles &amp;c
 </s>
 </p>
 <p>
 <s xml:id="echoid-s65" xml:space="preserve">
 Ketches.
 </s>
 </p>
 <pb file="0040.jpg" o="20v" n="40"/>
 <pb file="0041.jpg" o="21r" n="41"/>
 <head xml:id="echoid-head7" xml:space="preserve">
 Notes. of the officers of a ship
 </head>
 <p>
 <s xml:id="echoid-s66" xml:space="preserve">
 Captayne. <lb/>
 Master. <lb/>
 Masters mates, 2. <lb/>
 Quarter masters, 4.) to looke to the <lb/>
 grande table &amp; romage in holde. <lb/>
 to looke to the watches, &amp; for to <lb/>
 call the men <lb/>
 to the helme. <lb/>
 Boteswayne. <lb/>
 Boteswaynes mate. <lb/>
 Midshipmen. <lb/>
 Marinesr. Surgeon. <lb/>
 Youbers. <lb/>
 Boyes. <lb/>
 Swabber. <lb/>
 Swabbers mate. <lb/>
 Master Gunner. <lb/>
 His mate. <lb/>
 Quarter gunners. <lb/>
 Gunners. <lb/>
 Purser. <lb/>
 Steward. <lb/>
 Cooper. <lb/>
 Cooke &amp; his mate. <lb/>
 Cape merchant. in steed of the Captayne in [???] <lb/>
 Marchants or Factors. <lb/>
 Shifters (of vituayls)
 </s>
 </p>
 <p>
 <s xml:id="echoid-s67" xml:space="preserve">
 Leiuetenant <lb/>
 Auurient. <lb/>
 Serjeant. <lb/>
 Corporall. <lb/>
 Soldiers. <lb/>
 Drummers. <lb/>
 Trumpeters
 </s>
 </p>
 <p>
 <s xml:id="echoid-s68" xml:space="preserve">
 All <lb/>
 Starbord men on the masters side <lb/>
 &amp; larboard men of the mates side <lb/>
 or on bothe <lb/>
 the mates sides.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s69" xml:space="preserve">
 A watch is <lb/>
 8 glasses <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mo>\\frac</mo><mrow><mn>8</mn><mrow><mn>2</mn></mrow></mrow></mstyle></math> houres. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>=</mo><mn>4</mn></mstyle></math> houres.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s70" xml:space="preserve">
 The watch from 4 to 8 at night <lb/>
 is devided into two partes: <lb/>
 the later part from 6 to 8 they <lb/>
 call the <emph style="ul">looke out</emph>.
 </s>
 <lb/>
 <s xml:id="echoid-s71" xml:space="preserve">
 These two partes are as two <lb/>
 watches, that the same men <lb/>
 may not have the first watch. <lb/>
 The first watch beginnes <lb/>
 at 8 at night; then they <lb/>
 set the watch.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s72" xml:space="preserve">
 1. watch <lb/>
 2. watches <lb/>
 Day watch <lb/>
 or morning <lb/>
 watch.
 </s>
 </p>
 <pb file="0042.jpg" o="21v" n="42"/>
 <pb file="0043.jpg" o="22r" n="43"/>
 <head xml:id="echoid-head8" xml:space="preserve">
 Of ropes
 </head>
 <p>
 <s xml:id="echoid-s73" xml:space="preserve">
 11. Catharpins. to keepe the shroudes tought.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s74" xml:space="preserve">
 [Diagram] <lb/>
 shroudes <lb/>
 dedmaneye
 </s>
 </p>
 <p>
 <s xml:id="echoid-s75" xml:space="preserve">
 12. collars <emph style="super">of the stayes</emph> are short ropes coming about the <lb/>
 mastes (or timber) bothe endes being spliced &amp; brought <lb/>
 about a dedmaneye, &amp; the lower ende of the stay hath <lb/>
 a <emph style="st">ded</emph> deadmaneye also, thourough which eyes
 <emph style="st">are</emph> <emph style="super"/> is reeved <lb/>
 a rope to &amp; fro to <emph style="st">fasten</emph> make the stay &amp; coller <lb/>
 tought together &amp; this rope is called a lanier. <lb/>
 And the ends of the shroudes are dedmen eyes, &amp; in the <lb/>
 chaynes are other ded men eyes; &amp; those dedmen eyes <lb/>
 are coupled with lannieres.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s76" xml:space="preserve">
 13. Standing takles are within the shroudes, having <emph style="st">having</emph> <lb/>
 only a pendent with a long blocke of two shiners one above <lb/>
 an other, the end of <emph style="super">the</emph> pendent is fast under the top. then there <lb/>
 is a blocke of two shiners (parallel) with a hooke below hitching <lb/>
 into a ring on the chaynewale, unto this blocke is fast a rope <lb/>
 which is reeved thourough a shiner of the lower blocke &amp; so up agayne &amp; downe <lb/>
 to be set taught to stay the mastes till the shrouds be set <lb/>
 &amp; stand stil after to strengthen the shroudes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s77" xml:space="preserve">
 Gunners takles, have hookes &amp; blockes; &amp; are to be removed <lb/>
 &amp; taken away at pleasure. &amp; serve to bouse these peeces <lb/>
 in &amp; out; &amp; to remove them from place to place. <lb/>
 to bouse. i. hale <lb/>
 [???] bouse here
 </s>
 </p>
 <pb file="0044.jpg" o="22v" n="44"/>
 <pb file="0045.jpg" o="23r" n="45"/>
 <head xml:id="echoid-head9" xml:space="preserve">
 Of ropes
 </head>
 <p>
 <s xml:id="echoid-s78" xml:space="preserve">
 6.) The sprit sayle hath clew lines like the topsayles <lb/>
 but no bowlinges. &amp; sheates but no tackes. <lb/>
 hath also liftes as the other yardes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s79" xml:space="preserve">
 He hath garnets, one cometh from the middlest of the <lb/>
 the arme, to a blocke towards the top of the boltsprit <lb/>
 and so cometh downe by the boltsprit to the beake hed to <lb/>
 be haled. His office to ease the lift &amp; to help the sayle <lb/>
 vere by a wind. So the other.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s80" xml:space="preserve">
 The misons have but one lift which cometh from the top of <lb/>
 the small end above, of the yard, &amp; is reeved thourough a <lb/>
 pully at the top of the mast &amp; so cometh downe. <lb/>
 <emph style="st">hathe</emph> <emph style="super">hath </emph>
 one sheat, fast, at at the right angle, &amp; cometh to a blocke in <lb/>
 a bumkin without the ship asterne &amp; so cometh in to be haled <lb/>
 or thourough a blocke made fast aloft in the midst in <lb/>
 aftermost part of the ship aloft &amp; from there a little <lb/>
 forward to be haled. <lb/>
 His tacke is fast at the <emph style="st">sharpe</emph> tayle (sharp angle aslo) <lb/>
 &amp; his other end is rope to be brought over to the <lb/>
 wether side &amp; there to be belayed to a kebble.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s81" xml:space="preserve">
 The bowlinges are two ropes fast <lb/>
 to the lower end of the yard (with a <lb/>
 button of wood &amp; an eye) and from there <lb/>
 are reeved in two pullyes made <lb/>
 fast to <emph style="super">the</emph> aftermost mayne shroude <lb/>
 one on the one side &amp; and the other on the <lb/>
 other. the bowlinge is to be halyed <lb/>
 when they <emph style="st">will go</emph> set their mizon to <lb/>
 go by a wind. <lb/>
 When the sayle is furled, &amp; the yard up, they <lb/>
 being both hauled &amp; belayed do steddy the yard in the <lb/>
 middest of the ship.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s82" xml:space="preserve">
 [Diagram]
 mison sayle <lb/>
 sheat <lb/>
 lift <lb/>
 bowlinge <lb/>
 tacke
 </s>
 </p>
 <pb file="0046.jpg" o="23v" n="46"/>
 <pb file="0047.jpg" o="24r" n="47"/>
 <head xml:id="echoid-head10" xml:space="preserve">
 Of ropes
 </head>
 <p>
 <s xml:id="echoid-s83" xml:space="preserve">
 10. Bowlinges (bowlines) <lb/>
 Of the mayne bowling, <emph style="st">half a blocke or pully fitted fast about a</emph>
 <emph style="super">one end</emph> <lb/>
 is spliced fast about a pully having a shiner, &amp; thourough that <lb/>
 shiner passes a short rope having two deadmeneyes spliced <lb/>
 at the two endes thereof, thourough whihch eyes come other <lb/>
 small ropes making crow feet are spliced into <emph style="super">the</emph> side <lb/>
 bolt rope of the mayne sayle; this parte from the pully is called <lb/>
 the <emph style="super">bowling</emph> bridles; the other end of the bowling is reeved <lb/>
 thourough a block made fast with a strap nere towards <lb/>
 the foremaste on the top of the forecastle in the middest (of <lb/>
 bredth) &amp; from thence comes aft towards the mayne <lb/>
 maste there to be haled. &amp; is <emph style="super">belayed</emph> about kebble or some <lb/>
 bitte. And thourough a shiner of the same blocke on <lb/>
 the fore castle passes the bowling up the other side. <lb/>
 And his use is when they go by a wind (the tackes <lb/>
 being abord) &amp; sheates haled aft) then to be haled tought <lb/>
 &amp; belayde; that the wether leech (side) be kept tought <lb/>
 &amp; and not to lift or shake in the wind.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s84" xml:space="preserve">
 In like manner the fore bowlinge come thourough a blocke <lb/>
 with a double shiner made fast about the middest of <lb/>
 the bolt sprit &amp; so comes thourough a blocke fast at the <lb/>
 lower parte of the boltsprit (above the head beke) one <lb/>
 one side (for on the other is an other) &amp; so cometh into the <lb/>
 the forecastle or up alofte there to be haled &amp; belayed.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s85" xml:space="preserve">
 The <emph style="super">two</emph> top sayle bowlings are reeved thourough two blockes sezed <lb/>
 to the topmast stay <emph style="st">&amp; the</emph> &amp; the mayne topsayle boweling once <lb/>
 reeved agayne thourough two blockes <emph style="super">fast</emph> about the rayles of the after <lb/>
 part of the forecastle &amp; so into the ship to be haled. <lb/>
 but the foretopsayle bowlings are agayne thourough <lb/>
 two pullyes fast towards the top of teh boltsprit (&amp; so to <lb/>
 the <emph style="st">top fo</emph> foretop then to be haled) or are reeved agayne <lb/>
 agayne in two pullys at the lower part of the boltsprit <lb/>
 &amp; thence to the forecastle to be haled.
 </s>
 </p>
 <pb file="0048.jpg" o="24v" n="48"/>
 <pb file="0049.jpg" o="25r" n="49"/>
 <head xml:id="echoid-head11" xml:space="preserve">
 Of ropes
 </head>
 <p>
 <s xml:id="echoid-s86" xml:space="preserve">
 The foresayle hath sheates and tackes made fast to teh clewes <lb/>
 in like manner as <emph style="super">the</emph> mayne sayle. <lb/>
 One <emph style="super">end</emph> of the sheat is fastened at the middest of the maste or nere on <lb/>
 the out side, &amp; so reeved thourough the block with a strap at the clew <lb/>
 &amp; reeved thourough a <emph style="st">pully</emph> shiner in the ships side nere the mayne <lb/>
 maste &amp; there is to be haled &amp; belayed about <emph style="super">a</emph> kebble nere hand.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s87" xml:space="preserve">
 The foretackes goe thourough two holes in a cleate (a peece of wood nayled <lb/>
 to the bomkin (like a peece of a maste under the beake head fastened [???] in <lb/>
 bord) the small endes passing thourough are brought up on the contrary <lb/>
 side of the <emph style="super">fore</emph> maste throug orover the forecastle &amp; there to be haled <lb/>
 to bring the tacke abord; where <emph style="super">is</emph> the clew to the bomkin or as nere as it can.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s88" xml:space="preserve">
 7. <emph style="super">the</emph>
 Clew garnet of the maynesayle one end is fastened at the clew &amp; the <lb/>
 other reeved thourough a blocke fastened under the mayne yard <lb/>
 towarde the maste on the same side or arme &amp; so cometh downe to be <lb/>
 haled to bring the clewes to the yard when the sayle is striken downe <lb/>
 &amp; then they use to furle up the sayle &amp; ty it up with gaskets <lb/>
 (yarn platted with nooses at the greater end) fastened with a rope yarn <lb/>
 to a grummet (a nayle with a ring) driven into the yard &amp; coming about <lb/>
 the sayle they make it fast in a other grummet. They are many of them <lb/>
 alongst the yard, but the middle two (or 4) being greater &amp; <lb/>
 longer than the rest are called breech gaskets; &amp; when the <lb/>
 sayle is to be let fall they order as many as they can &amp; then cut <lb/>
 the rope yarnes of the breech gaskets last of all &amp; both together.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s89" xml:space="preserve">
 8. <emph style="super">The</emph>
 Martenet line, one end is fastened under the top &amp; reeved <emph style="st">thourough</emph> <lb/>
 thourough a double pully with 3 shiners (2 one way &amp; one another) that is <lb/>
 thourough the single shiner &amp; so comes backe to a pully under the top &amp; so <lb/>
 goes downe by the foremost shorude there to be haled; thourough the double <lb/>
 shiners of the pully come one on one side &amp; the other on <lb/>
 the other of the yard; at whose endes are dead men eyes. And thourough <lb/>
 the holes of the dead men eyes are peeces of small line bothe endes of <lb/>
 which line are spliced fast into the bolterope on the side &amp; make <lb/>
 crow feet. The us <emph style="st">by</emph> is by haling the martenet line to bring <lb/>
 the sayle close to the yard at the yardarmes end &amp; forwards <lb/>
 In like sort also are the martenets of the foresayle.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s90" xml:space="preserve">
 The luffe hooke, is a rope with a hooke having an eye or <lb/>
 hole, thorugh which a rope is reeved &amp; spliced; whose use <lb/>
 put the hooke into <emph style="super">the</emph> earing of the clew of the sayle <lb/>
 if only the bonnet be on; or bonnet if drabble be on &amp; the <lb/>
 other end goeth thourough a hole in the ships side &amp; there is haled <lb/>
 in tought &amp; belayed to helpe the tacke for feare of breaking. <lb/>
 the mayne &amp; foresayle only have this luffe hooke.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s91" xml:space="preserve">
 [Diagram] <lb/>
 a dead man eye <lb/>
 a luffe hooke
 </s>
 </p>
 <pb file="0050.jpg" o="25v" n="50"/>
 <pb file="0051.jpg" o="26r" n="51"/>
 <head xml:id="echoid-head12" xml:space="preserve">
 Of ropes. <lb/>
 for sayles.
 </head>
 <p>
 <s xml:id="echoid-s92" xml:space="preserve">
 4. Sheates; which are fatened to the clewes (lower corners <lb/>
 like nooses or eares alofte) <lb/>
 of the <emph style="super">mayne</emph> topsayle sheat, one end is fast to the clew <lb/>
 of the top sayle &amp; is reeved thourough a blocke made fast <lb/>
 to the end of the mayne yard arme, &amp; thourough an other <lb/>
 blocke fast on the same yard arme nere the maste &amp; <lb/>
 so cometh down to a shener in a poste upon the deck nere <lb/>
 the maste. &amp; serveth to hale out the clewes to the end <lb/>
 of the mayne yard arme.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s93" xml:space="preserve">
 5. The clew line. is a rope fast to the same clew (or corner) <lb/>
 &amp; is reeved thourough a block fast to the top sayle yard <lb/>
 nere the midest of the yard arme on the same side, &amp; so <lb/>
 cometh downe thourough a hole in the mayne top to a hole <lb/>
 <emph style="st">&amp; thourough</emph> a peece of wood bond fast to
 <emph style="st">the</emph> one of the <emph style="super">mayne</emph> <lb/>
 shroudes on the same side; &amp; there to be haled &amp; fastened <lb/>
 in taking in the sayle.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s94" xml:space="preserve">
 His office is to hale downe the top sayle (halyendes <lb/>
 being let go.) &amp; to hale up the clewes to the top sayle <lb/>
 yard arme, the top sayle sheates being let go <emph style="super">in</emph> taking it in. <lb/>
 in like manner the foretopsayle.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s95" xml:space="preserve">
 To the clew of the maynesayle is fastened a blocke with a strap <lb/>
 <emph style="st">and a button at the end by putting the button thourough</emph>
 <emph style="super">and a</emph> noose, <lb/>
 then one end of the main sheat is fast to a ring bolt <lb/>
 on the out side of the ship in the after part about the galley <lb/>
 &amp; is reeved thourough the sayd block with a strap, &amp; so cometh <lb/>
 reeved agayne thourough the mayne sheat block fastened <lb/>
 to the ship side with a strap in a ring bolt. &amp; so cometh into the <lb/>
 ship to be halyd. &amp; is to be <emph style="super">be</emph>layed about a kebble; which is <lb/>
 a peece of <emph style="super">wood</emph> fast to the ship side. <lb/>
 his office is to hale aft the clew of the sayle.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s96" xml:space="preserve">
 6. The mayne tacke, is fashion<emph style="super">ed</emph> taperwise bigger at one end then the other <lb/>
 at the great end is a knot like a button which is thrust thourough the nooose <lb/>
 of the clew, the noose of the strap of the sayd blocke being first put out or <lb/>
 <foreign xml:lang="lat">e contra</foreign>, so it is then fastened to the clew of the mayne sayle <lb/>
 &amp; the samller end cometh in<emph style="super">to</emph> a hole thourough the ship side <lb/>
 out the luffe which is nere the forecastle at the bow agaynst the pitch of <lb/>
 the sterne, &amp; is haled within bord thourough that hole, &amp; belayed about <lb/>
 some kebble at the ships sides or at the upper bitte. his office <emph style="super">is</emph> to hale forward <lb/>
 the rayle untill it come <emph style="st">abord the</emph> close aboard the ship side.
 </s>
 </p>
 <pb file="0052.jpg" o="26v" n="52"/>
 <pb file="0053.jpg" o="27r" n="53"/>
 <head xml:id="echoid-head13" xml:space="preserve">
 Of ropes
 </head>
 <p>
 <s xml:id="echoid-s97" xml:space="preserve">
 3. Slinges. a rope <emph style="st">for</emph> <emph style="super">the</emph> mayne yard &amp; fore yarde
 <emph style="super">used sometimes</emph> when the <lb/>
 yard is up to faten it or hang it in. least the [???] breake <lb/>
 or be shot asunder.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s98" xml:space="preserve">
 4. brases. for all the yardes. <emph style="super">except mizon yarders</emph>.
 fastened at the endes of the yardes <lb/>
 &amp; running thourough pullyes to turne about the yardes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s99" xml:space="preserve">
 5. liftes. for all the yardes. fastened at the endes of the yardes <lb/>
 &amp; coming thourough pullyes <emph style="super">alofte</emph>; to lift the endes of the yardes <lb/>
 up: not the yardes them selves.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s100" xml:space="preserve">
 6. In great ships only. The gere. to ease the tyes in hoysing <lb/>
 &amp; when it is up aloft also. for mayne and foreyarde only.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s101" xml:space="preserve">
 7. puddinges. short peeces of ropes nayled about the yardes <lb/>
 about a foot or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> asonder to keep the Raubins <lb/>
 (of the sayles) from slipping or sliding.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s102" xml:space="preserve">
 b. the brases have <emph style="super">a</emph> pendent part fastened at <lb/>
 the endes of the yardes with a block (as the tackles) <lb/>
 &amp; a running part. one end fast; &amp; the other end <lb/>
 to hale by. it reeved thourough the block of the <lb/>
 pendent.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s103" xml:space="preserve">
 a rope is unreeved when he is out of the <lb/>
 pully. reve the rope. i. put him inot his pully.
 </s>
 </p>
 <head xml:id="echoid-head14" xml:space="preserve">
 ropes for sayles
 </head>
 <p>
 <s xml:id="echoid-s104" xml:space="preserve">
 1. bolt rope, that goeth round about the sayle into which the <lb/>
 rayle is sowed; the uppermost is called <emph style="super">the</emph> head rope <lb/>
 (side rope, foot rope) leech line (side line) there use.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s105" xml:space="preserve">
 2. (<emph style="st">Cringles I thnke</emph>) that go round about the aylet holes like a <lb/>
 lace to strengthen them.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s106" xml:space="preserve">
 3. Raubins, made fast in the aylet holes alofte &amp; go round about <lb/>
 the yardes &amp; tyed; betwen the puddinges which keep them from <lb/>
 sliding or slipping.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s107" xml:space="preserve">
 The earinges. which are nooses at the corners of the sayle <lb/>
 are fastened to the endes of the yard armes with such rope <lb/>
 many times thourough.
 </s>
 </p>
 <pb file="0054.jpg" o="27v" n="54"/>
 <pb file="0055.jpg" o="28r" n="55"/>
 <head xml:id="echoid-head15" xml:space="preserve">
 Of ropes
 </head>
 <p>
 <s xml:id="echoid-s108" xml:space="preserve">
 All ropes belonging to a ship serve to <emph style="st">3</emph> <emph style="super">4</emph> uses.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s109" xml:space="preserve">
 for mastes <lb/>
 yardes <lb/>
 sayles <lb/>
 ankers
 </s>
 </p>
 <p>
 <s xml:id="echoid-s110" xml:space="preserve">
 mastes <lb/>
 <emph style="st">boltsprite</emph> bolesprite; boldsprite <lb/>
 foremaste <lb/>
 mayne mast <lb/>
 Bonaventure mizen <lb/>
 after mizen
 </s>
 </p>
 <p>
 <s xml:id="echoid-s111" xml:space="preserve">
 of mastes <lb/>
 stayes <lb/>
 forestayes, backstayes <lb/>
 shroudes <lb/>
 top rope; to beare up the top mastes <lb/>
 one for every top maste <lb/>
 tackles
 </s>
 </p>
 <p>
 <s xml:id="echoid-s112" xml:space="preserve">
 all have top mastes <lb/>
 upon the top of the mayne <lb/>
 maste &amp; foremast <lb/>
 top gallants <lb/>
 &amp; hier flagstaves
 </s>
 </p>
 <p>
 <s xml:id="echoid-s113" xml:space="preserve">
 stay <emph style="super">of the</emph> foretopmast stay;
 from the top of the foretopmast to the hier part of the bolesprit. <lb/>
 forestay <emph style="st">stay</emph> of the foremaste from the top of the foremast to the bolesprit. <lb/>
 backe stayes of the foretopmast, from the top thereof to the aftermost parte of <lb/>
 the forecastle 2 or 3.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s114" xml:space="preserve">
 The mastes themselves have no back stayes; but there shroudes that <lb/>
 come from the crosse trees under the tops to there chayne wales. <lb/>
 made faste there with lanniers (ropes going thourough dead men eyes to hale <lb/>
 them tought) the peeces of wood with a ring of [???] &amp; holes in them made <lb/>
 fast to chaynes under the cheyne wales are the <emph style="ul">dead men eyes</emph>. <lb/>
 In like manner are the other mastes. <lb/>
 But the top mast shroudes come to <emph style="super">the</emph> brim of the top &amp; are fastened with <lb/>
 lanniers thourough dead men eyes like the other.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s115" xml:space="preserve">
 All the top mastes have a forestay &amp; backe stayes. backstayes are standing <lb/>
 backestaye &amp; backestaye; two standing backestayes on either side <lb/>
 one belongs to one top mast made to the out side of the ship; &amp; the other within <lb/>
 being also two.
 </s>
 </p>
 <head xml:id="echoid-head16" xml:space="preserve">
 yardes
 </head>
 <p>
 <s xml:id="echoid-s116" xml:space="preserve">
 1. haliers, to hoyse them up with all, going thourough thourough <emph style="st">the ra</emph> head
 <emph style="super">and teh Knight.</emph>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s117" xml:space="preserve">
 2. tyes, fatened to the yardes coming thourough the houndes <lb/>
 which are holes thourough the cheekes (at the head of <lb/>
 the mastes) bearing up the crosse tree, having being <lb/>
 put thourough the vam head.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s118" xml:space="preserve">
 The <emph style="super">Mayne</emph> Knight is a peece of timber fast upon the slope <lb/>
 or second deck bolted fast to some beame. Having <lb/>
 shiners in it (wheles of pullyes) so that the mayne haliers <lb/>
 go thourgh the upper decks.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s119" xml:space="preserve">
 The fore Knight such an other <emph style="super">thourough which the fore haliers come</emph>
 but fastened to <emph style="st">the</emph> a <lb/>
 beame about the afterward part of the forecastle also upon the <lb/>
 slope or lower deck.
 </s>
 </p>
 <pb file="0056.jpg" o="28v" n="56"/>
 <pb file="0057.jpg" o="29r" n="57"/>
 <head xml:id="echoid-head17" xml:space="preserve">
 Ropes.
 </head>
 <p>
 <s xml:id="echoid-s120" xml:space="preserve">
 One end of the Cable is to be brought ont at the Hawse <lb/>
 and bent (mad fast) to the rynge of the Anchore, then <lb/>
 the other end must be brought to the Bytte (two upright <lb/>
 postes with a crosse peece of tymber bolted fast to beames alowe) <lb/>
 and ther be belayde.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s121" xml:space="preserve">
 then ther is a Bwye with a bwye rope, which rope is mad fast <lb/>
 to the corsse of the Anchore, by which the anchore is to be wayd which <lb/>
 a boat as occasion serveth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s122" xml:space="preserve">
 in letting fale the Anchore which hangeth in a stopper (as they <lb/>
 cale it) a cock bylle ready to let fale, that when the master caleth <lb/>
 they cast of the stoper) lett fale: then <emph style="st">when</emph> ther are many hands <lb/>
 readye to over sette the fakes of the cable and followe it for feare <lb/>
 of kinks, and one standeth by the stopper that when they crye <lb/>
 stope he presently clapes the stopper about the cable and vers <lb/>
 agayne as he is bydd the master as the shype cranes untyle <lb/>
 shee be brought upe to a Bytter.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s123" xml:space="preserve">
 The stopper is a strong rope about a fathome longe one end <lb/>
 wherof is fast to the shypps syde (afore by the mange neer the <lb/>
 Hawse.) at some rynge boult) or havinge a knott at one end is <lb/>
 thrust thorowhe a hole in some stronge peece of tymber standinge <lb/>
 conveniently neere the foresayd place, the other end is loose to be <lb/>
 suddenly brought about the cable two or .3. tyms to stoppe it. <lb/>
 And in wayinge they cast one the stopper upon the cable, and then <lb/>
 cat it off at the Bytte &amp; brynge the end to the capsten [???]. <lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s124" xml:space="preserve">
 When the Anchor is upe to the Hawser thyey have a great yron hooke <lb/>
 to which a rope is fast which is caled a fyshhooke, they lett it downe and <lb/>
 heech it about one of the flowkes of the Anchore, &amp; bringe the Rope <lb/>
 out to the end of a great peece of tymber thrust out over the syde <lb/>
 (which they cale a Davitt) &amp; then cry hale fish &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s125" xml:space="preserve">
 Ther is one either syde the shyppbefore a peece of tymber fast to <lb/>
 the shype syde standinge out with a shyner at the ende, caled the catte <lb/>
 throwe which shyner they reeve a rope caled the catt rope one ende <lb/>
 wher of they fasten to the rynge of teh Anchore &amp; hange this rope <lb/>
 putinge out the cable at the hawse they bringe it upe, &amp; then with <lb/>
 takels they bringe the Anchor to the Bowe agayne. hale out &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s126" xml:space="preserve">
 the greatest Anchor they cale the shoote Anchor the other Bowers <lb/>
 ther is a smale Anchor with a longe cabled hawser which is caled <lb/>
 a kedginge Anchor to warpe upon when occasion serveth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s127" xml:space="preserve">
 they lay out thsi smale Anchor with ther boat &amp; bringinge the end <lb/>
 aborde they heave the shipe to it &amp; then lett drope another smale <lb/>
 anchor under foote, &amp; then lay out the kedginge anchor againe which <lb/>
 they cale warpinge &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s128" xml:space="preserve">
 this is used to gett out of a harbore when the wynd which bloweth <lb/>
 would serve yf you were without the harbore, but they use it not but <lb/>
 in fayre weather when the wynd doth not over blowe, for this <lb/>
 lytle anchor would not then hould the shyppe.
 </s>
 </p>
 <pb file="0058.jpg" o="29v" n="58"/>
 <pb file="0059.jpg" o="30r" n="59"/>
 <head xml:id="echoid-head18" xml:space="preserve">
 Notes.
 </head>
 <p>
 <s xml:id="echoid-s129" xml:space="preserve">
 The keele in a ship (100 t) of 12 yardes deep; 10 yardes broad <lb/>
 The sterne post &amp; stern are below as the keele <lb/>
 but a loft the stern is thicker in &amp; out (&amp; otherwise also) <lb/>
 it ends in a quadrant, &amp; comes into the beake head as a stump. <lb/>
 the beake hed is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> or <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 keele in length. <lb/>
 The timbers (of 100 t) of the midship bend, are 7 inches in &amp; out <lb/>
 below &amp; 8 inches brode, &amp; a lofte about 3 inches every way. <lb/>
 The <emph style="super">lower</emph> wales are in thicknesse 5 yardes, &amp; about 6 in bredth, the other are lesse <lb/>
 the planke between is 3 inches &amp; so down to the keele, upward they <lb/>
 are thinner by degrees.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s130" xml:space="preserve">
 Upon the keel, the <emph style="super">floore timbers of the</emph> bendes are fastened with trennels; upon the <lb/>
 floore timbers the keelson runns alonge, being bolted to the keel <emph style="st">in</emph> <lb/>
 <emph style="st">divers places</emph> between the <emph style="st">floore</emph> bendes. then on both sides <lb/>
 the keelson is floored with plankes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s131" xml:space="preserve">
 <emph style="st">The</emph> A ship is sayd to leake in the hoodings when the leakes at the <lb/>
 stern where the endes of the plankes are fastened. Mr <emph style="super">Barker</emph> devised a <lb/>
 false stern joyning to the other whereupon the plankes are better <lb/>
 fastened. (I thinke it better to be called a sternson.)
 </s>
 </p>
 <p>
 <s xml:id="echoid-s132" xml:space="preserve">
 A David.
 </s>
 </p>
 <pb file="0060.jpg" o="30v" n="60"/>
 <pb file="0061.jpg" o="31r" n="61"/>
 <head xml:id="echoid-head19" xml:space="preserve">
 Notes. of ships of warre
 </head>
 <p>
 <s xml:id="echoid-s133" xml:space="preserve">
 wasteclothes. <emph style="st">that hang</emph> upon the rayles abaste &amp; afore <lb/>
 in the wastes are stancheons with holes <lb/>
 chaynes going thourough, to which they are made <lb/>
 fast with raubins.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s134" xml:space="preserve">
 nettinges are specially over the waste, to keepe men from sudden <lb/>
 entring.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s135" xml:space="preserve">
 top armores, shadowes of cloth about the toppes for hiding of men <lb/>
 from sight of the enemy.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s136" xml:space="preserve">
 trap hatches <emph style="super">for close fights</emph> in the waste upon the half deck <lb/>
 with loop holes to shoote thourough to scoure the decke. <lb/>
 They have <emph style="super">also</emph> loopes <emph style="super">for close fights</emph>
 at every bulke head &amp; out of the stridge.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s137" xml:space="preserve">
 for gallantry <lb/>
 flags <lb/>
 aunciente <lb/>
 stremers
 </s>
 </p>
 <pb file="0062.jpg" o="31v" n="62"/>
 <pb file="0063.jpg" o="32r" n="63"/>
 <head xml:id="echoid-head20" xml:space="preserve">
 Notes.
 </head>
 <p>
 <s xml:id="echoid-s138" xml:space="preserve">
 The beming <emph style="st">of</emph> of a ship: is the holding &amp; appliying of breming wales. <lb/>
 To pay on stuffe. this is not well payed. <lb/>
 <emph style="st">pa</emph> pay on more. <lb/>
 They pay on the stuffe with mappes. <lb/>
 All under water &amp; to the lower wales is don with brimston &amp; pitch
 <emph style="super">rosen</emph> mingled <lb/>
 together. or with cæment. <lb/>
 The upper worke is don pitch &amp; tar. only some use a rosen strake <lb/>
 that passeth by the waste.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s139" xml:space="preserve">
 dead rising
 </s>
 </p>
 <p>
 <s xml:id="echoid-s140" xml:space="preserve">
 heave, in sight; heave, in sight (the anker) <lb/>
 when sometimes it is out of sight.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s141" xml:space="preserve">
 beveueling <lb/>
 a shawe wedge. when to much is cut away in beueling they put in <lb/>
 a shawe wedge.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s142" xml:space="preserve">
 Thrum platts. made of of rope yarne with thrumms to keep the yardes from fretting <lb/>
 against the shrouds, &amp; in other places to save the sayles from fretting.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s143" xml:space="preserve">
 hight of mayne maste from mesures.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s144" xml:space="preserve">
 hatches <lb/>
 scuttles <lb/>
 scupper soles
 </s>
 </p>
 <p>
 <s xml:id="echoid-s145" xml:space="preserve">
 Water ledges, upon the deckes at the ship sides <lb/>
 to keepe the water from the seame. <lb/>
 Carlings. <lb/>
 is the timber that receveth the tops <lb/>
 of the bends in the waste &amp; maketh them fast to the ship side. <lb/>
 &amp; so in <lb/>
 a boat. <lb/>
 a Jury maste, is a maste <emph style="st">added to</emph> set to an after that is <lb/>
 spent.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s146" xml:space="preserve">
 The thicke planckes that runne fore &amp; aft <emph style="st">with</emph> on the inside of <lb/>
 the bende are called <emph style="st">[???]</emph> foot wales,
 in great ships <emph style="super">5 or</emph> 6 inches <lb/>
 thicke; about 12 inches broade or more. <emph style="st">The of great</emph> ordinary ships <lb/>
 have two foot wales on a side in hold, one below and one after hier <lb/>
 but planked between. <lb/>
 sleepers, are of the nature of footewales to helpe them. <lb/>
 riders, are helpers crosse wise as I think. <lb/>
 The plankes of great ships underwater <emph style="st">in</emph> &amp; between
 the <emph style="super">two</emph> lower wales <lb/>
 are <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> yardes &amp; 4. &amp; of smaller ships (of 100 t) .3. y.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s147" xml:space="preserve">
 Chamfering, is the taking away of the edges of the beames.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s148" xml:space="preserve">
 Ramminge is the boards in setting them up. ramming line. <lb/>
 shoringe the underlayinge &amp; propping
 </s>
 </p>
 <pb file="0064.jpg" o="32v" n="64"/>
 <pb file="0065.jpg" o="33r" n="65"/>
 <head xml:id="echoid-head21" xml:space="preserve">
 Notes.
 </head>
 <p>
 <s xml:id="echoid-s149" xml:space="preserve">
 The mayne mast stands in a step upon the Keelson in the <lb/>
 middest of the keele in length.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s150" xml:space="preserve">
 The step is a square hole in a peece of timber fast <lb/>
 upon the keelson.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s151" xml:space="preserve">
 The slates. halt in the slates of the lee tacke. <lb/>
 of the lee bowline <lb/>
 or any else <lb/>
 1. end that ends loose
 </s>
 </p>
 <p>
 <s xml:id="echoid-s152" xml:space="preserve">
 a passaredo. is <emph style="super">any short [???] about</emph> <emph style="super">that</emph>
 or the luffe hooke that on the clewe <lb/>
 of the <emph style="st">sayle</emph> mayne sayle specially when you are large <lb/>
 in a sea gate when the shippe is subject to yawing, to <lb/>
 steddy downe the clew. <lb/>
 clap on a passeredo &amp;c,
 </s>
 </p>
 <p>
 <s xml:id="echoid-s153" xml:space="preserve">
 Cringles are decke loops here &amp; there one spliced into the <lb/>
 lower bolt rope of mayne sayle, foresayle, sprit sayle &amp; bonnets <lb/>
 to take hold by putting <emph style="st">[???]</emph>
 an end <emph style="super">of a rope</emph> thourough, to hold the <lb/>
 sayle to, whyle they lace on the bonnet, and drabblers.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s154" xml:space="preserve">
 Clap on a guy. (i. guide), is <lb/>
 <emph style="st">to put</emph> in hoysing the boat, <lb/>
 if a ropes end be brought from <lb/>
 a fore &amp; an other about <emph style="st">thourough</emph> <lb/>
 <emph style="st">a</emph> thourough <emph style="super">a ring</emph> or about a though <lb/>
 of the boat, to keep her steddy in <lb/>
 hoysing.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s155" xml:space="preserve">
 The Furring of a ship is when she <lb/>
 will not beare sayle for want of breadth <lb/>
 is to make <emph style="super">bilde</emph> <emph style="ist">make</emph> her broader without <lb/>
 side with timber or the plankes &amp; thin <lb/>
 bord below &amp; thicker upward. So far <lb/>
 as is fit; &amp; housing it in upward <lb/>
 to agree with the upper wales by thinner <emph style="st">planckes</emph> <lb/>
 sides agayne. many marchants shippes are fyne <emph style="super">to</emph> be furred.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s156" xml:space="preserve">
 A ship will not stow 3 tire of <emph style="super">bunges or wine</emph> caske, excepte be 23 or 24 foote broade <lb/>
 the caske require 9 foote. the beames 10y thicke. underneth 4y planckes. <lb/>
 flore timbers, 7,y. 2, tire of caske will require 7, fo<emph style="super">t</emph>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>. <lb/>
 one stowing <emph style="st">in the [???]</emph>
 the Kunshions <emph style="super">(i. hollows)</emph> of <lb/>
 the other.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s157" xml:space="preserve">
 [Diagram] <lb/>
 aylet holes <lb/>
 cringles <lb/>
 latchets <lb/>
 bonnets <lb/>
 cringle <lb/>
 drabler <lb/>
 earinges
 </s>
 </p>
 <pb file="0066.jpg" o="33v" n="66"/>
 <pb file="0067.jpg" o="34r" n="67"/>
 <head xml:id="echoid-head22" xml:space="preserve">
 notes.
 </head>
 <p>
 <s xml:id="echoid-s158" xml:space="preserve">
 The tackles, serve to stay the mastes whyle they set up <lb/>
 the shroudes tought. <lb/>
 Also to hoyse in the boate or ordnance or heavy thinges.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s159" xml:space="preserve">
 There are two or 3 tackles of a side bolt to the mayne mast <lb/>
 &amp; fore maste for staying of the mastes &amp; help the shroudes <lb/>
 &amp; one <emph style="st">to be</emph> or other to be loosed for hoysing <emph style="super">in</emph>
 as occasion serveth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s160" xml:space="preserve">
 There is some hoysing tackle fast to the mayne stay to <lb/>
 hoyse in goods, having all the parts as the other; only <lb/>
 insteed of a pendent a block with a strap (short cord) <lb/>
 made fast to the stay.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s161" xml:space="preserve">
 The armes of a yared. two halves. [???] wastes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s162" xml:space="preserve">
 The brunt of the sayle, that <lb/>
 which swells. <lb/>
 A sayle cut with a good brunt. <lb/>
 (bent or bowing out).
 </s>
 </p>
 <p>
 <s xml:id="echoid-s163" xml:space="preserve">
 <emph style="st">catharpin</emph>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s164" xml:space="preserve">
 The top sayle yardes <lb/>
 are a third of there under <lb/>
 yardes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s165" xml:space="preserve">
 The mayne yard is the length <lb/>
 of the keele.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s166" xml:space="preserve">
 And I think the foreyard is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of the mayne. <lb/>
 &amp; the sprit sayle yarde <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> of that.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s167" xml:space="preserve">
 In a ship of 20f broad, the mayne mast is usually 20 yards. <lb/>
 In a ship of 40f (the Kings) brode, the mayne mast 32 yards. <lb/>
 In a ship of 16, foot broade; the mayne mast: 16 yardes and 4 foote.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s168" xml:space="preserve">
 The place where the maste goeth thourough the decke is <lb/>
 called the partners. They say: The mast is so many <lb/>
 inches thourough <emph style="st">at</emph> <emph style="super">in</emph> the partners. <lb/>
 &amp; so many at the head of the house.
 </s>
 </p>
 <pb file="0068.jpg" o="34v" n="68"/>
 <pb file="0069.jpg" o="35r" n="69"/>
 <head xml:id="echoid-head23" xml:space="preserve">
 Notes.
 </head>
 <p>
 <s xml:id="echoid-s169" xml:space="preserve">
 Serving of ropes, is with rope yarne wound round about to save them <lb/>
 from fretting agaynst wood.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s170" xml:space="preserve">
 Whipping of ropes endes. with twyne to fasten the ende to keep him <lb/>
 from fazing out: i. riveling.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s171" xml:space="preserve">
 Kinking of a cable, or stiffe rope. a fold that happens when <lb/>
 the cable runneth out to fast &amp; it doubles; for want of well <lb/>
 oversetting the flakes in paying out of <emph style="super">it</emph>; &amp; then they say <lb/>
 stopp stop to get out the kink.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s172" xml:space="preserve">
 A <emph style="st">flake</emph> <emph style="super">fake</emph> is one bout of the coyle of a cabble.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s173" xml:space="preserve">
 A coyle of ropes. they coyle with the sonne. to coyle.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s174" xml:space="preserve">
 A log line. <lb/>
 A lead line. A deep sea line. a deep sea leaad. <lb/>
 A clew line.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s175" xml:space="preserve">
 Takles. are ropes whose one <emph style="super">end</emph> is made fast at the head of the <lb/>
 maste &amp; the other end hath a <emph style="super">great</emph> pully <emph style="super">or blocke</emph>
 with <emph style="super">a</emph> shiner in it <lb/>
 &amp; that part they call a pendent. then there is a <emph style="st">blocke fast</emph> <lb/>
 <emph style="st">at the chayne wale having shiners</emph> ring in the cheyne <lb/>
 wale into which is put a hooke fastened to a block <lb/>
 with shiners (a great pully). Then there is a standing <lb/>
 parte of the takle which goeth thourough the blocke of the <lb/>
 pendent &amp; and hath <emph style="st">one other bl</emph> a long block with two shiners <lb/>
 one above an other at one end, &amp; the other end is reeved (put) <lb/>
 thourough the sayd ring &amp; there fastened about the ring to it self. <lb/>
 Then there is a running part <emph style="super">one end</emph> fastened to the foresayd block <lb/>
 with the hooke &amp; so rived thourough the upper shiner of the block <lb/>
 of the standing part &amp; one shiner <lb/>
 of the blocke with the hooke &amp; so up <lb/>
 &amp; downe agayne by the second <lb/>
 shiner of the blocke with hooke <lb/>
 &amp; then the end to be haled &amp; <lb/>
 to be fastened when they have <lb/>
 don about all the parts &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s176" xml:space="preserve">
 [Diagram] <lb/>
 a. the pendent <lb/>
 b. the standing part <lb/>
 c. the runnere
 </s>
 </p>
 <pb file="0070.jpg" o="35v" n="70"/>
 <pb file="0071.jpg" o="36r" n="71"/>
 <head xml:id="echoid-head24" xml:space="preserve">
 notes
 </head>
 <p>
 <s xml:id="echoid-s177" xml:space="preserve">
 Tackle <lb/>
 ground tackle <lb/>
 coyling of a cable <lb/>
 vering <lb/>
 paying
 </s>
 </p>
 <p>
 <s xml:id="echoid-s178" xml:space="preserve">
 to Travers, to lavere the [???] <lb/>
 to make way bordes <lb/>
 to turne
 </s>
 </p>
 <p>
 <s xml:id="echoid-s179" xml:space="preserve">
 overcast futtockes <lb/>
 cammering <lb/>
 hookes
 </s>
 </p>
 <p>
 <s xml:id="echoid-s180" xml:space="preserve">
 <emph style="st">a luffe in the wind</emph> <emph style="super">a luffe</emph>;
 i. stay her in the wind to hinder her way. <lb/>
 a luffe &amp; shake in the wind.
 </s>
 <lb/>
 <s xml:id="echoid-s181" xml:space="preserve">
 to heave up: to pay. to go from the wind. <lb/>
 that is brace up the helme.
 </s>
 <lb/>
 <s xml:id="echoid-s182" xml:space="preserve">
 roomer; all one; roome her. or geve her roome. <lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s183" xml:space="preserve">
 bittes <lb/>
 a bitter. i. a stopper
 </s>
 </p>
 <p>
 <s xml:id="echoid-s184" xml:space="preserve">
 cammering of <lb/>
 the beames, or <lb/>
 deck. is there <lb/>
 convexity. <lb/>
 an inch to a foote. <lb/>
 for the half bredth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s185" xml:space="preserve">
 to bring her upon the careen. i. to lay her upon one side on the water <lb/>
 that the garbell streak may be calked.
 </s>
 <lb/>
 <s xml:id="echoid-s186" xml:space="preserve">
 the garbell streake is that shaves next to the keele. <lb/>
 the spaniards do build some help on the side that must beare <lb/>
 other <emph style="st">streakes</emph> seames are called streakes. (or streakes of plankes)
 </s>
 <lb/>
 <s xml:id="echoid-s187" xml:space="preserve">
 to more: is to ankre with two ankers lesse than a cable distant <lb/>
 to more with foure.
 </s>
 <lb/>
 <s xml:id="echoid-s188" xml:space="preserve">
 to wend or turne
 </s>
 <lb/>
 <s xml:id="echoid-s189" xml:space="preserve">
 a shot of cable, is two cables, bent together; i. wound one about another
 <emph style="super">&amp; frayed</emph> i. tyed <lb/>
 to make at one in length.
 </s>
 <lb/>
 <s xml:id="echoid-s190" xml:space="preserve">
 a splice <emph style="super">i. a wynt.)</emph>. to splice is to joyne the ropes or cables together <lb/>
 by opening the ends &amp; working one in an other with a fid.
 </s>
 <lb/>
 <s xml:id="echoid-s191" xml:space="preserve">
 A Fid, <emph style="super">i. a bodkin.</emph> is an iron about a foot longe &amp; less;
 of the fashion of a <emph style="st">reeve</emph> <emph style="super">bodkin</emph>. <lb/>
 A Fid hammer: a hammer &amp; fid in one.
 </s>
 <lb/>
 <s xml:id="echoid-s192" xml:space="preserve">
 A crooked square pin going into the foote of the top maste to stay it <lb/>
 from sinking lower, is called a Fid also. <lb/>
 This fid stayes upon the crosse trees. (or tressle I think.)
 </s>
 </p>
 <pb file="0072.jpg" o="36v" n="72"/>
 <pb file="0073.jpg" o="37r" n="73"/>
 <head xml:id="echoid-head25" xml:space="preserve">
 Notes.
 </head>
 <p>
 <s xml:id="echoid-s193" xml:space="preserve">
 The sheathing of ship to keepe her from wormes, though bords below <lb/>
 <emph style="super">with which I think upward</emph> <emph style="super">upward, above the water</emph>
 with tar &amp; here between, with the tarre <lb/>
 some simple powder <emph style="super">as</emph> glasse.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s194" xml:space="preserve">
 The parrell. (i. apparell.) it <emph style="st">joy</emph> ioynes the yard <lb/>
 to the maste; a cheyne of truckles.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s195" xml:space="preserve">
 counters
 </s>
 </p>
 <p>
 <s xml:id="echoid-s196" xml:space="preserve">
 The Crosse peeces, are called transomes in the [???] peece. <lb/>
 Amiddes ship they are called Beames. <lb/>
 The Mayne beam.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s197" xml:space="preserve">
 pillers. pillerifing. posts that heave up <lb/>
 the beames whether <lb/>
 they be upright or oblike.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s198" xml:space="preserve">
 Knees <lb/>
 hookes &amp; runnel peeces <lb/>
 hoodinges, the fasteninges <emph style="super">of the workes</emph> at the sterne <lb/>
 boltes, rings &amp; forelocks <lb/>
 Trennels; i. wooden pinnes <lb/>
 Spikes, i. long great nayles. <lb/>
 The sheat anker. shoot anker <lb/>
 Keckling of cable, i. is the sheathing <lb/>
 platting of a cable <lb/>
 The channell is dorved up i. stopped (with mud or sand) <lb/>
 To warp with a <emph style="super">small</emph> kedging anker &amp; a hawser.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s199" xml:space="preserve">
 sparse decke
 </s>
 </p>
 <p>
 <s xml:id="echoid-s200" xml:space="preserve">
 sinet. <lb/>
 gaskets. <lb/>
 plats. <lb/>
 clew
 </s>
 </p>
 <p>
 <s xml:id="echoid-s201" xml:space="preserve">
 knittle; two yarnes knitted together.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s202" xml:space="preserve">
 Thoughts of a boat <lb/>
 the crosse peeces they <lb/>
 sit on a Â [???]
 </s>
 </p>
 <p>
 <s xml:id="echoid-s203" xml:space="preserve">
 Hawsers of ropes cable layed; (one rope made of 3 strandes, &amp; 3 make another <emph style="super">rope</emph> <lb/>
 cable layd, one strand many thirds.
 </s>
 <lb/>
 <s xml:id="echoid-s204" xml:space="preserve">
 to bevel. bevelling
 </s>
 <lb/>
 <s xml:id="echoid-s205" xml:space="preserve">
 buoy. buoy rope. made fast to teh buoy &amp; the crosse of the anker.
 </s>
 <lb/>
 <s xml:id="echoid-s206" xml:space="preserve">
 bote rope. to two the bote.
 </s>
 <lb/>
 <s xml:id="echoid-s207" xml:space="preserve">
 bolt ropes. that <emph style="st">the</emph> the sayles are sowed to:
 </s>
 <lb/>
 <s xml:id="echoid-s208" xml:space="preserve">
 keele rope; runnes along <emph style="st">by</emph>
 <emph style="super">upon</emph> the keele thourough the timber holes. <lb/>
 which are holes under every bend to geve passage <lb/>
 to the water to come to the pompe.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s209" xml:space="preserve">
 The ship is timber sicke, when the timbers stopped, &amp; the the <emph style="super">keel</emph> rope <lb/>
 is to clere it. they have besides here &amp; there spurcuts to pull up <lb/>
 to come to the rope, or holes. Spurcut a <emph style="st">peec</emph> aquare peece of wood <lb/>
 to stop up a place withall.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s210" xml:space="preserve">
 [Diagram] <lb/>
 Stock <lb/>
 flookes <lb/>
 a) the crosse
 </s>
 </p>
 <pb file="0074.jpg" o="37v" n="74"/>
 <pb file="0075.jpg" o="38r" n="75"/>
 <head xml:id="echoid-head26" xml:space="preserve">
 Notes.
 </head>
 <p>
 <s xml:id="echoid-s211" xml:space="preserve">
 For the length of the mayne maste. (from the step to the top or whole <lb/>
 length) <lb/>
 Mr Barkers rule <lb/>
 grounded on the experience of a ship of 20f broad doth very well <lb/>
 with a mast of 20 yards long.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s212" xml:space="preserve">
 breadth of the ship. high of the mast. <lb/>
 feet. yardes. feet. yardes. feet.
 </s>
 </p>
 <pb file="0076.jpg" o="38v" n="76"/>
 <pb file="0077.jpg" o="39r" n="77"/>
 <div xml:id="echoid-div3" type="page_commentary" level="2" n="3">
<p>
<s xml:id="echoid-s213" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s213" xml:space="preserve">
 Unfortunately, it has not been possible to trace any surviving copy of Edmund Marlow's
 <emph style="it">Ars naupegica</emph>.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head27" xml:space="preserve">
 Notes taken out Captayne Edmund Marloe his booke <lb/>
 intituled Ars Naupegica. or the art of ship building.
 </head>
 <p>
 <s xml:id="echoid-s215" xml:space="preserve">
 The Easterling, Dues or Fleming, build floty ships by reason those <lb/>
 countryes are subiect to flats &amp; shoulds. And because they often bring <lb/>
 them a ground they have much flat flore to rest them on. There sides <lb/>
 also are upright, and are built so for burthen &amp; small draught of water. <lb/>
 And they beare sayle not so much for there sides, but by reason of the <lb/>
 great weyght that lyeth below upon the flore, (being so broad &amp; long). <lb/>
 But these for the most part are evill conditioned ships in the sea: <lb/>
 being subiect to rowle, tumble, &amp; leape in a wrought sea; so that <lb/>
 you must allwayes keep some sayle abrode.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s216" xml:space="preserve">
 Contrarywise the Spaniard (not accustomed to bring his ships a ground) <lb/>
 but allwayes to ride aflote, and also to trimme his ships upon the <lb/>
 carine) buildeth sharpe deep ships, hanging of for the most part upon <lb/>
 the nayle. As you may se by there Carbells. And there Caractes <lb/>
 likewise for the most part flare much of aloft. Now these hold a <lb/>
 better wind &amp; are easier in a wrought sea, and will commonly hull well, <lb/>
 &amp; wether quoyle. But they draw much water &amp; are not well to be brought <lb/>
 a ground without good floring for feare they fall over.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s217" xml:space="preserve">
 The Frenchmen are nearest to perfection in bearing style &amp; going <lb/>
 well, being neat moulded ships. But they are not commmonly so great <lb/>
 in burthen as they loome for. They have lolng rakes &amp; sharp forward <lb/>
 on; and there decks steeve much forward. Where contrarywise, the <lb/>
 Easterling &amp; Dues have short upright rakes &amp; bloof ships forwards <lb/>
 on. Also there decks steeve or hung afterwardes on.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s218" xml:space="preserve">
 But our English ships are intended to have such perfection, that <lb/>
 (according to the intent of the builder) they hold burden with the <lb/>
 Fleming; bearing with the Spaniard; going well with the French &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s219" xml:space="preserve">
 Every nation aymeth at this to have there ships go well &amp; stear well <lb/>
 which proceedeth especially from the well weying of a ship fore &amp; afte <lb/>
 for the Runne &amp; Tuck.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s220" xml:space="preserve">
 These are the cheif propertyes of a ship in the sea. TO go well; to <lb/>
 stear well, &amp; beare a good sayle. As for the Burthen that belongeth <lb/>
 to the owners profit, which some to much affecting hath made us to <lb/>
 have so many furred ships.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s221" xml:space="preserve">
 Some have made a ship of 19 foot brode, to be 8 foot and a <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> in houlde, where-<lb/>
 by to carry three tyre of Burdeux cask, which cannot welbe don <lb/>
 in lesse then 21 feet brode. They have been fayne afterwards (when <lb/>
 they see to there greef that she will beare no sail) to fur her at <lb/>
 least a foot on a side more; all which is lost in hold to there hindrance.
 </s>
 </p>
 <pb file="0078.jpg" o="39v" n="78"/>
 <pb file="0079.jpg" o="40r" n="79"/>
 <head xml:id="echoid-head28" xml:space="preserve">
 The shipwrites order of <lb/>
 beveling.
 </head>
 <p>
 <s xml:id="echoid-s222" xml:space="preserve">
 These angles <lb/>
 here expressed are <lb/>
 not the true angles <lb/>
 of beveling for the <lb/>
 plot; but are fayned <lb/>
 only for example.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s223" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi></mstyle></math>, the angle of beveling the aftermost bend. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi><mi>f</mi></mstyle></math>, a right angle, the angle of bevelong of <lb/>
 the midship bend. <lb/>
 The beveling angles of the other bendes <lb/>
 are betweene after the manner as <lb/>
 here appeareth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s224" xml:space="preserve">
 The beveling is used at the lower &amp; upper narrowinges <lb/>
 only, the rest between is hewed to agree with there moulds <lb/>
 because some parte of them serve for every bende &amp;c.
 </s>
 </p>
 <pb file="0080.jpg" o="40v" n="80"/>
 <p>
 <s xml:id="echoid-s225" xml:space="preserve">
 The boteswayne with his ging. (company.) <lb/>
 bang the rope (tabe).
 </s>
 </p>
 <pb file="0081.jpg" o="41r" n="81"/>
 <head xml:id="echoid-head29" xml:space="preserve">
 Notes.
 </head>
 <p>
 <s xml:id="echoid-s226" xml:space="preserve">
 It is knowne by experience that a ship whose depth. 10, foote <lb/>
 bredth. 20 <lb/>
 length 50 by the keele <lb/>
 is of burden a 100 tonne.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s227" xml:space="preserve">
 M<emph style="super">r</emph>. Baker makes this rule &amp; findes it <lb/>
 little more or lesse than the truth otherwise tried: <lb/>
 he makes a solid nomber of 10. 20. &amp; 50; &amp; then <lb/>
 devides it by a hundred; the quotient is the tonnes of burden;
 <emph style="super">(in hold as I take it)</emph> <lb/>
 the sayd length depth &amp; bredth must be in feete for this rule.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s228" xml:space="preserve">
 ffor tonne &amp; tonnage of the Kinges ships he multiplyes as before <lb/>
 but devides by 70. &amp; the quotient is counted her tonnage. <lb/>
 By these rules <emph style="super">the</emph> tonnage of shipps is measured for the King.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s229" xml:space="preserve">
 Tonne &amp; tonnage is what a ship doth carry of ordinaure mastes <lb/>
 sayles &amp; yardes, together with that which she carry in hold: &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s230" xml:space="preserve">
 Ths solid nomber of 10. 20. 50. is: 10,000. And so many solide feet <lb/>
 is that parallelepiped. <lb/>
 Now it semeth to me that that parallelepipied is to the bulke of the <lb/>
 ship as 3 to 1. or nere. for devide the nomber by 3 &amp; then <lb/>
 the bulke bulke of the hsip is, 3,333. in feet. then every solide foot <lb/>
 holding 64 pound of water; I multiply it by 64 and it amounteth <lb/>
 to in pounds, 213, 312. which devided <lb/>
 by .2240. yieldeth 95, tonne. 20 times 112<emph style="super">lb</emph> being <lb/>
 the tonne. <lb/>
 but by 2000, yieldeth 106. tonne. reckoning 20 times <lb/>
 100, only for the tonne. <lb/>
 And so M<emph style="super">r</emph> Bakers rule <lb/>
 happeneth to be the meane.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s231" xml:space="preserve">
 In deviding it by 70, the <lb/>
 tonnage it is 143 tonnes. <lb/>
 That tonne being 2,240<emph style="super">lb</emph> <lb/>
 maketh the above sayd parall-<lb/>
 epiped to be just double to <lb/>
 the bulke. Therefore 5000 <lb/>
 multiplied by 64 maketh <lb/>
 320,000<emph style="super">lb</emph> &amp; devided by <lb/>
 2240. yieldeth 143.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s232" xml:space="preserve">
 But of this matter more is to be considered <lb/>
 by the true solidity of the ship gotten by <lb/>
 geometrciall measure. &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s233" xml:space="preserve">
 The caracte taken by S<emph style="super">r</emph> J. Barres <lb/>
 length. 100. foot <lb/>
 breadth. 47. f <lb/>
 depth. 31. f <lb/>
 by this recconing <lb/>
 of 1457. tonne <lb/>
 but counted 1600. tonne <lb/>
 see. voyages. 2. 198.
 </s>
 </p>
 <pb file="0082.jpg" o="41v" n="82"/>
 <p>
 <s xml:id="echoid-s234" xml:space="preserve">
 Sterne <lb/>
 Counters <lb/>
 The ruder <lb/>
 The keele
 </s>
 </p>
 <p>
 <s xml:id="echoid-s235" xml:space="preserve">
 quarters, abaft, <lb/>
 bowes, afore
 </s>
 </p>
 <p>
 <s xml:id="echoid-s236" xml:space="preserve">
 When they carry light goods they <emph style="super">must</emph> have kintledge
 <emph style="super">heavy goods</emph> (keel tonnage) <lb/>
 to ly be lowe, <emph style="super">as</emph> <emph style="st">eith</emph>
 lead, iron <emph style="super">or in steed</emph> stones or ballast (gravel or shingle (pebles
 </s>
 </p>
 <p>
 <s xml:id="echoid-s237" xml:space="preserve">
 The helme <lb/>
 The ship of the helme
 </s>
 </p>
 <p>
 <s xml:id="echoid-s238" xml:space="preserve">
 prora et pappis <lb/>
 prora et poop
 </s>
 </p>
 <p>
 <s xml:id="echoid-s239" xml:space="preserve">
 The rake of <lb/>
 the stem.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s240" xml:space="preserve">
 porte holes. 2. foote [???] <lb/>
 2, foot: above the [???] <lb/>
 for the carriadge [???] <lb/>
 10 or 11 for asunder [???] <lb/>
 the bends will geve [???] <lb/>
 timbers
 </s>
 </p>
 <p>
 <s xml:id="echoid-s241" xml:space="preserve">
 Shee lyes down like a crab. <lb/>
 Shee is a crab sided thing. <lb/>
 when shee will not bear sayle
 </s>
 </p>
 <p>
 <s xml:id="echoid-s242" xml:space="preserve">
 Shee is very thyte. i. not leaky. Shee is stanes (of the [???] <lb/>
 water of the [???] <lb/>
 pompe of [???]
 as thyte as a fish <lb/>
 Wee drinke more than we pomp.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s243" xml:space="preserve">
 The mayne corse. <lb/>
 The forecastle corse
 </s>
 </p>
 <p>
 <s xml:id="echoid-s244" xml:space="preserve">
 The printel of her rudder <lb/>
 the gudgeon. the iron that swallowes the pintel
 </s>
 </p>
 <p>
 <s xml:id="echoid-s245" xml:space="preserve">
 The fooke sayle
 </s>
 </p>
 <p>
 <s xml:id="echoid-s246" xml:space="preserve">
 (A plugge or stopple.)
 </s>
 </p>
 <p>
 <s xml:id="echoid-s247" xml:space="preserve">
 I skite well but I <lb/>
 plump not.
 </s>
 </p>
 <pb file="0083.jpg" o="42r" n="83"/>
 <head xml:id="echoid-head30" xml:space="preserve">
 Of the fashion peece.
 </head>
 <p>
 <s xml:id="echoid-s248" xml:space="preserve">
 The inner playne of the fashion peece tieth in the line ** which <lb/>
 is best to be made parallell, to the sterne post or if not parallell <lb/>
 to make an <emph style="st">obsu</emph> obtuser angle somewhat with the <emph style="st">sterne</emph> keele. <lb/>
 but in this plot inclineth somewhat the contrary way by which <lb/>
 this fashion peece is made. it is best that the uppermost starre <lb/>
 stand in an even bend (which here is the 23<emph style="super">th</emph>) in uppermost rising <lb/>
 line. <emph style="st">where</emph> Therefore in the parallell for the 23<emph style="super">th</emph> bend <lb/>
 in the playne of bredth &amp; length is to be taken <emph style="st">the length &amp; bredth</emph> <lb/>
 the narrowing &amp; bredth a loft for the fashion peece. <lb/>
 to which narrowing, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>e</mi></mstyle></math> is æquall; so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math> is the bredth a lofte. <lb/>
 The lower starre standing in the rising line <emph style="st">[???]</emph> is <lb/>
 represented by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi></mstyle></math>, so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>v</mi></mstyle></math> is æquall to ** <emph style="super">in the plot by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi><mi>s</mi></mstyle></math></emph>.
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi><mi>Ï&#134;</mi></mstyle></math> is æquall to <lb/>
 the rest of that line in the same playne to the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>G</mi></mstyle></math>. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi><mi>a</mi></mstyle></math> is æquall to the narrowing alow taken in the parallell that passeth <lb/>
 by the lower starre. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>β</mi></mstyle></math> is æquall to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>β</mi></mstyle></math> of the midship <lb/>
 bend. here <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi></mstyle></math> are over gon <emph style="st">of</emph> one the other (on contrary <lb/>
 sides) so that there is no floore.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s249" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi></mstyle></math>* &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>* sheweing the soothmarkes are æquall (as in all the bends) <lb/>
 to those of the midship mould. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi></mstyle></math> being known, the centers <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>μ</mi></mstyle></math>, are knowne &amp; all the rest <lb/>
 as in the 16<emph style="super">th</emph> bend, &amp; so the descriptions of the arkes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s250" xml:space="preserve">
 Then understand the forke here described to be away (for it <emph style="st">is to</emph> <lb/>
 shold not have ben don) &amp; <emph style="st">the [???]</emph> the mouldes cutting one an <lb/>
 other of <emph style="st">geveth the the whole fashioin</emph> <emph style="super">a little above <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi></mstyle></math></emph>
 leaveth the rest for the fashion <lb/>
 peece.
 </s>
 </p>
 <pb file="0084.jpg" o="42v" n="84"/>
 <pb file="0085.jpg" o="43r" n="85"/>
 <head xml:id="echoid-head31" xml:space="preserve">
 The 16<emph style="super">th</emph> bend. abaft.
 </head>
 <p>
 <s xml:id="echoid-s251" xml:space="preserve">
 Make the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>Ï&#134;</mi></mstyle></math> æquall to the perpendicular in the plot from the rising <lb/>
 a loft to the keel upon the 16<emph style="super"/> bend. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Ï&#134;</mi><mi>v</mi></mstyle></math> æquall to the rising alow <lb/>
 Then let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math> be æquall to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math> in the plot. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>e</mi></mstyle></math> the narrowing aloft <lb/>
 then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math> is the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> bredth of this bend. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>v</mi></mstyle></math> the depth of this bend. <lb/>
 make <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>v</mi><mi>a</mi></mstyle></math> æqualal to the narrowing below of this bend in the plott <lb/>
 let <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>β</mi></mstyle></math> be æquall to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>β</mi></mstyle></math> of the midship bend. <lb/>
 then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>β</mi></mstyle></math> is the floore of this bend. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi></mstyle></math>* &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>* shewing the sooth markes are æquall always in every bend <lb/>
 to those of the midship mould. <lb/>
 from the sooth marke to <emph style="st">to</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>v</mi></mstyle></math> <emph style="super">is æquall</emph>
 tp the halfe breadth below. (found in the plott.)
 </s>
 </p>
 <p>
 <s xml:id="echoid-s252" xml:space="preserve">
 Then for the centers thus: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>β</mi><mi>μ</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>m</mi></mstyle></math>: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>d</mi></mstyle></math>: <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>e</mi><mi>r</mi></mstyle></math>: ar æquall to <lb/>
 the same sweepes in the midship bend. likewise, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>m</mi></mstyle></math>:
 æquall <emph style="st">th</emph> to <emph style="st">the</emph> <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>n</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>m</mi></mstyle></math> in the sayd midship bend. <lb/>
 So that hereby mechanically are described the arkes <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>d</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>c</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>b</mi></mstyle></math>; &amp; there <lb/>
 correspondents.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s253" xml:space="preserve">
 Then at <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Ï&#134;</mi></mstyle></math>, downwards is to be allowed 2 inches in small shippes (of 100<emph style="super">t</emph>) <lb/>
 &amp; 3 ynches (of 800<emph style="super">t</emph>) <lb/>
 for dead rising for the timber hole; where <emph style="super">the timber</emph> must be so broad as the keel <lb/>
 &amp; this is to be allowed in the midship bend and all the rest <lb/>
 then from the upper edge of the keele which is all one with the bottome of the <lb/>
 dead rising, <emph style="st">must be an</emph> upward toward the sooth marke, they use the backe <lb/>
 side of one of the mouldes for a shallowing mould.
 </s>
 </p>
 <pb file="0086.jpg" o="43v" n="86"/>
 <pb file="0087.jpg" o="44r" n="87"/>
 <head xml:id="echoid-head32" xml:space="preserve">
 Notes. or observations. <lb/>
 of the midship bend. <lb/>
 or, the mould.
 </head>
 <p>
 <s xml:id="echoid-s254" xml:space="preserve">
 As. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math>, 120. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>m</mi></mstyle></math>, is between 60 &amp; 70. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>e</mi></mstyle></math>, not more than halfe <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math>. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>e</mi></mstyle></math>, must be shorter then the depth of the fashion peece <lb/>
 represented by ** alofte at the fashion peece in the plotte. <lb/>
 In a ship of 20 foote brode (100, tonne) the water marke <lb/>
 is counted, 1 foote under; in 40 fo: brode. (800 tonne) 2, foote.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s255" xml:space="preserve">
 In making of the mould from the flat floore is specialaly to be <lb/>
 considered the hanging of of the side 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>d</mi></mstyle></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. for which <lb/>
 they have no certayne rule but judgement by the ey. these thinges <lb/>
 being considered; the holding of goods, the sayling, &amp; bearing. <lb/>
 The greater the breadth is at the wrong heads the more they <lb/>
 carry, in weyght, but nindreth there going. <lb/>
 if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>d</mi></mstyle></math> be to round shee is subiect to rouling. &amp;c.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s256" xml:space="preserve">
 <emph style="st">[???]</emph> <emph style="it">Let</emph>
 the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>m</mi></mstyle></math> extended be double to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi></mstyle></math> let that be <emph style="st">any</emph> a <lb/>
 semidiameter. <emph style="st">from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math> a perpendicle to that line let be the after</emph> <lb/>
 of an elipe which must come by <emph style="st"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> (or</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>) then seke out the poynt <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi></mstyle></math> to make <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> an arke to go fayne upon the elipsis. then by assay <lb/>
 seek the center <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math> to make an arke to touch the arke <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math> &amp; come by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>. <lb/>
 then in the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>k</mi></mstyle></math>, take <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>e</mi></mstyle></math> <emph style="st">lesse then</emph> half or lesse then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math> <lb/>
 but see that in the successe it also be shorter then the depth of <emph style="super"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math></emph> fashion <lb/>
 peece as above. for marchants ships let the
 <emph style="st">sayd</emph> <emph style="super">same</emph> diameter of <lb/>
 the sayd elipsis be a quarter lesse or there abouts, becasue <lb/>
 the lesse the <emph style="super">semi</emph>diameter is, the fuller she is be low at the wrong heds.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s257" xml:space="preserve">
 An other way. Suppose a perpendicular line form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math> to the keel <lb/>
 then devide from (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>) to the perpendicular in
 <emph style="super">to any nomber of</emph> æquall partes (as 10) <lb/>
 then say as the biquadrate of 10, has to, 9. So hath the partes of the <lb/>
 perpendicular to the <emph style="st">the</emph> 9<emph style="super">th</emph>s in the same parte <lb/>
 &amp; so of the rest, to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <lb/>
 &amp; so have you a <emph style="st">line</emph> croked line nere like <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mstyle></math>, by which you <lb/>
 are by assay to find out the counters <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>o</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>, as before. And these <lb/>
 two wayes M<emph style="super">r</emph> Marlow useth for to consider of his mould in <lb/>
 intention which M<emph style="super">r</emph> Baker approveth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s258" xml:space="preserve">
 This mould being described, the mould of every other bend is <lb/>
 described by the same sweepes, as <emph style="st">as</emph> followeth for example <lb/>
 of the 16<emph style="super">th</emph> bend abaft
 </s>
 </p>
 <pb file="0088.jpg" o="44v" n="88"/>
 <pb file="0089.jpg" o="45r" n="89"/>
 <head xml:id="echoid-head33" xml:space="preserve">
 The Narrowings below are they made:
 </head>
 <p>
 <s xml:id="echoid-s259" xml:space="preserve">
 from <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>L</mi></mstyle></math> abafte, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>L</mi></mstyle></math> may be over <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math>, but if it be a little shorter <lb/>
 it is never the worse but better. therefore let end at the next <lb/>
 bend to it, which in the plot is 22. the greatest narrowing is <lb/>
 therefore here <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>I</mi><mi>L</mi><mo>=</mo><mi>P</mi><mi>R</mi></mstyle></math>, <emph style="super">amp;</emph> the other bends are narrowed <lb/>
 cubically as before is sayde.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s260" xml:space="preserve">
 Then forward the narrowing line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>R</mi><mi>Z</mi></mstyle></math>, ending on the bend <lb/>
 next to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>y</mi></mstyle></math> inward; (but may be agaynst <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>y</mi></mstyle></math> <emph style="st">but</emph> not beyond) <lb/>
 is mde cubically likewise, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>I</mi><mi>Z</mi><mo>-</mo><mi>R</mi><mi>P</mi></mstyle></math> being the greatest.
 </s>
 </p>
 <pb file="0090.jpg" o="45v" n="90"/>
 <pb file="0091.jpg" o="46r" n="91"/>
 <p>
 <s xml:id="echoid-s261" xml:space="preserve">
 Of the playne of lenght &amp; bredth. parallel to the horizon <lb/>
 halfe signified by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>M</mi><mi>N</mi><mi>O</mi><mi>q</mi></mstyle></math>. The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi><mi>M</mi></mstyle></math> is understode to be the <lb/>
 length <emph style="st">with</emph> &amp; all one with <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>P</mi></mstyle></math> ioyning to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>K</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi></mstyle></math>. So that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>P</mi><mi>Q</mi></mstyle></math> <lb/>
 is æquall <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>K</mi><mi>e</mi></mstyle></math>. the halfe breadth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s262" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>P</mi><mi>R</mi></mstyle></math> is half <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>P</mi><mi>Q</mi></mstyle></math> which 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 whole breadth, by which it made the <lb/>
 sooth markes represented by **, in the line of the floore timber; so that <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math>* is æquall to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>P</mi><mi>R</mi></mstyle></math>.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s263" xml:space="preserve">
 An other playne whose half is signified by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>M</mi><mi>T</mi><mi>R</mi><mi>V</mi><mi>q</mi></mstyle></math>. &amp; parallel to the <lb/>
 other &amp; under it as much as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>K</mi><mi>S</mi></mstyle></math>, which <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math> is in the line of the sooth markes <lb/>
 of this playne <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>P</mi></mstyle></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>R</mi></mstyle></math> is *.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s264" xml:space="preserve">
 In these two playnes are measured the narrowinges alofte &amp; a low, upon <lb/>
 every severall bend; on the parallels. <lb/>
 The forme of the upper narrowinges represented by the crooked line <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>M</mi><mi>Q</mi><mi>V</mi></mstyle></math> <lb/>
 &amp; is thus made: by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mo>.</mo><mi>M</mi></mstyle></math>.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s265" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi><mi>V</mi></mstyle></math>, the greatest narrowing abafte is æquall <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi><mi>R</mi></mstyle></math>, a quarter of the which breadth <lb/>
 for the narrowing of the next bend; example 22. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>o</mi></mstyle></math>, being the 24. <lb/>
 as the cube of 24 to the cube of 22, so <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi><mi>V</mi></mstyle></math> inches is to the narrowing <lb/>
 of that 22 bend inches, &amp; so of the rest to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math>.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s266" xml:space="preserve">
 Mr Baker way is, by describing of 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 a <lb/>
 circle. making <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>c</mi><mo>=</mo><mi>P</mi><mi>Q</mi></mstyle></math> half the breadth <lb/>
 taking <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac><mo>=</mo><mi>b</mi><mi>c</mi></mstyle></math> away; the dividing <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math> &amp; <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math>, int so many bendes as are betwixt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi></mstyle></math> <lb/>
 making <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi></mstyle></math> the greatest narrowing nere æquall to, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>O</mi><mi>V</mi></mstyle></math> <lb/>
 &amp; so so the rest betwixt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> &amp; the arke; which line <lb/>
 in the playne wilbe an elipsis. <lb/>
 The <emph style="super">same</emph> narrowing line he useth also a low on the <lb/>
 under playne aftewardes on.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s267" xml:space="preserve">
 But afore, the under narroiwngs he maketh <lb/>
 to end agaynst <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>y</mi></mstyle></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>P</mi><mi>R</mi></mstyle></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>S</mi></mstyle></math>* being æquall to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>f</mi></mstyle></math> here in the quadrant <lb/>
 then deviding <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> into so many bendes as are betwixt <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>y</mi></mstyle></math> &amp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, the narrowinges <lb/>
 are taken as before between <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math> &amp; the arke <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>f</mi></mstyle></math>.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s268" xml:space="preserve">
 After the upper narroiwng he carrieth a part of the same elipsis as was abafte till <lb/>
 he <emph style="super">come</emph> to the luffe nere agaynst the pith of the sterne
 <emph style="super">(<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>o</mi></mstyle></math>)</emph> and for the rest makes a circle <lb/>
 from the stern to tuch that elipse. &amp; this he doth by iudgement.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s269" xml:space="preserve">
 From <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>M</mi></mstyle></math> foreward the narroiwng is thus made by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mi>M</mi></mstyle></math>: form <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math> forward <lb/>
 4 bendes <emph style="super">in</emph> this plat hath no narrowing; &amp; from there it begineth to narroweth <lb/>
 cubically as before making <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>N</mi><mi>M</mi></mstyle></math> the greatest. it may be made from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math> <lb/>
 to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>M</mi></mstyle></math> by quadrants but then he thinketh it will come to full or bluffe as they <lb/>
 call it. if all <emph style="st">all</emph> were narrowed from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math> cubically to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>M</mi></mstyle></math>,
 <emph style="st">it</emph> the line wold <lb/>
 be to lanke or narrowe at the bowe. The srayte from <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Q</mi></mstyle></math> <emph style="super">he</emph> thinketh will <lb/>
 hold proportionally in other shippes.
 </s>
 </p>
 <pb file="0092.jpg" o="46v" n="92"/>
 <pb file="0093.jpg" o="47r" n="93"/>
 <p>
 <s xml:id="echoid-s270" xml:space="preserve">
 The rising line a low. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi><mi>x</mi><mi>a</mi><mi>y</mi><mi>f</mi></mstyle></math>. usually made by a circle
 <emph style="super">(or bore)</emph> tuching in <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, by <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi></mstyle></math>. <lb/>
 The heygh of the tucke <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>x</mi></mstyle></math>. 10. as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>a</mi></mstyle></math>, 18. the greatest, <lb/>
 or. 9. as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>a</mi></mstyle></math>, the least. <lb/>
 the measure <lb/>
 usually above <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>. <lb/>
 here <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>x</mi></mstyle></math> 48y. <lb/>
 The hygh of the grype. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>y</mi></mstyle></math>. 1. as, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>k</mi></mstyle></math> 9. comonly 12y <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>7</mn><mn>5</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mstyle></math> here.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s271" xml:space="preserve">
 Otherwise by M Mar: the line of rising is made thus: <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>x</mi></mstyle></math> being the 20<emph style="super">th</emph> bend: as the cube of 20. to the cube of, 18, so is <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>x</mi></mstyle></math> in inches 48. to the rising of the 18 bend. <lb/>]&amp; so of the rest to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>. <lb/>
 for the rysing line forward: as ateh cube of the <lb/>
 nomber of teh gype 10y which is the 10<emph style="super">th</emph> bend <lb/>
 that is, as the cube of 10, being 100 is to, <emph style="st">is to</emph> the cube of 9, or <lb/>
 11, the nomber of the next bend so &amp; so forth as before.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s272" xml:space="preserve">
 The rising line a lofte <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi><mi>k</mi><mi>r</mi></mstyle></math>, by which the greatest breadth of every <lb/>
 perticuler bend doth passe.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s273" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi><mi>A</mi></mstyle></math> is 1. as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>x</mi><mi>z</mi></mstyle></math> is, 3 by Mr. M) comonly [???]. here 16,y. <lb/>
 The risings <emph style="st">of</emph> in the other bende towards <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>y</mi></mstyle></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi></mstyle></math> and gotten by <lb/>
 cubes as the other below. and so form the 20<emph style="super">th</emph> bend at <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>k</mi></mstyle></math> <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi><mi>D</mi></mstyle></math> being made <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>, all to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s274" xml:space="preserve">
 In this playne of length &amp; depth is also to be conisdered: <lb/>
 the laying of the <emph style="st">[¿]decks[?]</emph> orlope &amp; decks. <lb/>
 the portes <lb/>
 &amp; the laying of the wales, or the outside.
 </s>
 </p>
 <head xml:id="echoid-head34" xml:space="preserve">
 More of this playne.
 </head>
 <p>
 <s xml:id="echoid-s275" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>w</mi><mi>D</mi><mi>F</mi></mstyle></math>. the stemme. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>H</mi><mi>K</mi></mstyle></math>. the sweep of the stem. never greater then <lb/>
 the whole body <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>e</mi></mstyle></math>, nor lesse then, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>k</mi></mstyle></math>. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>w</mi><mi>E</mi></mstyle></math>. the rake of the stem. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>w</mi><mi>k</mi></mstyle></math>. the thicknesse of the keele. at <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> somewhat <lb/>
 thicker. <lb/>
 In a ship of 100<emph style="super">tons</emph> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>w</mi><mi>k</mi></mstyle></math> is 12 ynches. the breadth 10y: keele &amp; stem below. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>s</mi><mi>q</mi></mstyle></math>. the sterne post. thickenes &amp; breadth as <emph style="super">the</emph> keele <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi><mi>G</mi></mstyle></math>. the perpendiculer of the post. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>G</mi></mstyle></math>. the rate of the post. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi><mi>g</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi><mi>u</mi></mstyle></math> as, 12 to 13.
 </s>
 </p>
 <pb file="0094.jpg" o="47v" n="94"/>
 <pb file="0095.jpg" o="48r" n="95"/>
 <head xml:id="echoid-head35" xml:space="preserve">
 The midship mould or midshp bende <lb/>
 the playne of breadth &amp; depth.
 </head>
 <p>
 <s xml:id="echoid-s276" xml:space="preserve">
 The greatest breadth must not be lesse the triple the depth. <lb/>
 nor greater then 3 times the depth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s277" xml:space="preserve">
 of this diagram. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math>. the half breadth. 102 ynches. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>a</mi></mstyle></math>. the depth. 92<emph style="super">y</emph> <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>b</mi></mstyle></math>. 27.y.the half floore. generally: <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi><mi>c</mi></mstyle></math>, the wrong. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi></mstyle></math>, the center, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi><mi>b</mi></mstyle></math>, the sweep. 60.<emph style="super">y</emph> <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>b</mi><mi>a</mi><mi>β</mi><mi>γ</mi></mstyle></math>. the floor timber. <lb/>
 <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>β</mi><mi>γ</mi></mstyle></math>. the wronges. <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>γ</mi></mstyle></math>. the wrong heds. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>d</mi></mstyle></math>. the Futtock. <emph style="super">or staddle or studdle by some of the contry.</emph>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi></mstyle></math>. center. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>o</mi><mi>c</mi></mstyle></math>. the sweep thereof. 156. y. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>f</mi><mi>g</mi></mstyle></math>. the top timber. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>f</mi></mstyle></math>. the upper sweep. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>. center. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>d</mi></mstyle></math>. 48.y. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>g</mi></mstyle></math>. arke. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>. center. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi><mi>f</mi><mo>=</mo><mi>o</mi><mi>c</mi></mstyle></math>. if <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi><mi>g</mi></mstyle></math> be strayt: it is called <lb/>
 by some the poste. <lb/>
 in times past a right line [tangent to] <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>f</mi></mstyle></math>. <lb/>
 as, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>k</mi><mi>e</mi></mstyle></math>. 3. so <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>h</mi><mi>g</mi></mstyle></math>. 2. usually. here 74.y.
 </s>
 </p>
 <head xml:id="echoid-head36" xml:space="preserve">
 The playne of lengthe &amp; depthe <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>q</mi><mi>r</mi><mi>u</mi><mi>n</mi></mstyle></math>.
 </head>
 <p>
 <s xml:id="echoid-s278" xml:space="preserve">
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>n</mi></mstyle></math>, the keele: unto <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>e</mi><mi>e</mi></mstyle></math> the breadth not above 3, to, 1. nor lesse then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> <lb/>
 comonly. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>. <lb/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi><mi>a</mi></mstyle></math>, to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>u</mi><mi>n</mi></mstyle></math>. generally. as. 2, to. 1.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s279" xml:space="preserve">
 The floor timber <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi><mi>b</mi><mi>a</mi><mi>β</mi><mi>y</mi></mstyle></math> being at rectangles with the keele <lb/>
 must have breadth &amp; thickenes as followeth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s280" xml:space="preserve">
 In a ship of 20 foote brode: the thickenes in &amp; out, 7 yardes. <lb/>
 the breadth, 8 inches. in 38 foot brode of kings ships. in &amp; out. 12,y. <lb/>
 14 &amp; 15 y broade.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s281" xml:space="preserve">
 The middest of the first bend standes on <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math>.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s282" xml:space="preserve">
 The second bendes flore timber must stand so farre of that the futtocke <lb/>
 may come betweene with some advantage which is called timber <lb/>
 &amp; space. where the flore tymbers are 8<emph style="super">y</emph> inch brode, tymber &amp; space is <lb/>
 used to be 18y. that is, 8y for timber &amp; so 10 ynches for space. <lb/>
 &amp; by such distances you must marke fore &amp; afte as farre as they <lb/>
 will go in <emph style="st">bre</emph> the playne of breadth &amp; length.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s283" xml:space="preserve">
 In this plot the lines represent every second bend. &amp; of 30<emph style="super">y</emph> distance.
 </s>
 </p>
 <pb file="0096.jpg" o="48v" n="96"/>
 <pb file="0097.jpg" o="49r" n="97"/>
 <pb file="0098.jpg" o="49v" n="98"/>
 <pb file="0099.jpg" o="50r" n="99"/>
 <div xml:id="echoid-div4" type="page_commentary" level="2" n="4">
<p>
<s xml:id="echoid-s284" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s284" xml:space="preserve">
 The word at the top of the page is from the Latin translation (apparently by Martin Crucius) of a Greek verse
 (perhaps also by Crucius) consisting of compound words. See also Add MS 6782, f. 147. <lb/>
 The remainder of the page contains an arrangement of 100 soldiers
 in such a way that those of the highest rank are best protected.
 (These ideas are continued on the reverse of the page.)
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p>
 <s xml:id="echoid-s286" xml:space="preserve">
 of the precedence of soldiers
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s287" xml:space="preserve">
 of the precedence of soldiers
 Bombardagladiofunhastiflammiloquentes
 <lb/>[<emph style="it">tr:
 Breathing bombs, swords, death, spears, and flames
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0100.jpg" o="50v" n="100"/>
 <div xml:id="echoid-div5" type="page_commentary" level="2" n="5">
<p>
<s xml:id="echoid-s288" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s288" xml:space="preserve">
 Rough working connected to the ideas on the previous page,
 the problem being to arrange men in a square in such a way that the highest ranks are the best protected.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="0101.jpg" o="51r" n="101"/>
 <pb file="0102.jpg" o="51v" n="102"/>
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 <pb file="0109.jpg" o="55r" n="109"/>
 <head xml:id="echoid-head37" xml:space="preserve" xml:lang="lat">
 Anno. 1603. lib. editis <lb/>
 pag. 302. Johnnes Baptista Villalpandus cordubensis <lb/>
 et Societate Jesu. In tractatu de ponderibus &amp; mensuris <lb/>
 lib. 1 cap. 5. pro. 16 <lb/>
 pag. 302.
 </head>
 <pb file="0110.jpg" o="55v" n="110"/>
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 <pb file="0233.jpg" o="117r" n="233"/>
 <p>
 <s xml:id="echoid-s290" xml:space="preserve">
 To my very good frende <lb/>
 Mr. Thomas Hariots <lb/>
 at Durham house <lb/>
 these
 </s>
 </p>
 <pb file="0234.jpg" o="117v" n="234"/>
 <div xml:id="echoid-div6" type="page_commentary" level="2" n="6">
<p>
<s xml:id="echoid-s291" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s291" xml:space="preserve">
 This important letter to Harriot from Nathaniel Torporley foretells Torporley's first meeting with
 François Viète, the 'French Apollon'. Unfortunately, although the letter is marked '16 Sept', no year is given.
 However, it must have been written before Viète's death in 1603. For further arguments about the dating, see below.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s292" xml:space="preserve">
 Later accounts of Torporley described him as 'amanusenis' or perhaps secretary to Viète.
 It seems, therefore, that, as suggested by this letter, Torporley did indeed stay for a few weeks or months in Paris,
 during which time he was in regular contact with Viète, perhaps copying or transcribing his mansucripts.
 This would explain the presence of a sheet in Harriot's mansucripts marked 'A problem of Viète from Torporley'.
 More importantly, it would explain Harriot's access to all the works of Viète,
 of which only a few copies were printed and which were not easily available even in France.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s293" xml:space="preserve">
 Harriot began working his way systematically through Viète's <emph style="it">Zeteticorum libri quinque</emph>
 on 29 August 1600 (see Add MS 6782, f. 481).
 This suggests either that Torporley had already returend to England by then, bringing with him copies of Viète's books,
 or that he had them sent to Harriot from Paris.
 The letter on this page, dated 16 September, must therefore have been written earlier, perhaps the previous year, 1599.
 Torporley's description of Viète as the French Apollon presumably derives from the latter's
 <emph style="it">Apollonius Gallus</emph>, published in Paris in 1600, but perhaps a copy of it,
 or at least its title, was already known to Torporley some months beforehand.
 It is difficult otherwise to reconcile the September date of Torporley's letter with the August date of Harriot's ntoes.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p>
 <s xml:id="echoid-s295" xml:space="preserve">
 Good Mr. Hariots, beinge certayne how welcome to you newes of [my] <lb/>
 discoveries wilbe; I sende you these briefe commendations from the new <lb/>
 founde Tropike of Paris. For such, by my farre travaile I fynde <lb/>
 the greatest obliquitie of my variable Zodiake; which, by the Tables <lb/>
 of equall motion, ought ot have extended to the clyme Diako[???] <lb/>
 And thus I geve yo to understande (in some voluntarie obscuritie, and <lb/>
 shaminge in playne termes to come in what <foreign xml:lang="lat">non putaram</foreign>) the summe <lb/>
 of my fortunes synce my departure from London. You may [???] <lb/>
 in what continuall motion I have bene, that have sene Grave, [???] <lb/>
 Calais, Amiens, &amp; and am now at Paris retrograde, &amp; <foreign xml:lang="lat">cursu vacuus</foreign>. <lb/>
 And even my stile (me thinkes) discovers my exchaunge agayne of <lb/>
 Mars for the muses; the rather now, because I am gathering up <lb/>
 my ruined wittes, the better to encounter that French Apollon: <lb/>
 if it fortune that either his courtsie or my bouldness effecte our <lb/>
 conference; tomorrow beinge the daye, when if I am appoynted [by] <lb/>
 his Printer, as little Zacheus to climbe the tree, to gayne <lb/>
 a viewe of that renouwned Analist. What after followes [???] <lb/>
 presence I hope shortly to relate, yet resolved to consume some <lb/>
 weekes heare, so longe it maye be tyll I maye heare agayne <lb/>
 out of Englande, I have for you, if not out of season, Sim: S[???] [???]
 his owne plotte of the laste siege of Grave, which, because I thinke <lb/>
 maye be common ynough with you ere now, I therefore make <lb/>
 no earnest haste to sende it, but will wait some beafore being <lb/>
 meane while commending you to your deserved good fortunes, &amp; my [???] <lb/>
 in all due respectes to your continued goodwill, I take my laeve as <lb/>
 Yours ever in true fidelitie <lb/>
 Nath. Torporley <lb/>
 16 Sept: <lb/>
 English
 </s>
 </p>
 <pb file="0235.jpg" o="118r" n="235"/>
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 <p>
 <s xml:id="echoid-s296" xml:space="preserve">
 The truth when it is seen <lb/>
 is knowne without other evidence.
 </s>
 </p>
 <pb file="0263.jpg" o="132r" n="263"/>
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 <pb file="0370.jpg" o="185v" n="370"/>
 <pb file="0371.jpg" o="186r" n="371"/>
 <pb file="0372.jpg" o="186v" n="372"/>
 <pb file="0373.jpg" o="187r" n="373"/>
 <pb file="0374.jpg" o="187v" n="374"/>
 <pb file="0375.jpg" o="188r" n="375"/>
 <pb file="0376.jpg" o="188v" n="376"/>
 <pb file="0377.jpg" o="189r" n="377"/>
 <pb file="0378.jpg" o="189v" n="378"/>
 <pb file="0379.jpg" o="190r" n="379"/>
 <pb file="0380.jpg" o="190v" n="380"/>
 <pb file="0381.jpg" o="191r" n="381"/>
 <pb file="0382.jpg" o="191v" n="382"/>
 <pb file="0383.jpg" o="192r" n="383"/>
 <pb file="0384.jpg" o="192v" n="384"/>
 <pb file="0385.jpg" o="193r" n="385"/>
 <pb file="0386.jpg" o="193v" n="386"/>
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 <div xml:id="echoid-div7" type="page_commentary" level="2" n="7">
<p>
<s xml:id="echoid-s297" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s297" xml:space="preserve">
 The calculation shows the conversion of 86 yards 2 feet into feet.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p>
 <s xml:id="echoid-s299" xml:space="preserve">
 Poules steeple before it was burnt was high from the <lb/>
 ground 178 yeards whereof the stonework was 86 yeards <lb/>
 and 2 foote and the tymber worke upon the stone <lb/>
 worke being covered all with leade was 91 yeards and one <lb/>
 foote.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s300" xml:space="preserve">
 260, foote the hiht of pebles.
 </s>
 </p>
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 <pb file="0450.jpg" o="225v" n="450"/>
 <pb file="0451.jpg" o="226r" n="451"/>
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 <div xml:id="echoid-div8" type="page_commentary" level="2" n="8">
<p>
<s xml:id="echoid-s301" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s301" xml:space="preserve">
 The answer to the question posed by Harriot on this page is that François de Foix, comte de Candale,
 was indeed the same person as Francis Flussas Candella, commentator on Euclid's <emph style="it">Elements</emph>.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p>
 <s xml:id="echoid-s303" xml:space="preserve">
 The experiments of François M. de Foix <foreign xml:lang="lat">le grand Archimede <lb/>
 de nostre aage et qui le præmier a descouvert la <lb/>
 vraye proportion des metaux en poids et en volume</foreign>. <lb/>
 as Bodin rendereth <emph style="super">in his</emph> discourse of [???] <lb/>
 &amp; embasing of moneys.
 <lb/>[<emph style="it">tr:
 François M. de Foix the great Archimedes of our age
 and who was the first to discover the true proportion of metals in weight and volume.
 </emph>]<lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s304" xml:space="preserve">
 Quære whether the <lb/>
 man be flussas.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s305" xml:space="preserve">
 ferlin, the name of the weight
 </s>
 </p>
 <p>
 <s xml:id="echoid-s306" xml:space="preserve">
 Lazarus Erken <lb/>
 folio 60b.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s307" xml:space="preserve">
 Æquall[???] Weight <lb/>
 Gold <lb/>
 Copper <lb/>
 Silver <lb/>
 Copper to Silver <lb/>
 Lead to Silver <lb/>
 Tin to Silver <lb/>
 Tin to Gold <lb/>
 Silver to Iron <lb/>
 Gold to Iron <lb/>
 Mercury to Gold
 </s>
 </p>
 <p>
 <s xml:id="echoid-s308" xml:space="preserve">
 The nombers as they are in Bodin <lb/>
 by examination we finde some <lb/>
 false printed, such as are above <lb/>
 cancelled.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s309" xml:space="preserve">
 The nombers of the author <lb/>
 we take <emph style="super">to be</emph> as followeth.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s310" xml:space="preserve">
 Other nombers of the same rate: <lb/>
 whereby appeareth <lb/>
 the difference <lb/>
 of Clavius <lb/>
 his experiments.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s311" xml:space="preserve">
 Gold. <lb/>
 Lead. <lb/>
 Silver. <lb/>
 Copper. <lb/>
 Iron. <lb/>
 Tin. <lb/>
 Mercury. <lb/>
 sulphur. <lb/>
 wax.
 </s>
 </p>
 <pb file="0458.jpg" o="229v" n="458"/>
 <pb file="0459.jpg" o="230r" n="459"/>
 <pb file="0460.jpg" o="230v" n="460"/>
 <pb file="0461.jpg" o="231r" n="461"/>
 <pb file="0462.jpg" o="231v" n="462"/>
 <pb file="0463.jpg" o="232r" n="463"/>
 <pb file="0464.jpg" o="232v" n="464"/>
 <pb file="0465.jpg" o="233r" n="465"/>
 <pb file="0466.jpg" o="233v" n="466"/>
 <pb file="0467.jpg" o="234r" n="467"/>
 <pb file="0468.jpg" o="234v" n="468"/>
 <pb file="0469.jpg" o="235r" n="469"/>
 <pb file="0470.jpg" o="235v" n="470"/>
 <pb file="0471.jpg" o="236r" n="471"/>
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 <pb file="0473.jpg" o="237r" n="473"/>
 <pb file="0474.jpg" o="237v" n="474"/>
 <pb file="0475.jpg" o="238r" n="475"/>
 <pb file="0476.jpg" o="238v" n="476"/>
 <pb file="0477.jpg" o="239r" n="477"/>
 <pb file="0478.jpg" o="239v" n="478"/>
 <pb file="0479.jpg" o="240r" n="479"/>
 <pb file="0480.jpg" o="240v" n="480"/>
 <pb file="0481.jpg" o="241r" n="481"/>
 <pb file="0482.jpg" o="241v" n="482"/>
 <pb file="0483.jpg" o="242r" n="483"/>
 <pb file="0484.jpg" o="242v" n="484"/>
 <pb file="0485.jpg" o="243r" n="485"/>
 <pb file="0486.jpg" o="243v" n="486"/>
 <pb file="0487.jpg" o="244r" n="487"/>
 <pb file="0488.jpg" o="244v" n="488"/>
 <pb file="0489.jpg" o="245r" n="489"/>
 <pb file="0490.jpg" o="245v" n="490"/>
 <pb file="0491.jpg" o="246r" n="491"/>
 <pb file="0492.jpg" o="246v" n="492"/>
 <pb file="0493.jpg" o="247r" n="493"/>
 <pb file="0494.jpg" o="247v" n="494"/>
 <pb file="0495.jpg" o="248r" n="495"/>
 <pb file="0496.jpg" o="248v" n="496"/>
 <pb file="0497.jpg" o="249r" n="497"/>
 <pb file="0498.jpg" o="249v" n="498"/>
 <pb file="0499.jpg" o="250r" n="499"/>
 <pb file="0500.jpg" o="250v" n="500"/>
 <div xml:id="echoid-div9" type="page_commentary" level="2" n="9">
<p>
<s xml:id="echoid-s312" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s312" xml:space="preserve">
 The last four sentences are anagrams of one another. For a frequency analysis of the letters see the next folio,
 Add MS 6788, f. 251v.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p xml:lang="lat">
 <s xml:id="echoid-s314" xml:space="preserve">
 privatum lumine solem <lb/>
 igneum ama res stabit (basem) <lb/>
 umbræ mutæ in vasitis mirum <lb/>
 plangite solem
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s315" xml:space="preserve">
 umbræ in vastis mutæ, solem plangite mirum. <lb/>
 umbræ in vastis miræ, solem plangite mutum. <lb/>
 umbræ miræ in mutis, solem plangite vastum. <lb/>
 umbræ vastæ in mutis <emph style="super">insitum</emph>, solem plangite mirum.
 </s>
 </p>
 <pb file="0501.jpg" o="251r" n="501"/>
 <pb file="0502.jpg" o="251v" n="502"/>
 <div xml:id="echoid-div10" type="page_commentary" level="2" n="10">
<p>
<s xml:id="echoid-s316" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s316" xml:space="preserve">
 This page contains a frequency analysis of the 37 letters in the last four sentences on the previous page,
 Add MS 6788, f. 250v. <lb/>
 For other sentences made from the same letters, see Add MS 6786, f. 321 and Add MS 6789, f. 455v.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="0503.jpg" o="252r" n="503"/>
 <pb file="0504.jpg" o="252v" n="504"/>
 <pb file="0505.jpg" o="253r" n="505"/>
 <pb file="0506.jpg" o="253v" n="506"/>
 <pb file="0507.jpg" o="254r" n="507"/>
 <pb file="0508.jpg" o="254v" n="508"/>
 <pb file="0509.jpg" o="255r" n="509"/>
 <pb file="0510.jpg" o="255v" n="510"/>
 <pb file="0511.jpg" o="256r" n="511"/>
 <pb file="0512.jpg" o="256v" n="512"/>
 <pb file="0513.jpg" o="257r" n="513"/>
 <div xml:id="echoid-div11" type="page_commentary" level="2" n="11">
<p>
<s xml:id="echoid-s318" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s318" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588), page 172.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head38" xml:space="preserve" xml:lang="lat">
 Ubald. pag. 172.
 </head>
 <pb file="0514.jpg" o="257v" n="514"/>
 <div xml:id="echoid-div12" type="page_commentary" level="2" n="12">
<p>
<s xml:id="echoid-s320" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s320" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588), page 172.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head39" xml:space="preserve" xml:lang="lat">
 Archimedes de <emph style="st">quadratura</emph> <emph style="super">centro gravitate</emph> parabolæ. Ubaldi: pag. 172.
 </head>
 <pb file="0515.jpg" o="258r" n="515"/>
 <pb file="0516.jpg" o="258v" n="516"/>
 <pb file="0517.jpg" o="259r" n="517"/>
 <pb file="0518.jpg" o="259v" n="518"/>
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 <pb file="0525.jpg" o="263r" n="525"/>
 <pb file="0526.jpg" o="263v" n="526"/>
 <pb file="0527.jpg" o="264r" n="527"/>
 <pb file="0528.jpg" o="264v" n="528"/>
 <pb file="0529.jpg" o="265r" n="529"/>
 <pb file="0530.jpg" o="265v" n="530"/>
 <pb file="0531.jpg" o="266r" n="531"/>
 <pb file="0532.jpg" o="266v" n="532"/>
 <div xml:id="echoid-div13" type="page_commentary" level="2" n="13">
<p>
<s xml:id="echoid-s322" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s322" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588), page 108.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head40" xml:space="preserve" xml:lang="lat">
 De centro gravitatis <lb/>
 Trapezij <lb/>
 ut Archimides
 </head>
 <p>
 <s xml:id="echoid-s324" xml:space="preserve">
 Guidus Ubaldus <lb/>
 pag. 208
 </s>
 </p>
 <pb file="0533.jpg" o="267r" n="533"/>
 <pb file="0534.jpg" o="267v" n="534"/>
 <div xml:id="echoid-div14" type="page_commentary" level="2" n="14">
<p>
<s xml:id="echoid-s325" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s325" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588), page 108.
 Harriot's diagram is the same as Guidobaldi's except that he has used instead of upper case letters.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head41" xml:space="preserve" xml:lang="lat">
 De centro gravitatis <lb/>
 Trapezij <lb/>
 ut Archimides
 </head>
 <p>
 <s xml:id="echoid-s327" xml:space="preserve">
 Guidus Ubaldus <lb/>
 pag. 108
 </s>
 </p>
 <pb file="0535.jpg" o="268r" n="535"/>
 <pb file="0536.jpg" o="268v" n="536"/>
 <pb file="0537.jpg" o="269r" n="537"/>
 <pb file="0538.jpg" o="269v" n="538"/>
 <pb file="0539.jpg" o="270r" n="539"/>
 <pb file="0540.jpg" o="270v" n="540"/>
 <pb file="0541.jpg" o="271r" n="541"/>
 <div xml:id="echoid-div15" type="page_commentary" level="2" n="15">
<p>
<s xml:id="echoid-s328" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s328" xml:space="preserve">
 The text followed by Harriot in this and surrounding pages was Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588).
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head42" xml:space="preserve" xml:lang="lat">
 Archimedes de æquipond:
 lib. 2. pr. 9.
 <lb/>[<emph style="it">tr:
 Archimedes, De æquiponderantibus, Book 2, Proposition 9
 </emph>]<lb/>
 </head>
 <pb file="0542.jpg" o="271v" n="542"/>
 <pb file="0543.jpg" o="272r" n="543"/>
 <pb file="0544.jpg" o="272v" n="544"/>
 <pb file="0545.jpg" o="273r" n="545"/>
 <pb file="0546.jpg" o="273v" n="546"/>
 <pb file="0547.jpg" o="274r" n="547"/>
 <pb file="0548.jpg" o="274v" n="548"/>
 <pb file="0549.jpg" o="275r" n="549"/>
 <pb file="0550.jpg" o="275v" n="550"/>
 <pb file="0551.jpg" o="276r" n="551"/>
 <pb file="0552.jpg" o="276v" n="552"/>
 <pb file="0553.jpg" o="277r" n="553"/>
 <pb file="0554.jpg" o="277v" n="554"/>
 <pb file="0555.jpg" o="278r" n="555"/>
 <div xml:id="echoid-div16" type="page_commentary" level="2" n="16">
<p>
<s xml:id="echoid-s330" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s330" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588), page 179.
 Harriot's diagrams are similar to those of Guidobaldi's on page 180
 except that he has used lower case instead of upper case letters.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head43" xml:space="preserve" xml:lang="lat">
 Guidus Ubaldus <lb/>
 pag. <lb/>
 179
 </head>
 <pb file="0556.jpg" o="278v" n="556"/>
 <pb file="0557.jpg" o="279r" n="557"/>
 <pb file="0558.jpg" o="279v" n="558"/>
 <pb file="0559.jpg" o="280r" n="559"/>
 <pb file="0560.jpg" o="280v" n="560"/>
 <pb file="0561.jpg" o="281r" n="561"/>
 <div xml:id="echoid-div17" type="page_commentary" level="2" n="17">
<p>
<s xml:id="echoid-s332" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s332" xml:space="preserve">
 The text followed by Harriot in this and surrounding pages was Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588).
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head44" xml:space="preserve" xml:lang="lat">
 De æquiponderantibus
 2. lib: prop. 9
 <lb/>[<emph style="it">tr:
 De æquiponderantibus, Book 2, Proposition 9
 </emph>]<lb/>
 </head>
 <p xml:lang="lat">
 <s xml:id="echoid-s334" xml:space="preserve">
 Sint quatuor continue proportionales
 <lb/>[<emph style="it">tr:
 Let there be four continued proportionals
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s335" xml:space="preserve">
 alicui lineæ quæ
 minor est <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>e</mi></mstyle></math>
 et sit <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi><mi>o</mi></mstyle></math>
 </s>
 </p>
 <pb file="0562.jpg" o="281v" n="562"/>
 <pb file="0563.jpg" o="282r" n="563"/>
 <div xml:id="echoid-div18" type="page_commentary" level="2" n="18">
<p>
<s xml:id="echoid-s336" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s336" xml:space="preserve">
 The text followed by Harriot in this and surrounding pages was Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588).
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head45" xml:space="preserve" xml:lang="lat">
 De æquiponderantibus
 2. lib: prop. 9
 <lb/>[<emph style="it">tr:
 De æquiponderantibus, Book 2, Proposition 9
 </emph>]<lb/>
 </head>
 <pb file="0564.jpg" o="282v" n="564"/>
 <pb file="0565.jpg" o="283r" n="565"/>
 <div xml:id="echoid-div19" type="page_commentary" level="2" n="19">
<p>
<s xml:id="echoid-s338" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s338" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588), page 190.
 Harriot's diagram is the same as Guidobaldi's except that he has used instead of upper case letters.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head46" xml:space="preserve" xml:lang="lat">
 De parabola.
 </head>
 <p>
 <s xml:id="echoid-s340" xml:space="preserve">
 Guidus Ubaldus <lb/>
 pag. 190
 </s>
 </p>
 <pb file="0566.jpg" o="283v" n="566"/>
 <pb file="0567.jpg" o="284r" n="567"/>
 <div xml:id="echoid-div20" type="page_commentary" level="2" n="20">
<p>
<s xml:id="echoid-s341" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s341" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588), page 171.
 Harriot's diagram is the same as Guidobaldi's except that he has used instead of upper case letters.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head47" xml:space="preserve" xml:lang="lat">
 De centro gravitates <lb/>
 parabolæ.
 </head>
 <p>
 <s xml:id="echoid-s343" xml:space="preserve">
 vide Guidum Ubaldum <lb/>
 pag 171
 </s>
 </p>
 <pb file="0568.jpg" o="284v" n="568"/>
 <pb file="0569.jpg" o="285r" n="569"/>
 <div xml:id="echoid-div21" type="page_commentary" level="2" n="21">
<p>
<s xml:id="echoid-s344" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s344" xml:space="preserve">
 The text followed by Harriot in this and surrounding pages was Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588).
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head48" xml:space="preserve" xml:lang="lat">
 Elementæ de frustro
 pyramedis.
 <lb/>[<emph style="it">tr:
 Elements of the frustrum of a pyramid
 </emph>]<lb/>
 </head>
 <pb file="0570.jpg" o="285v" n="570"/>
 <pb file="0571.jpg" o="286r" n="571"/>
 <pb file="0572.jpg" o="286v" n="572"/>
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 <div xml:id="echoid-div22" type="page_commentary" level="2" n="22">
<p>
<s xml:id="echoid-s346" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s346" xml:space="preserve">
 The reference on this page is to Guidobaldi del Monte (Guido Ubaldi),
 <emph style="it">In duos Archimedies aequiponderantium libros paraphrasis</emph> (1588).
 The page numberlost in the binding is probably 193.
 Guidbaldi's diagram first appears on page 193 but is also repeated on pages 194, 196, 198, 200.
 Harriot's diagram is the same as Guidobaldi's except that
 he has used lower case instead of upper case letters.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head49" xml:space="preserve" xml:lang="lat">
 De centro gravitates <lb/>
 frustri parabolæ <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi><mi>e</mi><mi>c</mi></mstyle></math>
 </head>
 <p>
 <s xml:id="echoid-s348" xml:space="preserve">
 Guidus Ubaldus <lb/>
 pag. [???]
 </s>
 </p>
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 <p>
 <s xml:id="echoid-s349" xml:space="preserve">
 [Kethya]
 </s>
 </p>
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 <head xml:id="echoid-head50" xml:space="preserve" xml:lang="lat">
 Comparatio observationum vernalium <lb/>
 Simonis Bredonis et Tychonis Brahe
 </head>
 <pb file="0881.jpg" o="441r" n="881"/>
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 <head xml:id="echoid-head51" xml:space="preserve" xml:lang="lat">
 Pro terminis paschalibus (memoriter) <lb/>
 Regula mea T.H.
 <lb/>[<emph style="it">tr:
 For the end of Passover (from memory), my rule T.H.
 </emph>]<lb/>
 </head>
 <p xml:lang="lat">
 <s xml:id="echoid-s350" xml:space="preserve">
 Habito termino paschali: (qui est decimaquarta <lb/>
 luna) Dominica proxime sequens est dies <lb/>
 paschatis secundum decretum Concilij Niceni.
 <lb/>[<emph style="it">tr:
 I have the end of Passover (which is fourteenth of the lunar month); the next Sunday following is Easter,
 according to the Council of Nicea.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s351" xml:space="preserve">
 Termini paschales
 <lb/>[<emph style="it">tr:
 End of Passover
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s352" xml:space="preserve">
 Dubella cycli solis, sive litera<emph style="super">rum</emph> Dominicalium, <lb/>
 incipiens ab anno 1600. et desinens 1627 <lb/>
 recipiet iterum anno 1628. &amp;c.
 <lb/>[<emph style="it">tr:
 [¿?] of the solar cyle, or the letters of Sunday, beginning from the year 1600 and ending in 1627;
 beginning again in the year 1628, etc.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s353" xml:space="preserve">
 [???] sub-<lb/>
 scripti, sunt <lb/>
 numeri cycli <lb/>
 [???] Dionysi-<lb/>
 [???] antiqum.
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s354" xml:space="preserve">
 Vide Clavium pag. 565.
 <lb/>[<emph style="it">tr:
 See Clavius, page 565.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s355" xml:space="preserve">
 Clavius <lb/>
 pag: 589.
 <lb/>[<emph style="it">tr:
 Clavius, page 589.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0914.jpg" o="457v" n="914"/>
 <p xml:lang="lat">
 <s xml:id="echoid-s356" xml:space="preserve">
 Concilium Niceum. 323.
 <lb/>[<emph style="it">tr:
 Council of Nicea, 323.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s357" xml:space="preserve">
 Ex clavio. 168. pag.
 <lb/>[<emph style="it">tr:
 From Clavius, page 168.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0915.jpg" o="458r" n="915"/>
 <div xml:id="echoid-div23" type="page_commentary" level="2" n="23">
<p>
<s xml:id="echoid-s358" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s358" xml:space="preserve">
 The <emph style="it">Prutenicae tabulae</emph> or Prussian tables were compiled by Erasmus Reinhold
 and publsihed in 1551.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p xml:lang="lat">
 <s xml:id="echoid-s360" xml:space="preserve">
 Ex tab. prutenicis <lb/>
 in Mart: 323
 <lb/>[<emph style="it">tr:
 From the Prutenicae tabulae, for March 323.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0916.jpg" o="458v" n="916"/>
 <head xml:id="echoid-head52" xml:space="preserve" xml:lang="lat">
 Ex Clavio. pag. 109. <lb/>
 <lb/>[<emph style="it">tr:
 From Clavius, page 109.
 </emph>]<lb/>
 </head>
 <p xml:lang="lat">
 <s xml:id="echoid-s361" xml:space="preserve">
 Christe
 <lb/>[<emph style="it">tr:
 Christian
 </emph>]<lb/>
 </s>
 </p>
 <pb file="0917.jpg" o="459r" n="917"/>
 <div xml:id="echoid-div24" type="page_commentary" level="2" n="24">
<p>
<s xml:id="echoid-s362" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s362" xml:space="preserve">
 The <emph style="it">Prutenicae tabulae</emph> or Prussian tables were compiled by Erasmus Reinhold
 and publsihed in 1551.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head53" xml:space="preserve" xml:lang="lat">
 Ex Tab: prutenicis
 <lb/>[<emph style="it">tr:
 From the Prutenicae tabulae.
 </emph>]<lb/>
 </head>
 <pb file="0918.jpg" o="459v" n="918"/>
 <div xml:id="echoid-div25" type="page_commentary" level="2" n="25">
<p>
<s xml:id="echoid-s364" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s364" xml:space="preserve">
 The <emph style="it">Prutenicae tabulae</emph> or Prussian tables were compiled by Erasmus Reinhold
 and publsihed in 1551.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head54" xml:space="preserve" xml:lang="lat">
 Ex Tab: prutenicis
 <lb/>[<emph style="it">tr:
 From the Prutenicae tabulae.
 </emph>]<lb/>
 </head>
 <pb file="0919.jpg" o="460r" n="919"/>
 <pb file="0920.jpg" o="460v" n="920"/>
 <div xml:id="echoid-div26" type="page_commentary" level="2" n="26">
<p>
<s xml:id="echoid-s366" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s366" xml:space="preserve">
 The <emph style="it">Prutenicae tabulae</emph> or Prussian tables were compiled by Erasmus Reinhold
 and publsihed in 1551.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head55" xml:space="preserve" xml:lang="lat">
 Ex Tab: prutenicis
 <lb/>[<emph style="it">tr:
 From the Prutenicae tabulae.
 </emph>]<lb/>
 </head>
 <pb file="0921.jpg" o="461r" n="921"/>
 <pb file="0922.jpg" o="461v" n="922"/>
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 <div xml:id="echoid-div27" type="page_commentary" level="2" n="27">
<p>
<s xml:id="echoid-s368" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s368" xml:space="preserve">
 The <emph style="it">Prutenicae tabulae</emph> or Prussian tables were compiled by Erasmus Reinhold
 and publsihed in 1551.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head56" xml:space="preserve" xml:lang="lat">
 Ex tab: prutenicis
 <lb/>[<emph style="it">tr:
 From the Prutenicae tabulae.
 </emph>]<lb/>
 </head>
 <pb file="0925.jpg" o="463r" n="925"/>
 <pb file="0926.jpg" o="463v" n="926"/>
 <head xml:id="echoid-head57" xml:space="preserve">
 Kepl. pag. 333.
 </head>
 <pb file="0927.jpg" o="464r" n="927"/>
 <pb file="0928.jpg" o="464v" n="928"/>
 <head xml:id="echoid-head58" xml:space="preserve" xml:lang="lat">
 De Motu. Kepler. pag. 333. <lb/>
 Ægip: annus motus aphelij.
 </head>
 <pb file="0929.jpg" o="465r" n="929"/>
 <pb file="0930.jpg" o="465v" n="930"/>
 <head xml:id="echoid-head59" xml:space="preserve" xml:lang="lat">
 De Mot. Kepler. pag. 333.
 </head>
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 <head xml:id="echoid-head60" xml:space="preserve">
 1. Some remembrances of taking <emph style="super">the</emph> altitude of sonne <lb/>
 by the Astrolabe and Sea Rings.
 </head>
 <p>
 <s xml:id="echoid-s370" xml:space="preserve">
 There are three instruments used at sea for taking of altitude, the <lb/>
 Astrolabe, The ring, &amp; the staffe. <emph style="st">Seamen use the Astrolabe</emph> The <lb/>
 Astolabe hath here most ancient &amp; is used commonly &amp; only for the <lb/>
 sonne; and serveth the seamans turne most specially when the sonne is <lb/>
 [???] becuase then they <emph style="st">if the</emph> find the staffe very uncertayne. And when <lb/>
 the sea is wrought it is very hard to make any observation by it <lb/>
 also; because of his agitation &amp; unquiet guaging.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s371" xml:space="preserve">
 But howsoever when there is need you must do as well as you may. <lb/>
 and therefore when you have your Astrolabe guaging as quietly as the time <lb/>
 will permit with his side toward the sonne according to the usual order, <lb/>
 you are to fit the Judex by moving it so long up &amp; downe till the former <lb/>
 shine thourough the holes of both the sights at the same time. Or you finding by reason <lb/>
 of his agitation that the sonne will not passe iustly thourough the lower sights but be <lb/>
 <emph style="st">[???]</emph> sometme higher &amp; sometime lower. where you finde the lyst of the syghts <lb/>
 now as much over as under: then your Judex standeth as precisely as if the <lb/>
 Astrolabe had hong quietly; &amp; sheweth the true altitude of the center of the sonne.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s372" xml:space="preserve">
 But if you doubt of the true guaging of the AStrolabe, you may move <lb/>
 your Judex quickly to the same signe on the other side &amp; hold it towards the sonne. <lb/>
 If you find the sonne shine thourough as before your Astrolabe hangeth well. <lb/>
 Otherwise you are also to move <emph style="st">your</emph> <emph style="super">the</emph> Judex,
 till you have also the altitude on <lb/>
 that side. Which had, compare with the other &amp; note the difference. The half of that <lb/>
 difference added to the lesse altitude or detract from the greater; And you have <lb/>
 the altitude of the sonne as exacte as if your Astrolabe had hung truly upright.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s373" xml:space="preserve">
 The other instrument called <emph style="super">Sea Ring</emph> is of late yeares in great use with the <lb/>
 Portingalls &amp; Spaniards, The making whereof &amp; use they had about 40 <lb/>
 yeares <emph style="super">past</emph> of a country man of their owne a learned mathematician called <lb/>
 Petrus Nonius who also hath written [???] of the arte of Navigating <lb/>
 as well in Latin as in Spanish. And is only for taking the altitude of the <lb/>
 sonne as the Astrolabe. but for ease &amp; space it much excelleth it <lb/>
 as also for exactnesse. for the degrees are as large agayne as in an <lb/>
 Astrolabe of the same signes. And in the use, there is no <emph style="st">noe</emph> troublesome <lb/>
 moving up &amp; downe any Judex as in an Astrolabe; but it guaging as the <lb/>
 Astrolabe, <emph style="st">the</emph> &amp; that side which hath a small pole
 <emph style="super">be of</emph> bing holden towards <lb/>
 the sonne; the light passing <emph style="st">thh</emph> thourough
 <emph style="super">presently</emph> sheweth upon the degrees noted <lb/>
 within the ring the altitude of the sonne you desire. you are to note <lb/>
 that the middle of the light be it round or long is your true marke. <lb/>
 And if the light play by reason of his unquiet hanging; then the <lb/>
 middle of the play is the <emph style="st">th</emph> hight. This instrument is continued <lb/>
 together for your use the last viadge with the Astrolabe , And upon your <lb/>
 returne it was geven to your servant Cap. Whidden, who now <emph style="st">hath</emph> <lb/>
 also hath it redy for your use. By our last practice <emph style="st">[???]</emph> I <lb/>
 found <emph style="super">it</emph> much lighter then it ought to be, which is a fault also in all <lb/>
 the Astrolabes I have seene. By reason of your
 <emph style="st">[???]</emph> speedy <emph style="st">setting</emph> <lb/>
 setting forth it cnnot more be remedied; but is to be used as conveni-
 </s>
 </p>
 <pb file="0970.jpg" o="485v" n="970"/>
 <p>
 <s xml:id="echoid-s374" xml:space="preserve">
 niently as it may &amp; the inconvenience <emph style="st">shall supply</emph> I will <lb/>
 there fore shall be <emph style="st">supply &amp;</emph> <emph style="super">[???]</emph>
 by the staffe in the next charte.
 </s>
 </p>
 <pb file="0971.jpg" o="486r" n="971"/>
 <head xml:id="echoid-head61" xml:space="preserve">
 1. <lb/>
 2. Of taking of altitudes of the sonne or <emph style="st">starre</emph> any <lb/>
 starre by the corsse staffe with more exactness <lb/>
 then hath ben used heretofore.
 </head>
 <p>
 <s xml:id="echoid-s375" xml:space="preserve">
 The <emph style="super">crosse</emph> staffe is <emph style="st">is</emph>
 the other instrument well knowne &amp; used at sea <lb/>
 <emph style="st">but</emph> <emph style="super">and</emph> especially of starres.
 But as is <emph style="st">it used</emph> hath ben used heretofore the <lb/>
 seamasters commit great errors then sometimes they are aware of <lb/>
 from which errors if it be purged it is then of more apte &amp; certayne use <lb/>
 also for the sonne then ether the Astrolabe or Ring which I meane in <lb/>
 this chapter to shew.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s376" xml:space="preserve">
 The staffe is devided with presuppose that the end thereof in
 <emph style="st">use</emph> <emph style="super">observing</emph> should <lb/>
 stand in the center of the sight. And though that cannot be performed, yet <lb/>
 the common practiser thinketh there is little errour in putting of it <lb/>
 close under <emph style="st">the</emph> <emph style="super">that</emph> ey they behold withall:
 some <emph style="st">under</emph> on the utmost corner of <lb/>
 that ey: some on the cheke bone: <emph style="st">&amp;</emph> <emph style="super">&amp;</emph>
 some on one side of the <emph style="st">nose</emph> <emph style="st">brid</emph> bridge of the nose. <lb/>
 All which placinges to some eyes, sometimes in some manner of observinges, <lb/>
 may prove true; &amp; for the utmost corner of the ey to some
 <emph style="st">unproportioned</emph> eyes, alwayes.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s377" xml:space="preserve">
 But all <emph style="st">eyes</emph> men that have not a seat for the staffe iust agaynst the center <lb/>
 of the sight, as most men have not, must needs find a full altitude still <lb/>
 &amp; <emph style="st">especially</emph> in great altitudes the errour wilbe so
 <emph style="st">great</emph> <emph style="super">palpable</emph> as that it cannot <lb/>
 be borne withall, without artificiall correction; meaning allowance or <lb/>
 abatement, which hitherto have not ben made. And wher the seamen have <lb/>
 espied it <emph style="st">by</emph> ether by great difference from there recconings, or comparison with <lb/>
 there Astrolabe; for such great altitudes they geve over the staffe.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s378" xml:space="preserve">
 How this errour may be knowne &amp; reformed I have demonstrated &amp; taught <lb/>
 11 yeares past in my booke called Arcticon. Now only I will remember unto <lb/>
 you out of the same, that which I shewed you sometime to fore &amp; sufficient for <lb/>
 your use.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s379" xml:space="preserve">
 The best place to set the end of your staffe is the utmost corner of the seat <lb/>
 of that ey which you mind to behold withall. because that place is firme &amp; <lb/>
 certayne without offense to the eye. <lb/>
 And then how farre the end of <emph style="st">[???]</emph> <emph style="super">the</emph>
 staffe doth stand <emph style="st">from</emph> <emph style="super">behind</emph> the center of your <lb/>
 sight according as it hath ben already observed
 <emph style="st">when by yourself</emph> by a staffe <lb/>
 I have for the purpose: I have marked in a spare place of <emph style="st">these</emph> both your <lb/>
 staves nere the note of 90 degrees.
 <emph style="super">Betwixt two parallel lines.</emph>
 And the same quantity I have found <lb/>
 to be in Cap. Whiddous; in Douglas the masters; &amp; many more
 <emph style="super">[???]</emph> else, as in yours <lb/>
 &amp; mine. The which quantity hereafter for brevity &amp; order sake according to <lb/>
 the nature of the thing I call the <emph style="st">per</emph> excentricity of the staffe.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s380" xml:space="preserve">
 The use of it is this: when you have according to the usuall manner <lb/>
 taken the sight of the sonne or starre &amp; noted the place where the crosee stand <lb/>
 <emph style="st">you are to remove him further from you &amp; by such a quantity as the excentri-</emph> <lb/>
 <emph style="st">city, which you may do by a pyre of compasses</emph> you are to consider what <lb/>
 sight that wilbe which is further from the ey by the quantity of the excentricity <lb/>
 which you may knowe by the helpe of a payre of compasses, <emph style="st">[???]</emph> &amp; doth <lb/>
 alwayes make it lesse then the former. And that sight or altitude is <lb/>
 as true as if the end of your staffe did stand in the center of your sight.
 </s>
 </p>
 <pb file="0972.jpg" o="486v" n="972"/>
 <pb file="0973.jpg" o="487r" n="973"/>
 <head xml:id="echoid-head62" xml:space="preserve">
 2.
 </head>
 <p>
 <s xml:id="echoid-s381" xml:space="preserve">
 or else you may note the altitude as you find it <emph style="st">first by</emph> by the <lb/>
 place of the crosse at first; &amp; after set downe so much <emph style="st">as a</emph> in degrees <lb/>
 or minutes as <emph style="st">it is</emph>
 from the place of the crosse answereth to the <emph style="st">qua</emph> quantity <lb/>
 of the excentricity, which hereafter is called the parallaxis of the staffe; <lb/>
 to remayne to be abated with some other things as shalbe taught <lb/>
 after.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s382" xml:space="preserve">
 If to the prime end of the staffe that is to say the end which is next the <lb/>
 eye nere ioyned a peece of wood of the length of the excentricity the use <lb/>
 wold now be somewhat reddier for your owne ey without removing the crosse <lb/>
 any otherwise then in the observation, or further consideration of <emph style="super">the staffes</emph> parallaxis.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s383" xml:space="preserve">
 There is yet an other thing to be noted in observing of altitude by the <lb/>
 staffe. The seamen use comonly to leave the horison open in
 <emph style="st">the observation</emph> <emph style="super">observing</emph>, <lb/>
 which in deed were good if they know how much, but because of the uncertayne <lb/>
 coniecture they may make greater greater error then is fit to be permitted. <lb/>
 They have the practice by tradition from one to the other. The reason thereof they <lb/>
 told none in there writings, nether being demanded to they answere <lb/>
 any otherwise then that not doing so, the altitude wold not be true, nor <lb/>
 agree with the Astrolabe. Which without doubt have ben found by comparing <lb/>
 the staffe &amp; the Astrolabe to gether.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s384" xml:space="preserve">
 By truth of demonstration which I have uttered in my Arcticon, which <lb/>
 here for brevity sake I omit. I have proved that the ey being above the <lb/>
 levell of the water at sea, doth see more then half the heavens. And therefore <lb/>
 from the zenith or highest poynt above our heads to the apparent horizon is <lb/>
 more then 90 degrees. And that surplus is the greater, according as the <lb/>
 ey is above the levell of the water. And therefore any high that is <lb/>
 taken by the staffe close, because it hath respecte to the visible horizon, is <lb/>
 greater then from the true horizon of the world.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s385" xml:space="preserve">
 Yet notwithstanding it is the surest way in using the staffe to take the <lb/>
 altitude close from the Horizon, because of the uncertayen opening that the <lb/>
 Mariners leave. Which altitude without respecte of parallaxis I call <lb/>
 the Apparent altitude. And then the surplus with the parallaxis <emph style="super">is</emph> together <lb/>
 are to be abated to make the true altitude desired.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s386" xml:space="preserve">
 The quantity of which surplus I have set downe in a litle speciall <lb/>
 table here following according to the sondry distances of the ey from <lb/>
 the levell of the water.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s387" xml:space="preserve">
 As when the ey is one pase that is 5 foote from the levell of the water, then the <lb/>
 abatement is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mo>Ê¹</mo></mstyle></math>. when 2 pases then <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mo>Ê¹</mo></mstyle></math> &amp; so forth as in the table. <lb/>
 Upon the poope of a tall ship the hight of the ey comonly is 4 or 5 pases &amp; <lb/>
 then your abatement is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mo>Ê¹</mo></mstyle></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mo>Ê¹</mo></mstyle></math>. Upon the decke in the waste <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mo>Ê¹</mo></mstyle></math>. &amp; at the <lb/>
 cheynes <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>4</mn><mo>Ê¹</mo></mstyle></math> wilbe the abatement, which by triall with the load &amp; line you may <lb/>
 find.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s388" xml:space="preserve">
 And this you ought generally to note that whensoever you observe <lb/>
 with the staffe, you make good your high, iust when your ship is <lb/>
 on the top of the surge of <emph style="super">the</emph> sea, otherwise you may err.
 </s>
 </p>
 <pb file="0974.jpg" o="487v" n="974"/>
 <pb file="0975.jpg" o="488r" n="975"/>
 <head xml:id="echoid-head63" xml:space="preserve">
 3.
 </head>
 <p>
 <s xml:id="echoid-s389" xml:space="preserve">
 Hight of the <lb/>
 ey above the <lb/>
 water in <lb/>
 pases.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s390" xml:space="preserve">
 Surplus of <lb/>
 the Horizon <lb/>
 in minuts.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s391" xml:space="preserve">
 those thinges being regarded which I have specifyed concerning <lb/>
 the staffe: you may henceforward make as true observations as need to <lb/>
 be: the starre or sonne being of any hight.
 <emph style="st">Which before</emph> <emph style="super">Heretofore</emph> the
 <emph style="st">seamaster</emph> <lb/>
 <emph style="st">ship</emph> seamaster durst not to trust to the altitude of the sonne or starre <lb/>
 being 60 degrees &amp; upward. because of the difference from the Astrolabe, <lb/>
 imputing the error to the uncertenty in beholding; when as in deed they <lb/>
 know not the abatement I before spake of. the parallaxis &amp; surplus <lb/>
 &amp; that is the cause <emph style="super">also</emph>
 of there experimental opening of <emph style="super">the</emph> Horizon. <lb/>
 And although the error about 30 degrees
 <emph style="super">in stars of ordinary [???] be</emph>
 <emph style="st">be but [???] as al</emph> no great <lb/>
 matter of some <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>0</mn><mo>Ê¹</mo></mstyle></math> or there aboute, yet in the hight of 60 &amp; upward it <lb/>
 amounteth to <emph style="ul">nere a degree, &amp; more</emph>. In starres of the largest size <lb/>
 the error was the lesse; but now by reason of the former correction, the <lb/>
 longer &amp; shorter sorte will agree.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s392" xml:space="preserve">
 ffor taking the sonnes high also by the staffe I thinke good also to <lb/>
 prescribe uncertenty, &amp; to remember unto you the meanes for it <lb/>
 may be done without offense to the ey.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s393" xml:space="preserve">
 Those men that set a glasse at the end of there staffe or end of the crosse <lb/>
 do <emph style="st">[???]</emph> <emph style="super">subiect them selves to</emph>
 error. It is manifest without any further reason by a common <lb/>
 experiment of looking thorugh glasse windows, that the thinges seene <lb/>
 thourough, are seen distorted, <emph style="super">or</emph> out of there <emph style="super">true</emph> places,
 by reason of refraction <lb/>
 of the visuall beames in the <emph style="st">[???]</emph> arte of optickes demonstratively appro-<lb/>
 ved. Therefore such meanes I wish to be left.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s394" xml:space="preserve">
 The best way that I can præscribe, which some do also use, is to take the high of <lb/>
 the upper edge of the sonne, hiding the whole body with the breadth of the crosse: <lb/>
 And when you have don, to abate 16 minuts; because the diameter or breadth <lb/>
 of the <emph style="st">sonne</emph> sonne is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>3</mn><mn>2</mn><mo>Ê¹</mo></mstyle></math>. and then you have the hight of the center of the <lb/>
 sonne which you ought to have.
 </s>
 </p>
 <pb file="0976.jpg" o="488v" n="976"/>
 <pb file="0977.jpg" o="489r" n="977"/>
 <head xml:id="echoid-head64" xml:space="preserve">
 4.
 </head>
 <p>
 <s xml:id="echoid-s395" xml:space="preserve">
 And this you may do without offendinge the ey, if you be wary. In the <lb/>
 beginning of your observation first hide the sonne with the crosse &amp; so keep <lb/>
 him hidden with the orderly moving of your body &amp; hand answerable to the <lb/>
 surge of the sea, &amp; you bring him downe by litle &amp; litle till you se only the <lb/>
 edge of the sonne; &amp; if you see the other end of the crosse upon quick sight <lb/>
 close with the Horizon, it is well. Otherwise you must pull to or put from the <lb/>
 crosse untill you find that agreement.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s396" xml:space="preserve">
 The summe of all <emph style="st">is this</emph> in taking altitudes by the staffe is <lb/>
 this.
 ffirst take the altitude close from the Horizon &amp; that is called <lb/>
 the Apparent altitude.
 ffrom it abate two thinges that is the parallaxis of the staffe &amp; the <lb/>
 surplus of the Horizon. The remaynder is the true hight <lb/>
 of the starre.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s397" xml:space="preserve">
 But if you take the higher edge of the sonne you must abate <lb/>
 16 minuts more &amp; <emph style="super">then</emph> you have the true altitude desired. <lb/>
 <emph style="super">Examples of the premisses you shall have
 in the chapters of taking the altitudes of the pole.</emph> <lb/>
 <emph style="st">There is yet is yet the altitude</emph>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s398" xml:space="preserve">
 If absolute exacteness were to be required then it is yet to be addded <lb/>
 to the <emph style="super">altitude of the</emph> sonne two thinges, that is to say his parallaxis of altitude, <lb/>
 &amp; angle of refraction caused by the <emph style="st">ayre</emph> highest superficies of <lb/>
 the ayre: And to the altitude of the starre only the angle of <lb/>
 refraction. but because in your voyadge they amount not <lb/>
 ether one or both <emph style="st">not</emph> to 3 <emph style="st">[???]</emph> minuts
 <emph style="super">when most</emph>, I leave them for <lb/>
 other place &amp; time to be uttered.
 </s>
 </p>
 <pb file="0978.jpg" o="489v" n="978"/>
 <pb file="0979.jpg" o="490r" n="979"/>
 <head xml:id="echoid-head65" xml:space="preserve">
 Three sea marriadges
 </head>
 <p>
 <s xml:id="echoid-s399" xml:space="preserve">
 <emph style="st">Many marriadges do I prefer to</emph> <lb/>
 These <emph style="super">new</emph> marriadges here are made <lb/>
 one of <emph style="super">the</emph> staffe &amp; <emph style="super">sea</emph> Astrolabe <lb/>
 <emph style="st">card &amp; compasse is another</emph> <lb/>
 <emph style="st">one is siter tother a brother</emph> <lb/>
 Of <emph style="super">the</emph> sonne &amp; starres is an other <lb/>
 Which now agree like sister &amp; brother. <lb/>
 And charde &amp; compasse which now at late <lb/>
 <emph style="st">May</emph> Will now agree like &amp; master &amp; mate. <lb/>
 If you use them well in <emph style="super">this</emph> your iourney <lb/>
 They will <emph style="st">make you a letter of</emph>
 <emph style="super">be the King of Spaynes</emph> Atorney <lb/>
 To <emph style="st">take up</emph> <emph style="super">bring you to</emph> silver &amp; Indian gold <lb/>
 Which will keep you <emph style="super">in age</emph> from hunger &amp; cold <lb/>
 God speed you well &amp; send you fayre wether <lb/>
 And that agayne we may meet to gether.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s400" xml:space="preserve">
 to teach. And Nonius himself if he had been an observer &amp; practiser of the [???] <lb/>
 <emph style="super">ether at sea or land</emph> wold quickly have found many incombrances &amp; inconveniences <lb/>
 besides teh difficultyes &amp; insufficientyes in observinge the meanes whence <lb/>
 the conclusions are sought.
 </s>
 </p>
 <pb file="0980.jpg" o="490v" n="980"/>
 <head xml:id="echoid-head66" xml:space="preserve">
 A table of the sonnes orientall and occidentall <lb/>
 Amplitude:
 </head>
 <p>
 <s xml:id="echoid-s401" xml:space="preserve">
 That is <emph style="st">to say</emph>: How much the sonne which riseth from <lb/>
 true east &amp; west, <emph style="super">in degrees &amp; minuts</emph>
 <emph style="st">in any observaiton of the pole under</emph> <lb/>
 <emph style="st">55 degrees &amp;</emph> acccording to any
 <emph style="super">degrees of his</emph> declination &amp; for any <lb/>
 observation of the pole to 54 degrees.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s402" xml:space="preserve">
 Whose use is speciall for to find the variation of <lb/>
 the compasse.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s403" xml:space="preserve">
 The figures that are written with red inke are the differences <lb/>
 in minutes from the next two amplitudes they stand betweene; <lb/>
 under &amp; over, or on ether side.
 </s>
 </p>
 <head xml:id="echoid-head67" xml:space="preserve">
 Here followeth A Table called <lb/>
 The Sonnes Regiment.
 </head>
 <p>
 <s xml:id="echoid-s404" xml:space="preserve">
 Conteyning the declination of the sonne for every <lb/>
 day of any month without a minute error untill the yeare <lb/>
 of <emph style="super">Christe</emph> 1620. Made &amp; calculated
 <emph style="st">for the [???]</emph> perticulerly <lb/>
 for the Meridian of the west of England, according to <lb/>
 late precise observations. And by proportion will serve <lb/>
 for all the worlde.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s405" xml:space="preserve">
 The figures written with red ink, the minutes of difference <lb/>
 of one dayes declination from another: or how much the sonne <lb/>
 moveth in declination in the space of 24 houres.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s406" xml:space="preserve">
 Degrees of the poles Elevation.
 </s>
 </p>
 <pb file="0981.jpg" o="491r" n="981"/>
 <head xml:id="echoid-head68" xml:space="preserve">
 How to know your course to sayle to any place assigned; &amp; in sayling <lb/>
 to <emph style="st">keep to</emph> make true recconing
 <emph style="super">to find</emph> where you are at any time; &amp; <lb/>
 how farre from any place desired.
 </head>
 <p>
 <s xml:id="echoid-s407" xml:space="preserve">
 In the art of Navigation it is præsupposed that <emph style="super">all</emph> plottes &amp; sea chartes have <lb/>
 the costes, Islands <emph style="super">portes</emph> and other
 <emph style="super">such</emph> places in them described &amp; situated proportionally <lb/>
 and answerable to those <emph style="st">thinges</emph> <emph style="super">places</emph> they represent.
 <emph style="st">as well for magnitude</emph> <lb/>
 <emph style="st">&amp; forme as true course &amp; distance</emph>
 as well for true course &amp; distance <lb/>
 as <emph style="super">forme &amp;</emph> magnitude <emph style="st"/> &amp; forme.
 So that those places that have <lb/>
 one latitude or altitude of the pole, stand in a true east &amp; west <lb/>
 course; &amp; those that <emph style="st">are in</emph> <emph style="super">have</emph> one meridian,
 stand in a <emph style="super">true</emph> North &amp; south <lb/>
 course; &amp; so per consequence all the <emph style="st">mid</emph> other meane courses <lb/>
 in the chartes signified, must be understoode to be according &amp; <lb/>
 answerable to the true <emph style="super">ppoyntes of the</emph> compasse, <lb/>
 &amp; not to <emph style="super">those of</emph> the common or any compasse <lb/>
 else that have variation. But if the compasse vary; by recconing <lb/>
 in sayling, allowance or abatement is to be made that the true <lb/>
 course may be knowne; else shall you be sure to misse your poste <lb/>
 or place desired.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s408" xml:space="preserve">
 And if in <emph style="super">making of</emph> chartes such respects be not had; but that places be <lb/>
 set downe by the common compasse, or other compasses as <lb/>
 they be found, <emph style="st">then where the compasse [???]</emph> <lb/>
 <emph style="super">without</emph> respect to there variation; then where the compasses do <lb/>
 vary, there do places stand out of there true latitudes
 <emph style="super">besides there true distances</emph>; &amp; <emph style="st">as</emph> in <lb/>
 navigation, [???] elevations of the poles for correcting your <lb/>
 dead reckonings would stand you in no steed. Neither could <lb/>
 any navigaton be performed, but only on such courses as <lb/>
 the planes were first found by. For upon other courses <emph style="st">accordi</emph> <lb/>
 according as <emph style="st">they are fur</emph> your deviation is greater or lesse <lb/>
 <emph style="st">so good be your [???]</emph> so much should you sayle of your <lb/>
 purpose wether you considered <emph style="st">but</emph> therein variation or not; <lb/>
 if the compasse in <emph style="st">those</emph> <emph style="super">such</emph> courses
 have a greater or lesse <lb/>
 variation then <emph style="super">before</emph> in the courses originall.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s409" xml:space="preserve">
 And although <emph style="super">no</emph> chartes have
 <emph style="st">[???]</emph> those planes so truly situa-<lb/>
 ted as they aought according to arte
 </s>
 </p>
 <pb file="0982.jpg" o="491v" n="982"/>
 <pb file="0983.jpg" o="492r" n="983"/>
 <pb file="0984.jpg" o="492v" n="984"/>
 <pb file="0985.jpg" o="493r" n="985"/>
 <pb file="0986.jpg" o="493v" n="986"/>
 <pb file="0987.jpg" o="494r" n="987"/>
 <head xml:id="echoid-head69" xml:space="preserve" xml:lang="lat">
 Comparationes Judeaum supplementum (vide publ: Midleburg:)
 </head>
 <pb file="0988.jpg" o="494v" n="988"/>
 <pb file="0989.jpg" o="495r" n="989"/>
 <head xml:id="echoid-head70" xml:space="preserve" xml:lang="lat">
 De motu solis. diagramma in Charta de <lb/>
 Anomalijs
 <lb/>[<emph style="it">tr:
 On the motion of the sun. Diagram in sheet on De anomalijs.
 </emph>]<lb/>
 </head>
 <pb file="0990.jpg" o="495v" n="990"/>
 <pb file="0991.jpg" o="496r" n="991"/>
 <pb file="0992.jpg" o="496v" n="992"/>
 <pb file="0993.jpg" o="497r" n="993"/>
 <p xml:lang="lat">
 <s xml:id="echoid-s410" xml:space="preserve">
 Dionysios Exigius, <lb/>
 abbas Romanos <lb/>
 paschales cyclos <lb/>
 orditur &amp;c. <lb/>
 Bunting.
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s411" xml:space="preserve">
 Era Dioclesiani <lb/>
 Christm. 433.p <lb/>
 Bunting.
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s412" xml:space="preserve">
 Anni Dionysiani: <lb/>
 Cycl. Christi.
 </s>
 </p>
 <pb file="0994.jpg" o="497v" n="994"/>
 <pb file="0995.jpg" o="498r" n="995"/>
 <pb file="0996.jpg" o="498v" n="996"/>
 <pb file="0997.jpg" o="499r" n="997"/>
 <pb file="0998.jpg" o="499v" n="998"/>
 <pb file="0999.jpg" o="500r" n="999"/>
 <pb file="1000.jpg" o="500v" n="1000"/>
 <pb file="1001.jpg" o="501r" n="1001"/>
 <pb file="1002.jpg" o="501v" n="1002"/>
 <pb file="1003.jpg" o="502r" n="1003"/>
 <pb file="1004.jpg" o="502v" n="1004"/>
 <pb file="1005.jpg" o="503r" n="1005"/>
 <pb file="1006.jpg" o="503v" n="1006"/>
 <pb file="1007.jpg" o="504r" n="1007"/>
 <pb file="1008.jpg" o="504v" n="1008"/>
 <pb file="1009.jpg" o="505r" n="1009"/>
 <pb file="1010.jpg" o="505v" n="1010"/>
 <pb file="1011.jpg" o="506r" n="1011"/>
 <pb file="1012.jpg" o="506v" n="1012"/>
 <pb file="1013.jpg" o="507r" n="1013"/>
 <head xml:id="echoid-head71" xml:space="preserve">
 Josephus
 </head>
 <pb file="1014.jpg" o="507v" n="1014"/>
 <pb file="1015.jpg" o="508r" n="1015"/>
 <pb file="1016.jpg" o="508v" n="1016"/>
 <pb file="1017.jpg" o="509r" n="1017"/>
 <p>
 <s xml:id="echoid-s413" xml:space="preserve">
 Adam. <lb/>
 Seth. <lb/>
 Enos. <lb/>
 Cainan. <lb/>
 Maleteel. <lb/>
 Jared. <lb/>
 Enoch. <lb/>
 Mathusala. <lb/>
 Lamech. <lb/>
 Noe. <lb/>
 Sem.
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s414" xml:space="preserve">
 Anno 600 Noe et <lb/>
 98. Sem. principiæ. <lb/>
 diluvij.
 <lb/>[<emph style="it">tr:
 The 600th year of Noah and 98th of Sem at the begninning of the flood.
 </emph>]<lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s415" xml:space="preserve">
 Arphaxad. <lb/>
 Cainan. <lb/>
 Sala. <lb/>
 Heber. <lb/>
 Phalag. <lb/>
 Rhagau. <lb/>
 Seruch. <lb/>
 Nachor. <lb/>
 Tharra. <lb/>
 Abram.
 </s>
 </p>
 <pb file="1018.jpg" o="509v" n="1018"/>
 <pb file="1019.jpg" o="510r" n="1019"/>
 <p>
 <s xml:id="echoid-s416" xml:space="preserve">
 Adam. <lb/>
 Scheth. <lb/>
 Enosch. <lb/>
 Kenan. <lb/>
 Mahalateel. <lb/>
 Jered. <lb/>
 Chanoc. <lb/>
 Methuschelach. <lb/>
 Lemec. <lb/>
 Noach. <lb/>
 Schem.
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s417" xml:space="preserve">
 Diluuij <lb/>
 principia
 <lb/>[<emph style="it">tr:
 Beginning of the flood
 </emph>]<lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s418" xml:space="preserve">
 Arpachshad. <lb/>
 Schelach. <lb/>
 Heber. <lb/>
 Peleg. <lb/>
 Rehu. <lb/>
 Scherug. <lb/>
 Nachor. <lb/>
 Theruc. <lb/>
 Abram.
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s419" xml:space="preserve">
 Anno 70 Abrami <lb/>
 Incipiunt: 430.
 <lb/>[<emph style="it">tr:
 The 70 years of Abraham begin in 430.
 </emph>]<lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s420" xml:space="preserve">
 Jitzchak <lb/>
 Jahakob <lb/>
 Joseph
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s421" xml:space="preserve">
 Mors Jo.
 <lb/>[<emph style="it">tr:
 Death of Joseph
 </emph>]<lb/>
 </s>
 </p>
 <pb file="1020.jpg" o="510v" n="1020"/>
 <pb file="1021.jpg" o="511r" n="1021"/>
 <pb file="1022.jpg" o="511v" n="1022"/>
 <pb file="1023.jpg" o="512r" n="1023"/>
 <p>
 <s xml:id="echoid-s422" xml:space="preserve">
 1. fathers father <lb/>
 3. mothers father <lb/>
 2. fathers mother <lb/>
 4. mothers mother <lb/>
 fathers fathers wife <lb/>
 fathers mothers husband <lb/>
 mothers fathers wife <lb/>
 mothers mothers husband <lb/>
 wives fathers father <lb/>
 wives fathers mother <lb/>
 wives mothers father <lb/>
 wives mothers mother <lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s423" xml:space="preserve">
 father <lb/>
 mother <lb/>
 fathers wife <lb/>
 mothers husband <lb/>
 wives father <lb/>
 wives mother
 </s>
 </p>
 <p>
 <s xml:id="echoid-s424" xml:space="preserve">
 man <lb/>
 wife <lb/>
 woman <lb/>
 husband
 </s>
 </p>
 <pb file="1024.jpg" o="512v" n="1024"/>
 <pb file="1025.jpg" o="513r" n="1025"/>
 <pb file="1026.jpg" o="513v" n="1026"/>
 <pb file="1027.jpg" o="514r" n="1027"/>
 <p>
 <s xml:id="echoid-s425" xml:space="preserve">
 A man shall <lb/>
 not marry <lb/>
 his.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s426" xml:space="preserve">
 mother <lb/>
 fathers wife <lb/>
 wives mother.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s427" xml:space="preserve">
 fathers daughter. sister. <lb/>
 mothers daughter. sister.
 </s>
 </p>
 <pb file="1028.jpg" o="514v" n="1028"/>
 <pb file="1029.jpg" o="515r" n="1029"/>
 <div xml:id="echoid-div28" type="page_commentary" level="2" n="28">
<p>
<s xml:id="echoid-s428" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s428" xml:space="preserve">
 The table begins with males aged 20 and 0 years, females aged 39 and 19 years.
 Each person bears a child (of the same gender) at the age of 20 and dies at the age of 40.
 In this way there are always four people alive at any one time.
 Their ages are shown in successive rows of the table.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p lang="lat">
 <s xml:id="echoid-s430" xml:space="preserve">
 Mares. Fem.
 <lb/>[<emph style="it">tr:
 Men. Women.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="1030.jpg" o="515v" n="1030"/>
 <div xml:id="echoid-div29" type="page_commentary" level="2" n="29">
<p>
<s xml:id="echoid-s431" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s431" xml:space="preserve">
 The table to which the heading refers is in Add MS 6788, f. 515.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head72" xml:space="preserve">
 Quomodo idem numerus personarum æqualiter possit <lb/>
 conservari, in generationibus suis.
 <lb/>[<emph style="it">tr:
 How the same number of persons may be conserved uniformly in the process of procreating.
 </emph>]<lb/>
 </head>
 <p>
 <s xml:id="echoid-s433" xml:space="preserve">
 numerus annorum <lb/>
 quæsitus, est, 40.
 <lb/>[<emph style="it">tr:
 number of years studied is 40.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="1031.jpg" o="516r" n="1031"/>
 <pb file="1032.jpg" o="516v" n="1032"/>
 <head xml:id="echoid-head73" xml:space="preserve">
 Genesis 10.
 </head>
 <pb file="1033.jpg" o="517r" n="1033"/>
 <pb file="1034.jpg" o="517v" n="1034"/>
 <div xml:id="echoid-div30" type="page_commentary" level="2" n="30">
<p>
<s xml:id="echoid-s434" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s434" xml:space="preserve">
 A small table on the right shows the number of men increasing by a factor of five every 30 years.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p>
 <s xml:id="echoid-s436" xml:space="preserve">
 men.
 </s>
 <lb/>
 <s xml:id="echoid-s437" xml:space="preserve">
 yeres
 </s>
 </p>
 <p>
 <s xml:id="echoid-s438" xml:space="preserve">
 men.
 </s>
 <lb/>
 <s xml:id="echoid-s439" xml:space="preserve">
 women.
 </s>
 </p>
 <pb file="1035.jpg" o="518r" n="1035"/>
 <pb file="1036.jpg" o="518v" n="1036"/>
 <div xml:id="echoid-div31" type="page_commentary" level="2" n="31">
<p>
<s xml:id="echoid-s440" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s440" xml:space="preserve">
 Conversions between solar, Julian, and Egyptian years.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p lang="lat">
 <s xml:id="echoid-s442">
 Annus: 365d. 5h. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>9</mn></mrow><mrow><mn>1</mn><mn>1</mn></mrow></mfrac></mstyle></math>
 <lb/>[<emph style="it">tr:
 A year: 365 days <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>5</mn><mfrac><mrow><mn>9</mn></mrow><mrow><mn>1</mn><mn>1</mn></mrow></mfrac></mstyle></math> hours
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s443">
 Hoc est:
 <lb/>[<emph style="it">tr:
 That is:
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s444">
 Annus Julianus: <lb/>
 365d 6h
 <lb/>[<emph style="it">tr:
 Julian year: 365 days 6 hours
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s445">
 Annus ægyptius. <lb/>
 365d
 <lb/>[<emph style="it">tr:
 Egyptian year: 365 days
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s446">
 Ergo: 48,212. anni Juliani = 48,213. anni solares
 <lb/>[<emph style="it">tr:
 Therefore: 48212 Julian years = 48213 solar years
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s447">
 Ergo: 12,053. anni Ægyptij = 12,045. anni solares
 <lb/>[<emph style="it">tr:
 Therefore: 12053 Egyptian years = 12045 solar years
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s448">
 (minimi termini)
 <lb/>[<emph style="it">tr:
 (in least terms)
 </emph>]<lb/>
 </s>
 </p>
 <pb file="1037.jpg" o="519r" n="1037"/>
 <pb file="1038.jpg" o="519v" n="1038"/>
 <pb file="1039.jpg" o="520r" n="1039"/>
 <pb file="1040.jpg" o="520v" n="1040"/>
 <pb file="1041.jpg" o="521r" n="1041"/>
 <pb file="1042.jpg" o="521v" n="1042"/>
 <pb file="1043.jpg" o="522r" n="1043"/>
 <pb file="1044.jpg" o="522v" n="1044"/>
 <pb file="1045.jpg" o="523r" n="1045"/>
 <pb file="1046.jpg" o="523v" n="1046"/>
 <pb file="1047.jpg" o="524r" n="1047"/>
 <pb file="1048.jpg" o="524v" n="1048"/>
 <pb file="1049.jpg" o="525r" n="1049"/>
 <pb file="1050.jpg" o="525v" n="1050"/>
 <pb file="1051.jpg" o="526r" n="1051"/>
 <pb file="1052.jpg" o="526v" n="1052"/>
 <pb file="1053.jpg" o="527r" n="1053"/>
 <pb file="1054.jpg" o="527v" n="1054"/>
 <pb file="1055.jpg" o="528r" n="1055"/>
 <pb file="1056.jpg" o="528v" n="1056"/>
 <pb file="1057.jpg" o="529r" n="1057"/>
 <pb file="1058.jpg" o="529v" n="1058"/>
 <pb file="1059.jpg" o="530r" n="1059"/>
 <pb file="1060.jpg" o="530v" n="1060"/>
 <pb file="1061.jpg" o="531r" n="1061"/>
 <pb file="1062.jpg" o="531v" n="1062"/>
 <pb file="1063.jpg" o="532r" n="1063"/>
 <pb file="1064.jpg" o="532v" n="1064"/>
 <pb file="1065.jpg" o="533r" n="1065"/>
 <pb file="1066.jpg" o="533v" n="1066"/>
 <pb file="1067.jpg" o="534r" n="1067"/>
 <pb file="1068.jpg" o="534v" n="1068"/>
 <pb file="1069.jpg" o="535r" n="1069"/>
 <pb file="1070.jpg" o="535v" n="1070"/>
 <pb file="1071.jpg" o="536r" n="1071"/>
 <div xml:id="echoid-div32" type="page_commentary" level="2" n="32">
<p>
<s xml:id="echoid-s449" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s449" xml:space="preserve">
 This is a key page in which Harriot sets out his calculations of population
 under the conditions set out in Add MS 6782, f. 31v, and Add MS 6788, f. 537,
 namely, that each male–female pair gives birth to a child each year, alternately male and female,
 and that those children begin to reproduce after 20 years.
 All survive indefinitely. <lb/>
 Harriot gives no verbal explanation of the calculations,
 and there are only a few surviving rough diagrams like that in Add MS 6788, f. 554. <lb/>
 Take the calculations for 30 years as an example.
 Now there are 15 males born to the original couple; these are marked 'a'.
 Meanwhile, the 5 oldest males have begun to reproduce, giving birth to 5 + 4 + 3 + 2 + 1 = 15 male children.
 This sum can be calculated by the rule <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>2</mn></mrow></mfrac></mstyle></math>, giving the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th triangular number.
 This calculation is marked 'b'. <lb/>
 The calculations for subsequent years follow a similar pattern.
 At 50 years, the second generation, measured by triangular numbers, has begun to reproduce.
 The third generation is therefore measured by sums of triangular numbers,
 that is, pyramidal numbers, calculated by the rule <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>6</mn></mrow></mfrac></mstyle></math>.
 This calculations is marked 'c'. <lb/>
 And so on.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p lang="lat">
 <s xml:id="echoid-s451" xml:space="preserve">
 progenies Maris et feminæ ad annos. 100
 <lb/>[<emph style="it">tr:
 the offspring of men and women for 100 years
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s452" xml:space="preserve">
 Mares
 <lb/>[<emph style="it">tr:
 In years. Men.
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s453" xml:space="preserve">
 feminæ
 <lb/>[<emph style="it">tr:
 women
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s454" xml:space="preserve">
 personæ
 <lb/>[<emph style="it">tr:
 persons
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s455" xml:space="preserve">
 a tribus <lb/>
 maribus <lb/>
 et ??
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s456" xml:space="preserve">
 Ad annos. 80.
 <lb/>[<emph style="it">tr:
 For 80 years.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s457" xml:space="preserve">
 [Etc.]
 </s>
 </p>
 <pb file="1072.jpg" o="536v" n="1072"/>
 <pb file="1073.jpg" o="537r" n="1073"/>
 <div xml:id="echoid-div33" type="page_commentary" level="2" n="33">
<p>
<s xml:id="echoid-s458" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s458" xml:space="preserve">
 This folio continues the calculations shown on Add MS 6788, f. 536, now up to 240 years.
 The suppositions underlying the model are set out in three numbered points. <lb/>
 This page appears to be the '<foreign lang="lat">charta</foreign> c'
 referred to in Add MS 6782, f. 31v, where the same suppositions are given and the results are summarized.
 Unfortunately, Harriot's lettering of the page has been lost in the binding.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p>
 <s xml:id="echoid-s460" xml:space="preserve">
 The issue from one man &amp; <lb/>one woman in 240 yeres.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s461" xml:space="preserve">
 Supposing:
 </s>
 <lb/>
 <s xml:id="echoid-s462" xml:space="preserve">
 [1]. That the first mand &amp; woman <lb/>
 have a child every yeare, one <lb/>
 yeare male &amp; another yere female.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s463" xml:space="preserve">
 2. That the children when they are <lb/>
 20 yeres old &amp; upward do also <lb/>
 every <emph style="super">yere</emph> beget a child, one yere <lb/>
 male &amp; an other yere female.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s464" xml:space="preserve">
 3. That all are living at the end <lb/>
 of 240 yeres.
 </s>
 </p>
 <p>
 [<emph style="it">Note:
 After adding the number of males and females, Harriot multiplies the total population by 3.
 This suggests that his calculations are related to the biblical chronology of some of the
 surrounding pages, the three pairs being the three sons of Noah (Shem, Ham, Japheth)
 and their wives.
  </emph>]<lb/>
 <s xml:id="echoid-s465" xml:space="preserve">
 In 240 <lb/>
 yeres.
 </s>
 <lb/>
 <s xml:id="echoid-s466" xml:space="preserve">
 males. 5,034,303,437.
 </s>
 <lb/>
 <s xml:id="echoid-s467" xml:space="preserve">
 females. 5,034,303,437.
 </s>
 <lb/>
 <s xml:id="echoid-s468" xml:space="preserve">
 persons. 10,068,606,874.
 </s>
 </p>
 <pb file="1074.jpg" o="537v" n="1074"/>
 <pb file="1075.jpg" o="538r" n="1075"/>
 <pb file="1076.jpg" o="538v" n="1076"/>
 <pb file="1077.jpg" o="539r" n="1077"/>
 <pb file="1078.jpg" o="539v" n="1078"/>
 <pb file="1079.jpg" o="540r" n="1079"/>
 <div xml:id="echoid-div34" type="page_commentary" level="2" n="34">
<p>
<s xml:id="echoid-s469" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s469" xml:space="preserve">
 This folio continues the calculations shown on Add MS 6788, f. 536,
 now for 260 years. <lb/>
 This page may be the '<foreign lang="lat">charta</foreign> db'
 referred to in Add MS 6782, f. 31v.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1080.jpg" o="540v" n="1080"/>
 <pb file="1081.jpg" o="541r" n="1081"/>
 <div xml:id="echoid-div35" type="page_commentary" level="2" n="35">
<p>
<s xml:id="echoid-s471" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s471" xml:space="preserve">
 This folio continues the calculations shown on Add MS 6788, f. 536,
 now for 340 years. <lb/>
 This page appears to be the '<foreign lang="lat">charta</foreign> db'
 referred to in Add MS 6782, f. 31v.
 Unfortunately, Harriot's lettering of the page is obscured in the binding.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1082.jpg" o="541v" n="1082"/>
 <pb file="1083.jpg" o="542r" n="1083"/>
 <div xml:id="echoid-div36" type="page_commentary" level="2" n="36">
<p>
<s xml:id="echoid-s473" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s473" xml:space="preserve">
 This folio summarizes the calculations on Add MS 6788, f. 536 and f. 543v. <lb/>
 A second table in the lower half of the page shows the result of doubling the birth rate
 from one male every two years to one male every year.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <head xml:id="echoid-head74" xml:space="preserve" lang="lat">
 Progenies maris et feminæ. tota [???]
 </head>
 <p lang="lat">
 <s xml:id="echoid-s475" xml:space="preserve">
 In <lb/>
 Annis. personæ
 <lb/>[<emph style="it">tr:
 In years. Persons.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s476" xml:space="preserve">
 ponitur: <lb/>
 Quod annis quibuslibet binis <lb/>
 mares singuli gignunt marem <lb/>
 et feminam. Si agunt annos <lb/>
 viginti et ultra.
 <lb/>[<emph style="it">tr:
 supposed: <lb/>
 That every two years each man brings forth a male and a female. If they survive to twenty and more.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s477" xml:space="preserve">
 Hic ponitur: <lb/>
 Quilibet mas agens <lb/>
 anno 2 &amp; ultra: <lb/>
 singulis annis gignit <lb/>
 marem &amp; feminam
 <lb/>[<emph style="it">tr:
 Here it is supposed: <lb/>
 Any man surviving 20 years and more: each year brings forth a male and a female.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s478" xml:space="preserve">
 In annis. personæ. mares. mares.
 <lb/>[<emph style="it">tr:
 In years. persons. males. males.
 </emph>]<lb/>
 </s>
 </p>
 <pb file="1084.jpg" o="542v" n="1084"/>
 <pb file="1085.jpg" o="543r" n="1085"/>
 <div xml:id="echoid-div37" type="page_commentary" level="2" n="37">
<p>
<s xml:id="echoid-s479" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s479" xml:space="preserve">
 This folio shows a shorter calculation (or rough work) for the sequences shown in Add MS 6788, f. 555
 of males in the fourth and fifth generations. <lb/>
 The left hand column begins with a population of 220,
 from which the sequence 1, 3, 6, ..., 63, 69, 73 is successively subtracted,
 while the sequence 63, 69, 73, 75, 75, 73, .... 15, 10, 6 is successively added,
 giving rise to the sequence 220, 282, 348, ..., 660, 670, 660, .... <lb/>
 The right hand column begins with a population of 715,
 from which the sequence 1, 4, 10, ..., 348, 415, 450 is successively subtracted,
 while the sequence 282, 348, 415, ..., 663, 660, ... is successively added,
 giving rise to the sequence 715, 996, 1340, .... <lb/>
 Harriot makes an error in this column, adding 633 instead of 670 after subtracting 165,
 but this is rectified in the rightmost column.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1086.jpg" o="543v" n="1086"/>
 <div xml:id="echoid-div38" type="page_commentary" level="2" n="38">
<p>
<s xml:id="echoid-s481" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s481" xml:space="preserve">
 This folio continues the calculations shown on Add MS 6788, f. 536,
 now for 70, 90, 102, 110, and 120 years. <lb/>
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p lang="lat">
 <s xml:id="echoid-s483" xml:space="preserve">
 progenies maris et feminæ. ad anno 102 <lb/>
 tot sunt a Diluvio ad Peleg.
 <lb/>[<emph style="it">tr:
 the offspring of a man and woman for 102 years, as many as from the flood to P
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s484" xml:space="preserve">
 mares.
 <lb/>[<emph style="it">tr:
 men
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s485" xml:space="preserve">
 feminæ
 <lb/>[<emph style="it">tr:
 women
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s486" xml:space="preserve">
 personæ
 <lb/>[<emph style="it">tr:
 persons
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s487" xml:space="preserve">
 Ad annos. 120.
 <lb/>[<emph style="it">tr:
 For 80 years.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s488" xml:space="preserve">
 ad annos. 90.
 <lb/>[<emph style="it">tr:
 For 80 years.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s489" xml:space="preserve">
 Ad annos. 110.
 <lb/>[<emph style="it">tr:
 For 80 years.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s490" xml:space="preserve">
 Ad annos. 70.
 <lb/>[<emph style="it">tr:
 For 80 years.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s491" xml:space="preserve">
 in alia charta
 <lb/>[<emph style="it">tr:
 on the other sheet
 </emph>]<lb/>
 </s>
 </p>
 <pb file="1087.jpg" o="544r" n="1087"/>
 <pb file="1088.jpg" o="544v" n="1088"/>
 <pb file="1089.jpg" o="545r" n="1089"/>
 <div xml:id="echoid-div39" type="page_commentary" level="2" n="39">
<p>
<s xml:id="echoid-s492" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s492" xml:space="preserve">
 This folios takes up the calculation suggested in Add MS 6788, f. 554.
 The numbered list across the top of the sheet shows the numbers of male children for three generations,
 assuming that each male fathers a male child every two years for 20 years. <lb/>
 The first ten entries are the offspring of a single male. <lb/>
 The next twenty entries show the number of males in the second generation,
 numbered by the sequence 1, 2, 3, 4, ..., 8, 9, 10, 9, 8, ..., 4, 3, 2, 1. <lb/>
 The enxt twenty entries who the number of males in the third generation,
 numbered by the sequence 1, 3, 6, 10, ..., 55, 62, 69, 73, 75, 75, 73, ...
 (see also Add MS 6788, f. 544).<lb/>
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1090.jpg" o="545v" n="1090"/>
 <div xml:id="echoid-div40" type="page_commentary" level="2" n="40">
<p>
<s xml:id="echoid-s494" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s494" xml:space="preserve">
 Calculations for the table in the lower half of Add MS 6788, f. 542.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p lang="lat">
 <s xml:id="echoid-s496" xml:space="preserve">
 ponatur hic <lb/>
 genetur singuli annus
 <lb/>[<emph style="it">tr:
 supposed here born each year
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s497" xml:space="preserve">
 In annis. Mares
 <lb/>[<emph style="it">tr:
 In years. Men.
 </emph>]<lb/>
 </s>
 </p>
 <p lang="lat">
 <s xml:id="echoid-s498" xml:space="preserve">
 Summa
 <lb/>[<emph style="it">tr:
 Sum
 </emph>]<lb/>
 </s>
 </p>
 <pb file="1091.jpg" o="546r" n="1091"/>
 <div xml:id="echoid-div41" type="page_commentary" level="2" n="41">
<p>
<s xml:id="echoid-s499" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s499" xml:space="preserve">
 The left hand column begins with a population of 2002,
 from which the sequence 1, 5, 15, ..., 4335, 4840 is successively subtracted,
 while the sequence 996, 1340, ..., 4840, 4335 is successively added,
 giving rise to the sequence 2002, 2997, 4332, .... <lb/>
 The right hand column begins with a population of 5005,
 from which the sequence 1, 6, 21, ...,1287, 2002 is successively subtracted,
 while the sequence 2997, 4332,..., 25927, 30492 is successively added,
 giving rise to the sequence 5005, 8001, 12327, ....
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1092.jpg" o="546v" n="1092"/>
 <pb file="1093.jpg" o="547r" n="1093"/>
 <pb file="1094.jpg" o="547v" n="1094"/>
 <div xml:id="echoid-div42" type="page_commentary" level="2" n="42">
<p>
<s xml:id="echoid-s501" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s501" xml:space="preserve">
 This folio is a rougher version of Add MS 6782, f. 31. <lb/>
 At the top there is an alphabetic mnemonic for the first 8 digits of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>π</mi></mstyle></math>.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p xml:lang="lat">
 <s xml:id="echoid-s503" xml:space="preserve">
 cadaeibf <lb/>
 31415926
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s504" xml:space="preserve">
 35,408,794,100,000 = circulus = <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> superficies terræ et aquæ.
 <lb/>[<emph style="it">tr:
 a plane circle equal 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> the surface of land and water.
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s505" xml:space="preserve">
 141,635,176,400,000 =
 <reg norm="superficies" type="abbr">superf:</reg> maris et terræ.
 <lb/>[<emph style="it">tr:
 The surface of sea and land. <lb/>
 </emph>]<lb/>
 </s>
 <lb/>
 <s xml:id="echoid-s506" xml:space="preserve">
 70,817,588,200,000 =
 <reg norm="superficies" type="abbr">superf:</reg> terræ
 <lb/>[<emph style="it">tr:
 The surface of the land.
 </emph>]<lb/>
 </s>
 </p>
 <p>
 <s xml:id="echoid-s507" xml:space="preserve">
 <sc>
 Saxton's map: Christopher Saxton's atlas of the counties of England and Wales, published around 1580.
 </sc>
 49,987 miles square in England
 (<foreign xml:lang="lat">ut alibi</foreign> by Saxtons map) <lb/>
 after 60 miles to a degree <lb/>
 including rivers &amp; all wastes.
 </s>
 <lb/>
 <s xml:id="echoid-s508" xml:space="preserve">
 It lacketh but 13 miles of 50,000.
 </s>
 </p>
 <p>
 <s xml:id="echoid-s509" xml:space="preserve">
 50,000 miles. 5,000,000 persons. <lb/>
 1 mile. 100 persons. 70,817,588 miles. 7,081,758,800. persons (in the earth).
 </s>
 </p>
 <p>
  <s xml:id="echoid-s510" xml:space="preserve">[<emph style="it">Note:
 This subcalculation gives 10,000 square pases per person,
 converted next to 250,000 square feet, then to 5 and 8/11 acres.
 </emph>]</s><lb/>
 <s xml:id="echoid-s511" xml:space="preserve">
 1,000,000 pp. 100 persons. <lb/>
 10000 pp. 1 person. <lb/>
 10000 [square pases] = <lb/>
 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.
 (note rivers &amp; waste included <lb/>
 as above.)
 </s>
 </p>
 <pb file="1095.jpg" o="548r" n="1095"/>
 <pb file="1096.jpg" o="548v" n="1096"/>
 <pb file="1097.jpg" o="549r" n="1097"/>
 <head xml:id="echoid-head75" xml:space="preserve">
 Computatio annorum 450. Act. 13.
 <lb/>[<emph style="it">tr:
 Computation of 450 years.
 </emph>]<lb/>
 </head>
 <pb file="1098.jpg" o="549v" n="1098"/>
 <pb file="1099.jpg" o="550r" n="1099"/>
 <head xml:id="echoid-head76" xml:space="preserve" xml:lang="lat">
 Computatio annorum 480. quæ 1. Reg. Ex Beroaldo
 <lb/>[<emph style="it">tr:
 Computation of 480 years. Kings I. From Beroaldo
 </emph>]<lb/>
 </head>
 <pb file="1100.jpg" o="550v" n="1100"/>
 <pb file="1101.jpg" o="551r" n="1101"/>
 <head xml:id="echoid-head77" xml:space="preserve" xml:lang="lat">
 Josephus pag. 125.114. Ex sacris literis.
 <lb/>[<emph style="it">tr:
 Josephus pages 125, 114. <lb/>
 From holy scriptures.
 </emph>]<lb/>
 </head>
 <pb file="1102.jpg" o="551v" n="1102"/>
 <pb file="1103.jpg" o="552r" n="1103"/>
 <pb file="1104.jpg" o="552v" n="1104"/>
 <div xml:id="echoid-div43" type="page_commentary" level="2" n="43">
<p>
<s xml:id="echoid-s512" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s512" xml:space="preserve">
 A fair copy of the totals arrived at in Add MS 6788, f. 554v, f. 555, f. 543, f.546.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1105.jpg" o="553r" n="1105"/>
 <div xml:id="echoid-div44" type="page_commentary" level="2" n="44">
<p>
<s xml:id="echoid-s514" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s514" xml:space="preserve">
 The continuation of Add MS 6788, f. 552v;
 a fair copy of the totals arrived at in Add MS 6788, f. 554v, f. 555, f. 543, f.546,
 showing the populations sequences up to the eighth generation of males.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1106.jpg" o="553v" n="1106"/>
 <pb file="1107.jpg" o="554r" n="1107"/>
 <div xml:id="echoid-div45" type="page_commentary" level="2" n="45">
<p>
<s xml:id="echoid-s516" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s516" xml:space="preserve">
 The calculations in Add MS 6788, f. 536, f. 537, f. 540, f. 541, f. 542, f. 543v, f. 545
 assumed that ten males would give rise to a steadily increasing population,
 measured by the triangular numbers 1, 3, 6, 10, ....
 This is the situation indicated in the first 20 rows of the sketch on the left.
 In this folio, however, Harriot assumes that each male dies (or ceases to reproduce) at the age of 40.
 In this case their (male) offspring are measured by the series written across the top of the page,
 reaching a peak of 75 after 15 years.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1108.jpg" o="554v" n="1108"/>
 <div xml:id="echoid-div46" type="page_commentary" level="2" n="46">
<p>
<s xml:id="echoid-s518" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s518" xml:space="preserve">
 The continuation of Add MS 6788, f. 555 as far as the eighth generation.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1109.jpg" o="555r" n="1109"/>
 <div xml:id="echoid-div47" type="page_commentary" level="2" n="47">
<p>
<s xml:id="echoid-s520" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s520" xml:space="preserve">
 Given the sequence 1, 3, 6, ..., 63, 69, 73, 75, 75, 73, ..., 6, 3, 1
 for the number of males in the third generation (see Add MS 6788, f 545),
 this folio shows the calculation for the number of males in the fourth generation,
 namely, 1, 4, 10, 20, ...220, 282, ...660, 670, 660, ..., reaching a peak of 670 in year 19. <lb/>
 Further lists show sequences for the fifth and sixth generations.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <pb file="1110.jpg" o="555v" n="1110"/>
 <pb file="1111.jpg" o="556r" n="1111"/>
 <head xml:id="echoid-head78" xml:space="preserve" xml:lang="lat">
 periodus Judaica 696
 </head>
 <pb file="1112.jpg" o="556v" n="1112"/>
 <p xml:lang="lat">
 <s xml:id="echoid-s522" xml:space="preserve">
 p. Midelb.
 </s>
 </p>
 <pb file="1113.jpg" o="557r" n="1113"/>
 <p xml:lang="lat">
 <s xml:id="echoid-s523" xml:space="preserve">
 p. Midelb.
 </s>
 </p>
 <pb file="1114.jpg" o="557v" n="1114"/>
 <p xml:lang="lat">
 <s xml:id="echoid-s524" xml:space="preserve">
 primus annus Nabonassari <lb/>
 fiat Judaicus 3134.
 <lb/>[<emph style="it">tr:
 The first year of Nabonassar becomes the Judaic year 3134.
 </emph>]<lb/>
 </s>
 </p>
 <p xml:lang="lat">
 <s xml:id="echoid-s525" xml:space="preserve">
 sed Scaliger pag: 368 <lb/>
 habet. 5. 23. 7. 34. Adar <lb/>
 feria sexta.
 <lb/>[<emph style="it">tr:
 But Scaliger on page 368 has ...
 </emph>]<lb/>
 </s>
 </p>
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 <head xml:id="echoid-head79" xml:space="preserve" xml:lang="lat">
 De primo anno Nabonbonassari. ex Ptol: lib. 6. cap. 2.
 <lb/>[<emph style="it">tr:
 On the first year of Nabonassar, from Ptolemy, Book 6, Chapter 2.
 </emph>]<lb/>
 </head>
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 <div xml:id="echoid-div48" type="page_commentary" level="2" n="48">
<p>
<s xml:id="echoid-s526" xml:space="preserve">[<emph style="it">Note:
 <p>
 <s xml:id="echoid-s526" xml:space="preserve">
 The author of this fragment is unkown but the form of address is simlar to that on Add MS 6786, f. 490v.
 </s>
 </p>
 </emph>]
<lb/><lb/></s></p></div>
 <p>
 <s xml:id="echoid-s528" xml:space="preserve">
 To his worthy and muche <lb/>
 respected frende Mr. <lb/>
 Thomas Hariot at <lb/>
 Syon geve these.
 </s>
 </p>
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 <!--
          <head xml:space="preserve">
          Upon sundry suppositions certayne conclusions <lb/>
          of the number of persons that are born ?? <lb/>
          &and; generally in England.
          </head>

<p>
<s xml:space="preserve">
<emph style="st">
The mayne supposition is that the ?? being so populous as <emph style="st">that</emph> the of <lb/>
of the land naturally ?eded, or by arte raysed; or prpoduce thorough <lb/>
the labouris of mand &amp; trade is able well to mayntayne with food &amp; such <lb/>
??messages?? as used <emph style="st">for desire</emph> for the ?? of life.
</emph>
</s>
</p>

<p>
<s xml:space="preserve">
The mayne suppositions is that there as many living soules one ??
as there is in any other continually.
</s>
</p>
      -->
 <pb file="1134.jpg" o="567v" n="1134"/>
 </div>
 </text>
</echo>
author	casties
date	Fri, 07 Dec 2012 17:05:22 +0100
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