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annotate texts/XML/echo/en/Harriot_Add_MS_6786_TRMFCPMB.xml @ 29:90b1eda1b0a9

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Some new special instructions
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Fri, 02 Dec 2016 14:37:22 +0100
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1 <?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC">
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2 <metadata>
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3 <dcterms:identifier>ECHO:TRMFCPMB.xml</dcterms:identifier>
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4 <dcterms:creator>Harriot, Thomas</dcterms:creator>
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5 <dcterms:title xml:lang="en">Mss. 6786</dcterms:title>
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6 <dcterms:date xsi:type="dcterms:W3CDTF">o. J.</dcterms:date>
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7 <dcterms:language xsi:type="dcterms:ISO639-3">eng</dcterms:language>
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8 <dcterms:rights>CC-BY-SA</dcterms:rights>
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9 <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license>
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10 <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder>
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11 <echodir>/permanent/library/TRMFCPMB</echodir>
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12 <log>Automatically generated by bare_xml.py on Tue Nov 15 14:20:54 2011</log>
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13 </metadata>
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15 <text xml:lang="eng" type="free">
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16 <div xml:id="echoid-div1" type="section" level="1" n="1">
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381 <p>
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382 <s xml:id="echoid-s1" xml:space="preserve">
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383 S. JS. Harriman. <lb/>
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384 Mr Huss. <lb/>
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385 Mr Alisbury. <lb/>
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386 Mr Thorperly. <lb/>
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387 Mr Marlo.
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388 </s>
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389 </p>
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456 <pb file="add_6786_f216" o="216" n="431"/>
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457 <pb file="add_6786_f216v" o="216v" n="432"/>
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458 <pb file="add_6786_f217" o="217" n="433"/>
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459 <pb file="add_6786_f217v" o="217v" n="434"/>
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460 <pb file="add_6786_f218" o="218" n="435"/>
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461 <pb file="add_6786_f218v" o="218v" n="436"/>
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462 <pb file="add_6786_f219" o="219" n="437"/>
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463 <pb file="add_6786_f219v" o="219v" n="438"/>
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464 <pb file="add_6786_f220" o="220" n="439"/>
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465 <pb file="add_6786_f220v" o="220v" n="440"/>
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466 <pb file="add_6786_f221" o="221" n="441"/>
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467 <pb file="add_6786_f221v" o="221v" n="442"/>
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468 <pb file="add_6786_f222" o="222" n="443"/>
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469 <pb file="add_6786_f222v" o="222v" n="444"/>
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470 <pb file="add_6786_f223" o="223" n="445"/>
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471 <head xml:id="echoid-head1" xml:space="preserve">
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472 Euclides opticks
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473 </head>
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474 <pb file="add_6786_f223v" o="223v" n="446"/>
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475 <pb file="add_6786_f224" o="224" n="447"/>
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476 <div xml:id="echoid-div1" type="page_commentary" level="2" n="1">
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477 <p>
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478 <s xml:id="echoid-s2" xml:space="preserve">[<emph style="it">Note:
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479 <p>
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480 <s xml:id="echoid-s2" xml:space="preserve">
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481 This page refers to Propositions I.36 and I.37 of Book I of Apollonius,
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482 <emph style="it">Conicorum libri quattuor</emph>.
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483 </s>
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484 <lb/>
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485 <quote>
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486 I.36.
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487 If some straight line, meeting the transverse side of the figure touches an hyperbola
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488 or ellipse or circumference of a circle, and if a straight line is dropped from the point of contact
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489 as an ordinate to the diameter, then as the straight line cut off by the tangent
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490 from the end of the transverse side is to the straight line cut off by the tangent from the other end of that side,
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491 so will the straight line cut off by the ordinate from the end of the side be
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492 to the straight line cut off by the ordinate from the other end of the side in such a way that
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493 the corresponding straight lines are continuous; and another straight line will not fall into the space
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494 between the tangent and the section of the cone.
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495 </quote>
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496 <lb/>
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497 <quote>
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498 I.37
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499 If a straight line touching an hyperbola or ellipse or circumference of a circle meets the diameter,
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500 and from the point of contact to the diameter a straight line is dropped as ordinate,
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501 then the straight line cut off by the ordinate from the centre of the section
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502 with the straight line cut off by the tangent from the centre of the section will contain
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503 an area equal to the square on the radius of the section,
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504 and with the straight line between the ordinate and the tangent will contain an area
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505 having the ratio to the square on the ordinate which the transverse has to the upright.
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506 </quote>
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507 </p>
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508 </emph>]
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509 <lb/><lb/></s></p></div>
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510 <head xml:id="echoid-head2" xml:space="preserve" xml:lang="lat">
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511 Appollo: lib. 1.
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512 <lb/>[<emph style="it">tr:
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513 Apollonius, Book I
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514 </emph>]<lb/>
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515 </head>
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516 <p xml:lang="lat">
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517 <s xml:id="echoid-s4" xml:space="preserve">
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518 37.p <lb/>
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519 36. dia:
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520 <lb/>[<emph style="it">tr:
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521 Propositions 36, 37; diameter:
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522 </emph>]<lb/>
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523 </s>
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524 </p>
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525 <pb file="add_6786_f224v" o="224v" n="448"/>
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526 <pb file="add_6786_f225" o="225" n="449"/>
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527 <pb file="add_6786_f225v" o="225v" n="450"/>
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528 <pb file="add_6786_f226" o="226" n="451"/>
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529 <head xml:id="echoid-head3" xml:space="preserve" xml:lang="lat">
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530 Atomi
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531 </head>
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532 <p>
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533 <s xml:id="echoid-s5" xml:space="preserve">[<emph style="it">Note:
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534 A calculation of the number of atoms in 1 foot, 1 pase (= 5 feet), and 1 mile (= 1000 pases).
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535 </emph>]</s><lb/>
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536 <s xml:id="echoid-s6" xml:space="preserve">
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537 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mn>0</mn><mn>0</mn><mn>0</mn><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math> foote.
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538 </s>
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539 <lb/>
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540 <s xml:id="echoid-s7" xml:space="preserve">
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541 10,000. foote.
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542 </s>
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543 <lb/>
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544 <s xml:id="echoid-s8" xml:space="preserve">
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545 50,000. pase.
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546 </s>
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547 <lb/>
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548 <s xml:id="echoid-s9" xml:space="preserve">
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549 50,000,000. mile.
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550 </s>
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551 </p>
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552 <p xml:lang="lat">
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553 <s xml:id="echoid-s10" xml:space="preserve">
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554 <sc>
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555 The number of miles in the circumference of the earth.
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556 </sc>
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557 60,000. <foreign xml:lang="eng">miles</foreign> <reg norm="circa" type="abbr">circ</reg>. terra
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558 </s>
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559 <lb/>
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560 <s xml:id="echoid-s11" xml:space="preserve">
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561 <sc>
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562 The number of atoms in the circumference of the earth.
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563 </sc>
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564 3,000,000,000,000. <reg norm="atomi" type="abbr">ato</reg>.
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565 <reg norm="circa" type="abbr">circ</reg>. <reg norm="terra" type="abbr">ter</reg>.
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566 </s>
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567 <lb/>
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568 <s xml:id="echoid-s12" xml:space="preserve">
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569 <sc>
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570 The number of atoms in the diameter of the earth.
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571 </sc>
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572 1,000,000,000,000. diameter
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573 </s>
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574 <lb/>
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575 <s xml:id="echoid-s13" xml:space="preserve">
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576 <sc>
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577 The number of atoms in 2,000 earth diameters, the supposed distance to the sun.
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578 </sc>
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579 2,000. diametri ad solem
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580 </s>
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581 </p>
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582 <p xml:lang="lat">
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583 <s xml:id="echoid-s14" xml:space="preserve">
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584 <sc>
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585 The number of atoms from the earth to the sun.
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586 </sc>
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587 <reg norm="atomi" type="abbr">ato</reg>. ad solem
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588 </s>
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589 </p>
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590 <p xml:lang="lat">
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591 <s xml:id="echoid-s15" xml:space="preserve">
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592 <sc>
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593 The number of atoms in 2000 times the distance to the sun, the supposed distance to the fixed stars.
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594 </sc>
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595 <reg norm="atomi" type="abbr">ato</reg>. ad [¿]stellæ[?] [???]
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596 </s>
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597 <lb/>
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598 <s xml:id="echoid-s16" xml:space="preserve">
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599 <sc>
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600 Approximately double the previous line, that is, the number of atoms in the diameter of the sphere of the fixed stars.
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601 </sc>
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602 maior diameter
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603 </s>
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604 <lb/>
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605 <s xml:id="echoid-s17" xml:space="preserve">
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606 <sc>
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607 The cube of the previous line, that is, a rough and ready calculation of the number of atoms in the universe.
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608 </sc>
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609 cubus maior sphæræ
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610 </s>
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611 </p>
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612 <pb file="add_6786_f226v" o="226v" n="452"/>
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613 <pb file="add_6786_f227" o="227" n="453"/>
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614 <div xml:id="echoid-div2" type="page_commentary" level="2" n="2">
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615 <p>
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616 <s xml:id="echoid-s18" xml:space="preserve">[<emph style="it">Note:
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617 <p>
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618 <s xml:id="echoid-s18" xml:space="preserve">
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619 Calculations relating to formula (3) on pages 27 to 34 of the 'Magisteria' (Add MS 6782, f. 134 to f. 142).
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620 </s>
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621 </p>
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622 </emph>]
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623 <lb/><lb/></s></p></div>
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624 <pb file="add_6786_f227v" o="227v" n="454"/>
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625 <pb file="add_6786_f228" o="228" n="455"/>
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626 <pb file="add_6786_f228v" o="228v" n="456"/>
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627 <pb file="add_6786_f229" o="229" n="457"/>
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628 <pb file="add_6786_f229v" o="229v" n="458"/>
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629 <div xml:id="echoid-div3" type="page_commentary" level="2" n="3">
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630 <p>
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631 <s xml:id="echoid-s20" xml:space="preserve">[<emph style="it">Note:
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632 <p>
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633 <s xml:id="echoid-s20" xml:space="preserve">
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634 This page refers to Euclid X.37. In modern editions the relevant proposition is X.36,
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635 but Harriot's numbering matches that of both Commandino and Clavius.
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636 </s>
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637 <lb/>
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638 <s xml:id="echoid-s21" xml:space="preserve">
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639 <emph style="it">
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640 If two ratioinal straight lines commensurable in square only be added together,
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641 the whole is irrational; and let it be called binomial.
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642 </emph>
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643 </s>
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644 <lb/>
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645 <s xml:id="echoid-s22" xml:space="preserve">
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646 Harriot's example is <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>2</mn><mo>+</mo><msqrt><mrow><mn>5</mn></mrow></msqrt></mstyle></math>.
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647 </s>
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648 <lb/>
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649 <s xml:id="echoid-s23" xml:space="preserve">
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650 There is also a reference below the diagram to Euclid VI.1: <lb/>
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651 Triangles and parallelograms which are under the same height are to one another as their bases.
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652 </s>
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653 </p>
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654 </emph>]
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655 <lb/><lb/></s></p></div>
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656 <head xml:id="echoid-head4" xml:space="preserve" xml:lang="lat">
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657 Lib, 10: prop. 37.
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658 <lb/>[<emph style="it">tr:
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659 Book X, Proposition 37.
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660 </emph>]<lb/>
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661 </head>
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662 <p xml:lang="lat">
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663 <s xml:id="echoid-s25" xml:space="preserve">
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664 Si duae rationales potentia solum commensurabiles componantur, <lb/>
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665 tota irrationalis erit, nocetur autem ex binis nominibus.
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666 <lb/>[<emph style="it">tr:
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667 If two quantities commensurable in power only are combined, the whole will be irrational,
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668 moreover separated into two parts.
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669 </emph>]<lb/>
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670 </s>
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671 </p>
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672 <pb file="add_6786_f230" o="230" n="459"/>
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673 <head xml:id="echoid-head5" xml:space="preserve" xml:lang="lat">
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674 Definitiones decimi Euclidis <lb/>
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675 explicates per exempla numerorum
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676 <lb/>[<emph style="it">tr:
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677 Definitions from the tenth book of Eculid, shown by numerical examples.
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678 </emph>]<lb/>
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679 </head>
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680 <p xml:lang="lat">
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681 <s xml:id="echoid-s26" xml:space="preserve">
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682 1.) Magnitudeines (sive numeri) commensurabiles
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683 <lb/>[<emph style="it">tr:
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684 Commensurable magnitudes (or numbers)
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685 </emph>]<lb/>
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686 </s>
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687 <lb/>
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688 <s xml:id="echoid-s27" xml:space="preserve">
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689 2.) Incommensurabiles
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690 <lb/>[<emph style="it">tr:
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691 Incommensurables
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692 </emph>]<lb/>
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693 </s>
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694 <lb/>
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695 <s xml:id="echoid-s28" xml:space="preserve">
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696 3.) Commensurabiles potentia
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697 <lb/>[<emph style="it">tr:
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698 Commensurables in power
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699 </emph>]<lb/>
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700 </s>
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701 <lb/>
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702 <s xml:id="echoid-s29" xml:space="preserve">
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703 4.) Incomensurabiles
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704 <lb/>[<emph style="it">tr:
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705 Incommensurables
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706 </emph>]<lb/>
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707 </s>
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708 </p>
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709 <pb file="add_6786_f230v" o="230v" n="460"/>
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710 <p xml:lang="lat">
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711 <s xml:id="echoid-s30" xml:space="preserve">
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712 [<emph style="it">Note:
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713 See also Add MS 6785, f. 210v.
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714 </emph>]<lb/>
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715 de numeris perfectis
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716 <lb/>[<emph style="it">tr:
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717 on perfect numbers
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718 </emph>]<lb/>
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719 </s>
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720 </p>
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721 <p>
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722 <s xml:id="echoid-s31" xml:space="preserve">
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723 Leida <lb/>
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724 Haga <lb/>
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725 Gouda <lb/>
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726 Leida <lb/>
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727 Ultrajestorum <lb/>
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728 Gouda
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729 </s>
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730 </p>
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731 <pb file="add_6786_f231" o="231" n="461"/>
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732 <pb file="add_6786_f231v" o="231v" n="462"/>
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733 <pb file="add_6786_f232" o="232" n="463"/>
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734 <div xml:id="echoid-div4" type="page_commentary" level="2" n="4">
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735 <p>
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736 <s xml:id="echoid-s32" xml:space="preserve">[<emph style="it">Note:
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737 <p>
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738 <s xml:id="echoid-s32" xml:space="preserve">
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739 This sheet contains an analysis of the first 40 propositions of Book X of
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740 Euclid's <emph style="it">Elements</emph>, showing how each proposition depends on previous ones.
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741 The reference to Clavius is to his <emph style="it">Euclidis Elementorum libri XV</emph> (1574, 1589, 1591, 1603, 1607).
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742 </s>
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743 </p>
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744 </emph>]
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745 <lb/><lb/></s></p></div>
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746 <head xml:id="echoid-head6" xml:space="preserve" xml:lang="lat">
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747 Clavius). 10. lib. Euclid. propositionum
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748 </head>
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749 <pb file="add_6786_f232v" o="232v" n="464"/>
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750 <pb file="add_6786_f233" o="233" n="465"/>
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751 <pb file="add_6786_f233v" o="233v" n="466"/>
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752 <p>
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753 <s xml:id="echoid-s34" xml:space="preserve">
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754 If you call hym ffather which without respect of parson iudgeth <lb/>
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755 according to everie mans worke passe the time of your dwelling here in franc. <lb/>
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756 If you call hym ffather which without respect of parson iudgeth <lb/>
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757 according to everie mans worke passe the time of your dwelling <lb/>
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758 here in franc. <lb/>
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759 Banberynam John
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760 </s>
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761 </p>
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762 <pb file="add_6786_f234" o="234" n="467"/>
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763 <pb file="add_6786_f234v" o="234v" n="468"/>
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764 <pb file="add_6786_f235" o="235" n="469"/>
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765 <pb file="add_6786_f235v" o="235v" n="470"/>
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766 <pb file="add_6786_f236" o="236" n="471"/>
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767 <pb file="add_6786_f236v" o="236v" n="472"/>
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768 <p>
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769 <s xml:id="echoid-s35" xml:space="preserve">
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770 ffather <lb/>
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771 But afarre
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parents:
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772 </s>
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773 </p>
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774 <pb file="add_6786_f237" o="237" n="473"/>
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775 <p>
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776 <s xml:id="echoid-s36" xml:space="preserve">
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777 A man of wordes and not of deedes is like a garden full of weedes <lb/>
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778 A man of deedes and not of wordes is like a privifull of tourdes. <lb/>
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779 A man of wordes
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780 </s>
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781 </p>
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782 <pb file="add_6786_f237v" o="237v" n="474"/>
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783 <pb file="add_6786_f238" o="238" n="475"/>
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784 <pb file="add_6786_f238v" o="238v" n="476"/>
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785 <pb file="add_6786_f239" o="239" n="477"/>
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786 <pb file="add_6786_f239v" o="239v" n="478"/>
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787 <pb file="add_6786_f240" o="240" n="479"/>
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788 <pb file="add_6786_f240v" o="240v" n="480"/>
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789 <pb file="add_6786_f241" o="241" n="481"/>
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790 <pb file="add_6786_f241v" o="241v" n="482"/>
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791 <pb file="add_6786_f242" o="242" n="483"/>
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792 <pb file="add_6786_f242v" o="242v" n="484"/>
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793 <pb file="add_6786_f243" o="243" n="485"/>
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794 <pb file="add_6786_f243v" o="243v" n="486"/>
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795 <pb file="add_6786_f244" o="244" n="487"/>
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796 <pb file="add_6786_f244v" o="244v" n="488"/>
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797 <pb file="add_6786_f245" o="245" n="489"/>
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798 <pb file="add_6786_f245v" o="245v" n="490"/>
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799 <pb file="add_6786_f246" o="246" n="491"/>
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800 <p xml:lang="lat">
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801 <s xml:id="echoid-s37" xml:space="preserve">
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802 Vuolffgangius [???], Per aliquot gentium migrationibus &amp; lib. 12. fol. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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803 Decades duæ devoniarum gentium emmigrationibus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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804 in Illyrici occidentalis tractum. <lb/>
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805 Tonstall. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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806 Lypsius de Machinis.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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807 </s>
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808 </p>
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809 <p>
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810 <s xml:id="echoid-s38" xml:space="preserve">
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811 Filtring paper. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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812 4 &amp; 8 &amp; [???] glasses <lb/>
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813 2 glasses with elliptical <lb/>
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814 [???] for coyne.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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815 </s>
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816 </p>
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817 <pb file="add_6786_f246v" o="246v" n="492"/>
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818 <pb file="add_6786_f247" o="247" n="493"/>
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819 <pb file="add_6786_f247v" o="247v" n="494"/>
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820 <p xml:lang="lat">
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821 <s xml:id="echoid-s39" xml:space="preserve">
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822 Annus lunaris.
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823 </s>
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824 <lb/>
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825 <s xml:id="echoid-s40" xml:space="preserve">
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826 hoc est,
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827 </s>
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828 <lb/>
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829 <s xml:id="echoid-s41" xml:space="preserve">
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830 Ergo: Mensis lunaris.
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831 </s>
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832 </p>
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833 <pb file="add_6786_f248" o="248" n="495"/>
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834 <div xml:id="echoid-div5" type="page_commentary" level="2" n="5">
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835 <p>
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836 <s xml:id="echoid-s42" xml:space="preserve">[<emph style="it">Note:
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837 <p>
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838 <s xml:id="echoid-s42" xml:space="preserve">
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839 From right to left, the columns list: <lb/>
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840 units (1, 1, 1, 1,...) <lb/>
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841 lengths (1, 2, 3, 4,...) <lb/>
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842 triangular numbers (1, 3, 6, 10,...) <lb/>
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843 triangular-pyramidal numbers (1, 4, 10, 20,...) <lb/>
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844 triangular-pyramido-pyramidal numbers (1, 5, 15, 35,...).
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845 </s>
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846 </p>
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847 </emph>]
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848 <lb/><lb/></s></p></div>
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849 <pb file="add_6786_f248v" o="248v" n="496"/>
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850 <pb file="add_6786_f249" o="249" n="497"/>
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851 <pb file="add_6786_f249v" o="249v" n="498"/>
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852 <pb file="add_6786_f250" o="250" n="499"/>
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853 <pb file="add_6786_f250v" o="250v" n="500"/>
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854 <pb file="add_6786_f251" o="251" n="501"/>
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855 <pb file="add_6786_f251v" o="251v" n="502"/>
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856 <pb file="add_6786_f252" o="252" n="503"/>
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857 <pb file="add_6786_f252v" o="252v" n="504"/>
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858 <pb file="add_6786_f253" o="253" n="505"/>
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859 <pb file="add_6786_f253v" o="253v" n="506"/>
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860 <pb file="add_6786_f254" o="254" n="507"/>
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862 <pb file="add_6786_f255" o="255" n="509"/>
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863 <pb file="add_6786_f255v" o="255v" n="510"/>
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864 <pb file="add_6786_f256" o="256" n="511"/>
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865 <pb file="add_6786_f256v" o="256v" n="512"/>
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867 <pb file="add_6786_f257v" o="257v" n="514"/>
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869 <pb file="add_6786_f258v" o="258v" n="516"/>
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870 <pb file="add_6786_f259" o="259" n="517"/>
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871 <pb file="add_6786_f259v" o="259v" n="518"/>
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872 <pb file="add_6786_f260" o="260" n="519"/>
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873 <div xml:id="echoid-div6" type="page_commentary" level="2" n="6">
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874 <p>
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875 <s xml:id="echoid-s44" xml:space="preserve">[<emph style="it">Note:
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876 <p>
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877 <s xml:id="echoid-s44" xml:space="preserve">
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878 Harriot 19s letters refer to the diagram on page 3v of Commandino's
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879 <emph style="it">Ptolemaei planisphaerium</emph> (1558).
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880 </s>
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881 </p>
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882 </emph>]
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883 <lb/><lb/></s></p></div>
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884 <head xml:id="echoid-head7" xml:space="preserve" xml:lang="lat">
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885 Annotationes in rationes scenographices Federico
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886 Comandino, post ptolemae planisphaerum
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887 <lb/>[<emph style="it">tr:
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888 Annotations on the scenographic ratios of Federico Comandino, in
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889 </emph>]<lb/>
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890 </head>
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891 <p>
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892 <s xml:id="echoid-s46" xml:space="preserve">
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893 pag. 3
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894 </s>
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895 </p>
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896 <pb file="add_6786_f260v" o="260v" n="520"/>
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897 <pb file="add_6786_f261" o="261" n="521"/>
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898 <pb file="add_6786_f261v" o="261v" n="522"/>
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899 <pb file="add_6786_f262" o="262" n="523"/>
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900 <pb file="add_6786_f262v" o="262v" n="524"/>
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901 <pb file="add_6786_f263" o="263" n="525"/>
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902 <pb file="add_6786_f263v" o="263v" n="526"/>
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903 <pb file="add_6786_f264" o="264" n="527"/>
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904 <pb file="add_6786_f264v" o="264v" n="528"/>
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905 <pb file="add_6786_f265" o="265" n="529"/>
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906 <pb file="add_6786_f265v" o="265v" n="530"/>
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907 <pb file="add_6786_f266" o="266" n="531"/>
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908 <pb file="add_6786_f266v" o="266v" n="532"/>
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909 <pb file="add_6786_f267" o="267" n="533"/>
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910 <pb file="add_6786_f267v" o="267v" n="534"/>
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911 <pb file="add_6786_f268" o="268" n="535"/>
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912 <pb file="add_6786_f268v" o="268v" n="536"/>
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913 <pb file="add_6786_f269" o="269" n="537"/>
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914 <pb file="add_6786_f269v" o="269v" n="538"/>
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915 <pb file="add_6786_f270" o="270" n="539"/>
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916 <pb file="add_6786_f270v" o="270v" n="540"/>
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917 <pb file="add_6786_f271" o="271" n="541"/>
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918 <pb file="add_6786_f271v" o="271v" n="542"/>
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919 <pb file="add_6786_f272" o="272" n="543"/>
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920 <pb file="add_6786_f272v" o="272v" n="544"/>
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921 <pb file="add_6786_f273" o="273" n="545"/>
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922 <pb file="add_6786_f273v" o="273v" n="546"/>
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923 <pb file="add_6786_f274" o="274" n="547"/>
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924 <pb file="add_6786_f274v" o="274v" n="548"/>
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925 <pb file="add_6786_f275" o="275" n="549"/>
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926 <pb file="add_6786_f275v" o="275v" n="550"/>
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927 <pb file="add_6786_f276" o="276" n="551"/>
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928 <pb file="add_6786_f276v" o="276v" n="552"/>
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929 <pb file="add_6786_f277" o="277" n="553"/>
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930 <pb file="add_6786_f277v" o="277v" n="554"/>
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931 <pb file="add_6786_f278" o="278" n="555"/>
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932 <pb file="add_6786_f278v" o="278v" n="556"/>
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933 <pb file="add_6786_f279" o="279" n="557"/>
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934 <div xml:id="echoid-div7" type="page_commentary" level="2" n="7">
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935 <p>
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936 <s xml:id="echoid-s47" xml:space="preserve">[<emph style="it">Note:
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937 <p>
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938 <s xml:id="echoid-s47" xml:space="preserve">
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939 This page appears to be related to page 177 of Stevin's <emph style="it">L 19arithmetique pratique</emph> (1585).
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940 The problem that Stevin addresses there, as stated on page 174, is: <lb/>
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941 <emph style="it" xml:lang="fr">
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942 Estant donné ligne droicte, &amp; deux nombres:
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943 Trouer vne ligne droicte en telle raison à la donnée, comme le nombre au nombre. <lb/>
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944 Stevin's examples are numerical, but Harriot is working in letters
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945 (as also in further notes on Stevin in Add MS 6782, f. 231).
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946 </emph></s>
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947 </p>
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948 </emph>]
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949 <lb/><lb/></s></p></div>
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950 <p>
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951 <s xml:id="echoid-s49" xml:space="preserve">
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952 Stevin. 177.
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953 </s>
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954 </p>
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955 <pb file="add_6786_f279v" o="279v" n="558"/>
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956 <pb file="add_6786_f280" o="280" n="559"/>
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957 <pb file="add_6786_f280v" o="280v" n="560"/>
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958 <pb file="add_6786_f281" o="281" n="561"/>
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959 <pb file="add_6786_f281v" o="281v" n="562"/>
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960 <div xml:id="echoid-div8" type="page_commentary" level="2" n="8">
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961 <p>
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962 <s xml:id="echoid-s50" xml:space="preserve">[<emph style="it">Note:
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963 <p>
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964 <s xml:id="echoid-s50" xml:space="preserve">
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965 The first half of a diagram continued on Add MS 6786, f. 282.
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966 </s>
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967 </p>
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968 </emph>]
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969 <lb/><lb/></s></p></div>
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970 <pb file="add_6786_f282" o="282" n="563"/>
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971 <div xml:id="echoid-div9" type="page_commentary" level="2" n="9">
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972 <p>
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973 <s xml:id="echoid-s52" xml:space="preserve">[<emph style="it">Note:
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974 <p>
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975 <s xml:id="echoid-s52" xml:space="preserve">
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976 The second half of the diagram from Add MS 6876, f. 281v.
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977 </s>
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978 </p>
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979 </emph>]
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980 <lb/><lb/></s></p></div>
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981 <p>
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982 <s xml:id="echoid-s54" xml:space="preserve">
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983 A water worke found below <lb/>
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984 my Lord Chamberlayne at <lb/>
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985 his house in blacke friers <lb/>
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986 the 23 of January 1600/1601.
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987 </s>
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988 </p>
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989 <pb file="add_6786_f282v" o="282v" n="564"/>
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990 <p>
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991 <s xml:id="echoid-s55" xml:space="preserve">
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992 The Lord <lb/>
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993 Chamberlaynes <lb/>
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994 Water Worke <lb/>
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995 Jan. 23. <lb/>
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996 1600 <lb/>
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997 1601.
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998 </s>
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999 </p>
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1000 <p>
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1001 <s xml:id="echoid-s56" xml:space="preserve">
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1002 The plomber [???]
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1003 </s>
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1004 </p>
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1005 <pb file="add_6786_f283" o="283" n="565"/>
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1006 <pb file="add_6786_f283v" o="283v" n="566"/>
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1007 <div xml:id="echoid-div10" type="page_commentary" level="2" n="10">
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1008 <p>
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1009 <s xml:id="echoid-s57" xml:space="preserve">[<emph style="it">Note:
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1010 <p>
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1011 <s xml:id="echoid-s57" xml:space="preserve">
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1012 The numersals 1 to 9 written with dots, and with various other symbols invented by Harriot for the purpose.
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1013 </s>
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1014 </p>
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1015 </emph>]
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1016 <lb/><lb/></s></p></div>
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1017 <pb file="add_6786_f284" o="284" n="567"/>
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1018 <pb file="add_6786_f284v" o="284v" n="568"/>
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1019 <pb file="add_6786_f285" o="285" n="569"/>
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1020 <pb file="add_6786_f285v" o="285v" n="570"/>
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1021 <pb file="add_6786_f286" o="286" n="571"/>
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1022 <pb file="add_6786_f286v" o="286v" n="572"/>
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1023 <pb file="add_6786_f287" o="287" n="573"/>
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1024 <pb file="add_6786_f287v" o="287v" n="574"/>
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1025 <pb file="add_6786_f288" o="288" n="575"/>
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1026 <div xml:id="echoid-div11" type="page_commentary" level="2" n="11">
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1027 <p>
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1028 <s xml:id="echoid-s59" xml:space="preserve">[<emph style="it">Note:
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1029 <p>
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1030 <s xml:id="echoid-s59" xml:space="preserve">
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1031 A calculation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>3</mn><mo>.</mo><mn>4</mn><mn>5</mn><mn>8</mn><mn>7</mn><mn>6</mn><mn>4</mn><mn>5</mn><mn>1</mn><mn>3</mn><mo>.</mo><mo>.</mo><mo>.</mo></mrow></msqrt></mstyle></math>.
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1032 </s>
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1033 </p>
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1034 </emph>]
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1035 <lb/><lb/></s></p></div>
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1036 <pb file="add_6786_f288v" o="288v" n="576"/>
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1037 <pb file="add_6786_f289" o="289" n="577"/>
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1038 <pb file="add_6786_f289v" o="289v" n="578"/>
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1039 <pb file="add_6786_f290" o="290" n="579"/>
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1040 <pb file="add_6786_f290v" o="290v" n="580"/>
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1041 <pb file="add_6786_f291" o="291" n="581"/>
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1042 <div xml:id="echoid-div12" type="page_commentary" level="2" n="12">
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1043 <p>
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1044 <s xml:id="echoid-s61" xml:space="preserve">[<emph style="it">Note:
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1045 <p>
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1046 <s xml:id="echoid-s61" xml:space="preserve">
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1047 Combinations of quantities generated by multiplication. <lb/>
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1048 The letters <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>p</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>m</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>f</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>s</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi></mstyle></math> stand for
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1049 <foreign xml:lang="lat">pondus</foreign> (weight),
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1050 <foreign xml:lang="lat">magnitudo</foreign> (magnitude),
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1051 <foreign xml:lang="lat">figura</foreign> (area),
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1052 <foreign xml:lang="lat">situs</foreign> (place),
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1053 <foreign xml:lang="lat">altitudo</foreign> (altitude)
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1054 (see also Add MS 6782, f. 181 and f. 48v).
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1055 </s>
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1056 </p>
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1057 </emph>]
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1058 <lb/><lb/></s></p></div>
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1059 <pb file="add_6786_f291v" o="291v" n="582"/>
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1060 <pb file="add_6786_f292" o="292" n="583"/>
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1061 <pb file="add_6786_f292v" o="292v" n="584"/>
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1062 <pb file="add_6786_f293" o="293" n="585"/>
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1063 <pb file="add_6786_f293v" o="293v" n="586"/>
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1064 <pb file="add_6786_f294" o="294" n="587"/>
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1065 <pb file="add_6786_f294v" o="294v" n="588"/>
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1066 <pb file="add_6786_f295" o="295" n="589"/>
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1067 <pb file="add_6786_f295v" o="295v" n="590"/>
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1068 <pb file="add_6786_f296" o="296" n="591"/>
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1069 <pb file="add_6786_f296v" o="296v" n="592"/>
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1070 <pb file="add_6786_f297" o="297" n="593"/>
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1071 <pb file="add_6786_f297v" o="297v" n="594"/>
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1072 <pb file="add_6786_f298" o="298" n="595"/>
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1073 <pb file="add_6786_f298v" o="298v" n="596"/>
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1074 <pb file="add_6786_f299" o="299" n="597"/>
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1075 <pb file="add_6786_f299v" o="299v" n="598"/>
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1076 <pb file="add_6786_f300" o="300" n="599"/>
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1077 <pb file="add_6786_f300v" o="300v" n="600"/>
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1078 <pb file="add_6786_f301" o="301" n="601"/>
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1079 <pb file="add_6786_f301v" o="301v" n="602"/>
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1080 <pb file="add_6786_f302" o="302" n="603"/>
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1081 <pb file="add_6786_f302v" o="302v" n="604"/>
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1082 <pb file="add_6786_f303" o="303" n="605"/>
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1083 <div xml:id="echoid-div13" type="page_commentary" level="2" n="13">
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1084 <p>
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1085 <s xml:id="echoid-s63" xml:space="preserve">[<emph style="it">Note:
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1086 <p>
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1087 <s xml:id="echoid-s63" xml:space="preserve">
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1088 Here Harriot appears to be devising new words for a counting system,
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1089 with systematic endings for each new power of ten.
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1090 In the first paragraph the basic numerals are: en, ben, tren, quen, quin, sinus, spinus, ...,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1091 which bear some resemblance to number words in languages derived from Latin,
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1092 but in the second paragraph Harriot has adopted an alphabetical system: hon, an, ban, can, dan, .....
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1093 </s>
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1094 </p>
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1095 </emph>]
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1096 <lb/><lb/></s></p></div>
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1097 <p>
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1098 <s xml:id="echoid-s65" xml:space="preserve">
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1099 en ogen otem otille. emes emies illies <lb/>
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1100 ben Begen Beten Betillia <lb/>
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1101 tren trigen tritem tritilla <lb/>
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1102 quen quagen quatem quatiliia <lb/>
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1103 quinus quigen quitem quitillia <lb/>
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1104 sinus sigen sitem sigillia <lb/>
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1105 spinus spigen spitem spigillia
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1106 </s>
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1107 </p>
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1108 <p>
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1109 <s xml:id="echoid-s66" xml:space="preserve">
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1110 homilantu hoceman holeman honan holemil hobemil homil hocen hoben hon <lb/>
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1111 amilantu aceman abeman anan acamil abemil amill acen aben an <lb/>
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1112 cabeman banan bucemil cabemil bumilli bacen baben ban <lb/>
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1113 cacen caben can <lb/>
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1114 dacen daben dan <lb/>
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1115 ecen eben en <lb/>
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1116 fecen feben fen <lb/>
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1117 gecen geben gen
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1118 </s>
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1119 </p>
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1120 <pb file="add_6786_f303v" o="303v" n="606"/>
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1121 <pb file="add_6786_f304" o="304" n="607"/>
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1122 <pb file="add_6786_f304v" o="304v" n="608"/>
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1123 <pb file="add_6786_f305" o="305" n="609"/>
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1124 <pb file="add_6786_f305v" o="305v" n="610"/>
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1125 <pb file="add_6786_f306" o="306" n="611"/>
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1126 <pb file="add_6786_f306v" o="306v" n="612"/>
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1127 <pb file="add_6786_f307" o="307" n="613"/>
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1128 <pb file="add_6786_f307v" o="307v" n="614"/>
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1129 <pb file="add_6786_f308" o="308" n="615"/>
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1130 <pb file="add_6786_f308v" o="308v" n="616"/>
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1131 <pb file="add_6786_f309" o="309" n="617"/>
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1132 <pb file="add_6786_f309v" o="309v" n="618"/>
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1133 <pb file="add_6786_f310" o="310" n="619"/>
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1134 <pb file="add_6786_f310v" o="310v" n="620"/>
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1135 <pb file="add_6786_f311" o="311" n="621"/>
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1136 <pb file="add_6786_f311v" o="311v" n="622"/>
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1137 <pb file="add_6786_f312" o="312" n="623"/>
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1138 <pb file="add_6786_f312v" o="312v" n="624"/>
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1139 <pb file="add_6786_f313" o="313" n="625"/>
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1140 <pb file="add_6786_f313v" o="313v" n="626"/>
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1141 <pb file="add_6786_f314" o="314" n="627"/>
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1142 <pb file="add_6786_f314v" o="314v" n="628"/>
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1143 <pb file="add_6786_f315" o="315" n="629"/>
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1144 <pb file="add_6786_f315v" o="315v" n="630"/>
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1145 <pb file="add_6786_f316" o="316" n="631"/>
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1146 <pb file="add_6786_f316v" o="316v" n="632"/>
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1147 <p>
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1148 <s xml:id="echoid-s67" xml:space="preserve">
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1149 STevin problemata <lb/>
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1150 Pappus <lb/>
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1151 Apollonius <lb/>
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1152 Clavius
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1153 </s>
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1154 </p>
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1155 <pb file="add_6786_f317" o="317" n="633"/>
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1156 <div xml:id="echoid-div14" type="page_commentary" level="2" n="14">
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1157 <p>
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1158 <s xml:id="echoid-s68" xml:space="preserve">[<emph style="it">Note:
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1159 <p>
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1160 <s xml:id="echoid-s68" xml:space="preserve">
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1161 This page lists and compares the definitions in Book V of Euclid's <emph style="it">Elements</emph>,
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1162 as given by: <lb/>
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1163 Federico Commandino, <emph style="it">Euclidis Elementorum libri XV</emph> (1572), <lb/>
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1164 Christophor Clavius, <emph style="it">Euclidis Elementorum libri XV</emph> (1574, 1589, 1591, 1603, 1607), <lb/>
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1165 and unnamed Greek writers.
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1166 </s>
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1167 </p>
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1168 </emph>]
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1169 <lb/><lb/></s></p></div>
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1170 <head xml:id="echoid-head8" xml:space="preserve" xml:lang="lat">
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1171 Definitionies Quinti libri
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1172 <lb/>[<emph style="it">tr:
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1173 Definitions in the fifth book
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1174 </emph>]<lb/>
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1175 </head>
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1176 <p xml:lang="lat">
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1177 <s xml:id="echoid-s70" xml:space="preserve">
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1178 Comandinus
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1179 </s>
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1180 <lb/>
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1181 <s xml:id="echoid-s71" xml:space="preserve">
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1182 Græces prior
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1183 <lb/>[<emph style="it">tr:
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1184 Earlier Greeks
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1185 </emph>]<lb/>
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1186 </s>
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1187 <lb/>
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1188 <s xml:id="echoid-s72" xml:space="preserve">
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1189 Clavius
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1190 </s>
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1191 </p>
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1192 <pb file="add_6786_f317v" o="317v" n="634"/>
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1193 <div xml:id="echoid-div15" type="page_commentary" level="2" n="15">
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1194 <p>
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1195 <s xml:id="echoid-s73" xml:space="preserve">[<emph style="it">Note:
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1196 <p>
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1197 <s xml:id="echoid-s73" xml:space="preserve">
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1198 A rough attempt at an analysis of teh contents and structure of Eculid's
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1199 <emph style="it">Elements</emph>, Book I.
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1200 For a more polished version see Add MS 6785, f. 337.
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1201 </s>
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1202 </p>
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1203 </emph>]
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1204 <lb/><lb/></s></p></div>
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1205 <pb file="add_6786_f318" o="318" n="635"/>
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1206 <pb file="add_6786_f318v" o="318v" n="636"/>
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1207 <pb file="add_6786_f319" o="319" n="637"/>
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1208 <pb file="add_6786_f319v" o="319v" n="638"/>
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1209 <pb file="add_6786_f320" o="320" n="639"/>
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1210 <pb file="add_6786_f320v" o="320v" n="640"/>
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1211 <pb file="add_6786_f321" o="321" n="641"/>
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1212 <div xml:id="echoid-div16" type="page_commentary" level="2" n="16">
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1213 <p>
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1214 <s xml:id="echoid-s75" xml:space="preserve">[<emph style="it">Note:
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1215 <p>
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1216 <s xml:id="echoid-s75" xml:space="preserve">
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1217 The third line is very nearly an anagram of the first; neither makes much sense in its own right.
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1218 For frequency analyses of the letters see Add MS 6788, f. 251v and Add MS 6789, f, 456.
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1219 </s>
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1220 </p>
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1221 </emph>]
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1222 <lb/><lb/></s></p></div>
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1223 <p xml:lang="lat">
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1224 <s xml:id="echoid-s77" xml:space="preserve">
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1225 Sum mutatus amati mire præ sole lumen abigui <lb/>
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1226 musa mutata mutis. <lb/>
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1227 Sumamus amemus præbet illum origine Titan.
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1228 </s>
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1229 </p>
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1230 <pb file="add_6786_f321v" o="321v" n="642"/>
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1231 <pb file="add_6786_f322" o="322" n="643"/>
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1232 <pb file="add_6786_f322v" o="322v" n="644"/>
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1233 <pb file="add_6786_f323" o="323" n="645"/>
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1234 <pb file="add_6786_f323v" o="323v" n="646"/>
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1235 <pb file="add_6786_f324" o="324" n="647"/>
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1236 <pb file="add_6786_f324v" o="324v" n="648"/>
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1237 <pb file="add_6786_f325" o="325" n="649"/>
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1238 <pb file="add_6786_f325v" o="325v" n="650"/>
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1239 <pb file="add_6786_f326" o="326" n="651"/>
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1240 <pb file="add_6786_f326v" o="326v" n="652"/>
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1241 <pb file="add_6786_f327" o="327" n="653"/>
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1242 <pb file="add_6786_f327v" o="327v" n="654"/>
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1243 <pb file="add_6786_f328" o="328" n="655"/>
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1244 <pb file="add_6786_f328v" o="328v" n="656"/>
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1245 <pb file="add_6786_f329" o="329" n="657"/>
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diff changeset
1246 <pb file="add_6786_f329v" o="329v" n="658"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1247 <pb file="add_6786_f330" o="330" n="659"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1248 <pb file="add_6786_f330v" o="330v" n="660"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1249 <pb file="add_6786_f331" o="331" n="661"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1250 <pb file="add_6786_f331v" o="331v" n="662"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1251 <pb file="add_6786_f332" o="332" n="663"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1252 <pb file="add_6786_f332v" o="332v" n="664"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1253 <pb file="add_6786_f333" o="333" n="665"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1254 <pb file="add_6786_f333v" o="333v" n="666"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1255 <div xml:id="echoid-div17" type="page_commentary" level="2" n="17">
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diff changeset
1256 <p>
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diff changeset
1257 <s xml:id="echoid-s78" xml:space="preserve">[<emph style="it">Note:
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diff changeset
1258 <p>
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diff changeset
1259 <s xml:id="echoid-s78" xml:space="preserve">
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diff changeset
1260 A double-page calculation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mo maxsize="1">(</mo><mn>2</mn><mo>+</mo><msqrt><mrow><mn>2</mn></mrow></msqrt></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1261 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1262 </p>
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diff changeset
1263 </emph>]
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diff changeset
1264 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1265 <pb file="add_6786_f334" o="334" n="667"/>
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1266 <pb file="add_6786_f334v" o="334v" n="668"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1267 <div xml:id="echoid-div18" type="page_commentary" level="2" n="18">
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1268 <p>
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1269 <s xml:id="echoid-s80" xml:space="preserve">[<emph style="it">Note:
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diff changeset
1270 <p>
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1271 <s xml:id="echoid-s80" xml:space="preserve">
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diff changeset
1272 A calculation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mo maxsize="1">(</mo><mn>2</mn><mo>+</mo><msqrt><mrow><mn>2</mn></mrow></msqrt></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1273 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1274 </p>
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1275 </emph>]
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diff changeset
1276 <lb/><lb/></s></p></div>
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1277 <pb file="add_6786_f335" o="335" n="669"/>
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1278 <pb file="add_6786_f335v" o="335v" n="670"/>
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1279 <pb file="add_6786_f336" o="336" n="671"/>
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1280 <pb file="add_6786_f336v" o="336v" n="672"/>
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1281 <pb file="add_6786_f337" o="337" n="673"/>
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1282 <pb file="add_6786_f337v" o="337v" n="674"/>
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1283 <pb file="add_6786_f338" o="338" n="675"/>
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1284 <pb file="add_6786_f338v" o="338v" n="676"/>
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1285 <pb file="add_6786_f339" o="339" n="677"/>
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1286 <pb file="add_6786_f339v" o="339v" n="678"/>
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1287 <pb file="add_6786_f340" o="340" n="679"/>
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1288 <pb file="add_6786_f340v" o="340v" n="680"/>
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1289 <pb file="add_6786_f341" o="341" n="681"/>
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1290 <pb file="add_6786_f341v" o="341v" n="682"/>
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1291 <pb file="add_6786_f342" o="342" n="683"/>
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1292 <pb file="add_6786_f342v" o="342v" n="684"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1293 <pb file="add_6786_f343" o="343" n="685"/>
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1294 <pb file="add_6786_f343v" o="343v" n="686"/>
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1295 <pb file="add_6786_f344" o="344" n="687"/>
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1296 <pb file="add_6786_f344v" o="344v" n="688"/>
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1297 <pb file="add_6786_f345" o="345" n="689"/>
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1298 <pb file="add_6786_f345v" o="345v" n="690"/>
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1299 <pb file="add_6786_f346" o="346" n="691"/>
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1300 <pb file="add_6786_f346v" o="346v" n="692"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1301 <div xml:id="echoid-div19" type="page_commentary" level="2" n="19">
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1302 <p>
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1303 <s xml:id="echoid-s82" xml:space="preserve">[<emph style="it">Note:
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1304 <p>
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1305 <s xml:id="echoid-s82" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1306 The reduction shows that 1101101 represents 64 + 32 + 8 + 4 + 1 = 109. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1307 Conversely, breaking down 109 into 64 + 32 + 8 + 4 + 1 shows that its binary representation is 1101101.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1308 </s>
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1309 </p>
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1310 </emph>]
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1311 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1312 <p xml:lang="lat">
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1313 <s xml:id="echoid-s84" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1314 Reductio. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1315 <lb/>[<emph style="it">tr:
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1316 Reduction.
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1317 </emph>]<lb/>
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1318 </s>
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1319 </p>
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1320 <p xml:lang="lat">
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1321 <s xml:id="echoid-s85" xml:space="preserve">
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1322 Conversio <lb/>
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1323 <lb/>[<emph style="it">tr:
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1324 Converse
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1325 </emph>]<lb/>
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1326 </s>
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1327 </p>
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1328 <pb file="add_6786_f347" o="347" n="693"/>
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1329 <div xml:id="echoid-div20" type="page_commentary" level="2" n="20">
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1330 <p>
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1331 <s xml:id="echoid-s86" xml:space="preserve">[<emph style="it">Note:
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1332 <p>
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1333 <s xml:id="echoid-s86" xml:space="preserve">
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1334 Examples of binary subtraction, addition, and multiplication,
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1335 the latter done both directly and by successive addition.
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1336 </s>
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1337 </p>
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1338 </emph>]
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1339 <lb/><lb/></s></p></div>
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1340 <p xml:lang="lat">
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1341 <s xml:id="echoid-s88" xml:space="preserve">
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1342 <emph style="st">Additionis</emph> <emph style="super">Subductionis</emph> exempla.
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1343 <lb/>[<emph style="it">tr:
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1344 An example of <emph style="st">addition</emph> <emph style="super">subtraction</emph>.
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1345 </emph>]<lb/>
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1346 </s>
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1347 </p>
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1348 <p xml:lang="lat">
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1349 <s xml:id="echoid-s89" xml:space="preserve">
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1350 Additionis Exempla.
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1351 <lb/>[<emph style="it">tr:
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1352 An example of addition.
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1353 </emph>]<lb/>
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1354 </s>
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1355 </p>
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1356 <p xml:lang="lat">
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1357 <s xml:id="echoid-s90" xml:space="preserve">
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1358 Multiplicatio.
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1359 <lb/>[<emph style="it">tr:
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1360 Multiplication.
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1361 </emph>]<lb/>
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1362 </s>
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1363 </p>
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1364 <p xml:lang="lat">
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1365 <s xml:id="echoid-s91" xml:space="preserve">
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1366 Aliter, cum additionem <lb/>
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1367 successiva.
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1368 <lb/>[<emph style="it">tr:
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1369 Another way, as successive addition.
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1370 </emph>]<lb/>
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1371 </s>
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1372 </p>
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1373 <pb file="add_6786_f347v" o="347v" n="694"/>
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1374 <pb file="add_6786_f348" o="348" n="695"/>
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1375 <div xml:id="echoid-div21" type="page_commentary" level="2" n="21">
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1376 <p>
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1377 <s xml:id="echoid-s92" xml:space="preserve">[<emph style="it">Note:
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1378 <p>
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1379 <s xml:id="echoid-s92" xml:space="preserve">
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1380 A list of numbers, names, and dates.
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1381 </s>
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1382 </p>
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1383 </emph>]
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1384 <lb/><lb/></s></p></div>
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1385 <p>
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1386 <s xml:id="echoid-s94" xml:space="preserve">
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1387 202. Iantgennius Hessiæ. No. 11 <lb/>
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1388 245. [???] 12. No. <lb/>
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1389 249. <lb/>
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1390 250. 12. oct. <lb/>
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1391 288. Cornelius Gemma. 14. N. <lb/>
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1392 306. Ræslin. <lb/>
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1393 320. Hagesius. 10. N. <lb/>
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1394 369. Scultetus. <lb/>
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1395 425. Nolthinus. <lb/>
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1396 438. Winklerus. <lb/>
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1397 448. alij multi.
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1398 </s>
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1399 </p>
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1400 <pb file="add_6786_f348v" o="348v" n="696"/>
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1401 <pb file="add_6786_f349" o="349" n="697"/>
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1402 <pb file="add_6786_f349v" o="349v" n="698"/>
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1403 <p>
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1404 <s xml:id="echoid-s95" xml:space="preserve">
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1405 Gordianus Nodus. <lb/>
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1406 Labyrinthus Dædali. <lb/>
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1407 Clava Herculis. Democritus his reason pro atomis. <lb/>
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1408 Achilles. [???] reason. <lb/>
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1409 Cerberus. <lb/>
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1410 Tenebræ Farturea. <lb/>
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1411 Cimmeriæ tenebræ. <lb/>
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1412 Tentyritæ crcodilos non timent.
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1413 </s>
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1414 </p>
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1415 <p>
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1416 <s xml:id="echoid-s96" xml:space="preserve">
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1417 The problem of a rectilinear rumbe <lb/>
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1418 infinitely turning about the center <lb/>
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1419 and yet the line finite to be moved <lb/>
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1420 in an hour or any other given time to <lb/>
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1421 be made <lb/>
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1422 double to <lb/>
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1423 passe to two <lb/>
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1424 corners.
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1425 </s>
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1426 </p>
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1427 <pb file="add_6786_f350" o="350" n="699"/>
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1428 <pb file="add_6786_f350v" o="350v" n="700"/>
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1429 <pb file="add_6786_f351" o="351" n="701"/>
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1430 <pb file="add_6786_f351v" o="351v" n="702"/>
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1431 <pb file="add_6786_f352" o="352" n="703"/>
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1432 <pb file="add_6786_f352v" o="352v" n="704"/>
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1433 <pb file="add_6786_f353" o="353" n="705"/>
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1434 <pb file="add_6786_f353v" o="353v" n="706"/>
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1435 <pb file="add_6786_f354" o="354" n="707"/>
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1436 <pb file="add_6786_f354v" o="354v" n="708"/>
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1437 <pb file="add_6786_f355" o="355" n="709"/>
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1438 <pb file="add_6786_f355v" o="355v" n="710"/>
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1439 <pb file="add_6786_f356" o="356" n="711"/>
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1440 <pb file="add_6786_f356v" o="356v" n="712"/>
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1441 <pb file="add_6786_f357" o="357" n="713"/>
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1442 <pb file="add_6786_f357v" o="357v" n="714"/>
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1443 <pb file="add_6786_f358" o="358" n="715"/>
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1444 <pb file="add_6786_f358v" o="358v" n="716"/>
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1445 <pb file="add_6786_f359" o="359" n="717"/>
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1446 <pb file="add_6786_f359v" o="359v" n="718"/>
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1447 <pb file="add_6786_f360" o="360" n="719"/>
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1448 <pb file="add_6786_f360v" o="360v" n="720"/>
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1449 <pb file="add_6786_f361" o="361" n="721"/>
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1450 <pb file="add_6786_f361v" o="361v" n="722"/>
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1451 <pb file="add_6786_f362" o="362" n="723"/>
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1452 <pb file="add_6786_f362v" o="362v" n="724"/>
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1453 <pb file="add_6786_f363" o="363" n="725"/>
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1454 <pb file="add_6786_f363v" o="363v" n="726"/>
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1455 <pb file="add_6786_f364" o="364" n="727"/>
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1456 <pb file="add_6786_f364v" o="364v" n="728"/>
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1457 <pb file="add_6786_f365" o="365" n="729"/>
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1458 <div xml:id="echoid-div22" type="page_commentary" level="2" n="22">
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1459 <p>
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1460 <s xml:id="echoid-s97" xml:space="preserve">[<emph style="it">Note:
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1461 <p>
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1462 <s xml:id="echoid-s97" xml:space="preserve">
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1463 Diagrams representing various combinations of points (.), lines (-), and circles (o).
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1464 </s>
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1465 </p>
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1466 </emph>]
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1467 <lb/><lb/></s></p></div>
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1468 <p xml:lang="lat">
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1469 <s xml:id="echoid-s99" xml:space="preserve">
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1470 melius
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1471 <lb/>[<emph style="it">tr:
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1472 better
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1473 </emph>]<lb/>
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1474 </s>
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1475 </p>
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1476 <pb file="add_6786_f365v" o="365v" n="730"/>
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1477 <pb file="add_6786_f366" o="366" n="731"/>
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1478 <pb file="add_6786_f366v" o="366v" n="732"/>
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1479 <pb file="add_6786_f367" o="367" n="733"/>
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1480 <pb file="add_6786_f367v" o="367v" n="734"/>
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1481 <pb file="add_6786_f368" o="368" n="735"/>
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1482 <pb file="add_6786_f368v" o="368v" n="736"/>
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1483 <pb file="add_6786_f369" o="369" n="737"/>
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1484 <div xml:id="echoid-div23" type="page_commentary" level="2" n="23">
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1485 <p>
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1486 <s xml:id="echoid-s100" xml:space="preserve">[<emph style="it">Note:
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1487 <p>
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1488 <s xml:id="echoid-s100" xml:space="preserve">
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1489 A plan for supplying water to a number of areas and buildings,
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1490 including one that appears to be for Harriot's personal use.
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1491 </s>
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1492 </p>
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1493 </emph>]
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1494 <lb/><lb/></s></p></div>
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1495 <p>
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1496 <s xml:id="echoid-s102" xml:space="preserve">
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1497 cestern in the bathing room <lb/>
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1498 cellar <lb/>
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1499 cellar <lb/>
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1500 privye <lb/>
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1501 laundry <lb/>
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1502 privy T. H. <lb/>
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1503 The Stables <lb/>
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1504 a cesperall for emptying the pipes <lb/>
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1505 the plane <lb/>
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1506 The farme <lb/>
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1507 S. F. Darcy of Think <lb/>
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1508 The Spring Seat
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1509 </s>
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1510 </p>
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1511 <pb file="add_6786_f369v" o="369v" n="738"/>
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1512 <pb file="add_6786_f370" o="370" n="739"/>
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1513 <pb file="add_6786_f370v" o="370v" n="740"/>
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1514 <pb file="add_6786_f371" o="371" n="741"/>
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1515 <pb file="add_6786_f371v" o="371v" n="742"/>
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1516 <pb file="add_6786_f372" o="372" n="743"/>
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1517 <pb file="add_6786_f372v" o="372v" n="744"/>
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1518 <pb file="add_6786_f373" o="373" n="745"/>
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1519 <pb file="add_6786_f373v" o="373v" n="746"/>
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1520 <pb file="add_6786_f374" o="374" n="747"/>
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1521 <pb file="add_6786_f374v" o="374v" n="748"/>
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1522 <pb file="add_6786_f375" o="375" n="749"/>
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1523 <pb file="add_6786_f375v" o="375v" n="750"/>
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1524 <div xml:id="echoid-div24" type="page_commentary" level="2" n="24">
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1525 <p>
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1526 <s xml:id="echoid-s103" xml:space="preserve">[<emph style="it">Note:
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1527 <p>
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1528 <s xml:id="echoid-s103" xml:space="preserve">
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1529 This large folded sheet (f. 375v–376) is one of the few papers that Harriot dated: 12 December 1591.
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1530 It is concerned with the piling of bullets, for which two questions naturally arise:
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1531 1. Given the number of bullets and the required shape of the base, how many bullets must be placed at each level,
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1532 and how many levels?
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1533 2. Given a pile of a certain shape, how many bullets does it contain?
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1534 <lb/>
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1535 (a) Square and oblong numbers: <lb/>
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1536 The numbers 1, 2, 3, 4, ... down the key diagonal indicate the length of the shorter side of the base,
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1537 and therefore also the height of the pyramid. <lb/>
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1538 The numbers 1, 2, 3, 4, ... along the top indicate the length of the longer side of the base. <lb/>
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1539 Thus for an oblong pyramid on a 3 x 7 base,
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1540 move right from 3 in the key diagonal and down from 7 on the top line.
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diff changeset
1541 The entries in the appropriate square show that there are 21 bullets in the base and 38 in the pyramid as a whole. <lb/>
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1542 In particular, the square pyramidal numbers 1, 5, 14, 30, 55, 91 ...
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1543 appear in the squares immediately to the right of the key diagonal;
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diff changeset
1544 thus a square pyramid with base 3 x 3 has 9 bullets in its base and 14 bullets in total.
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1545 <lb/>
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1546 (b) Triangular numbers: <lb/>
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1547 The triangular pyramidal numbers 1, 4, 10, 20, 35, ...
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1548 appear as the lower entries in the squares below and to the left of the key diagonal,
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1549 to which they are joined by short lines.
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1550 Thus a triangular pyramid with three levels contains 6 bullets in its base and 10 bullets in total.
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diff changeset
1551 As Harriot points out in his note on f. 376, the triangular numbers 1, 3, 6, 10, 15, ...
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1552 may be read off as the differences of the oblong numbers in the previous row.
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1553 Conversely, the entire table can be generated by successive addition from the triangular and square numbers.
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1554 </s>
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1555 </p>
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1556 </emph>]
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1557 <lb/><lb/></s></p></div>
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1558 <p>
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1559 <s xml:id="echoid-s105" xml:space="preserve">
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1560 These are those speciall <lb/>
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1561 groundplats upon the which <lb/>
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1562 may be orderly piled bullets: <lb/>
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1563 The triangle: the square: and <lb/>
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1564 the oblonge.
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1565 </s>
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1566 </p>
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1567 <p>
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1568 <s xml:id="echoid-s106" xml:space="preserve">
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1569 Concerning piling there are two <lb/>
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1570 questions: one <emph style="st">which</emph> the nomber <lb/>
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1571 of bullets to be piled being given <lb/>
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1572 with the forme of the groundplat, <lb/>
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1573 to know how many must be placed <lb/>
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1574 in every rounde, with how many <lb/>
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1575 roundes in the sayd groundplat.
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1576 </s>
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1577 </p>
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1578 <pb file="add_6786_f376" o="376" n="751"/>
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1579 <p>
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1580 <s xml:id="echoid-s107" xml:space="preserve">
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1581 The second a pile being made to knowe <lb/>
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1582 the number of bullets therein conteyned. <lb/>
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1583 For the awnswering of which two questions <lb/>
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1584 this table of some <emph style="st">set downe</emph> calculations
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1585 for <emph style="st">for </emph> the purpose. December. 12. 1591.
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1586 </s>
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1587 </p>
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1588 <p>
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1589 <s xml:id="echoid-s108" xml:space="preserve">
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1590 The forme of the progression of the triangle row <lb/>
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1591 is the excesse of the progression <emph style="st">of the</emph> of the <lb/>
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1592 <emph style="st">square</emph> <emph style="super">oblong</emph> plats next adjoyning above.
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1593 </s>
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1594 <lb/>
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1595 <s xml:id="echoid-s109" xml:space="preserve">
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1596 as. 10 of 30, 40, 50 &amp;c. <lb/>
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1597 or. 15 of 55, 70, 85, &amp;c.
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1598 </s>
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1599 <lb/>
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1600 <s xml:id="echoid-s110" xml:space="preserve">
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1601 Thereby the squares &amp; triangles being knowne <lb/>
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1602 <emph style="st">all</emph> <emph style="super">any of</emph> the oblongs may be knowne by rule.
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1603 </s>
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1604 </p>
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1605 <pb file="add_6786_f376v" o="376v" n="752"/>
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1606 <pb file="add_6786_f377" o="377" n="753"/>
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1607 <div xml:id="echoid-div25" type="page_commentary" level="2" n="25">
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1608 <p>
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1609 <s xml:id="echoid-s111" xml:space="preserve">[<emph style="it">Note:
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1610 <p>
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1611 <s xml:id="echoid-s111" xml:space="preserve">
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1612 Arrangements of dots as singletons or pairs in rows of four. <lb/>
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1613 Perhaps a counting system in base 16?
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1614 </s>
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1615 </p>
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1616 </emph>]
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1617 <lb/><lb/></s></p></div>
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1618 <pb file="add_6786_f377v" o="377v" n="754"/>
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1619 <pb file="add_6786_f378" o="378" n="755"/>
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1620 <div xml:id="echoid-div26" type="page_commentary" level="2" n="26">
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1621 <p>
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1622 <s xml:id="echoid-s113" xml:space="preserve">[<emph style="it">Note:
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1623 <p>
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1624 <s xml:id="echoid-s113" xml:space="preserve">
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1625 Arrangements of dots in pattersn similar to those on the previous folio (Add MS 6786, f. 377),
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1626 now also in conjunction with signs of the zodiac.
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1627 </s>
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1628 </p>
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1629 </emph>]
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1630 <lb/><lb/></s></p></div>
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1631 <pb file="add_6786_f378v" o="378v" n="756"/>
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1632 <div xml:id="echoid-div27" type="page_commentary" level="2" n="27">
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1633 <p>
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1634 <s xml:id="echoid-s115" xml:space="preserve">[<emph style="it">Note:
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1635 <p>
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1636 <s xml:id="echoid-s115" xml:space="preserve">
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1637 Arrangements of dots in patterns similar to those on the previous folio (Add MS 6786, f. 377),
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1638 now arranged in a circle.
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1639 </s>
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1640 </p>
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1641 </emph>]
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1642 <lb/><lb/></s></p></div>
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1643 <pb file="add_6786_f379" o="379" n="757"/>
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1644 <pb file="add_6786_f379v" o="379v" n="758"/>
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1645 <pb file="add_6786_f380" o="380" n="759"/>
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1646 <pb file="add_6786_f380v" o="380v" n="760"/>
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1647 <pb file="add_6786_f381" o="381" n="761"/>
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1648 <pb file="add_6786_f381v" o="381v" n="762"/>
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1649 <pb file="add_6786_f382" o="382" n="763"/>
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1650 <pb file="add_6786_f382v" o="382v" n="764"/>
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1651 <pb file="add_6786_f383" o="383" n="765"/>
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1652 <pb file="add_6786_f383v" o="383v" n="766"/>
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1653 <pb file="add_6786_f384" o="384" n="767"/>
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1654 <pb file="add_6786_f384v" o="384v" n="768"/>
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1655 <pb file="add_6786_f385" o="385" n="769"/>
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1656 <pb file="add_6786_f385v" o="385v" n="770"/>
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1657 <pb file="add_6786_f386" o="386" n="771"/>
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1658 <pb file="add_6786_f386v" o="386v" n="772"/>
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1659 <pb file="add_6786_f387" o="387" n="773"/>
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1660 <pb file="add_6786_f387v" o="387v" n="774"/>
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1661 <pb file="add_6786_f388" o="388" n="775"/>
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1662 <pb file="add_6786_f388v" o="388v" n="776"/>
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1663 <div xml:id="echoid-div28" type="page_commentary" level="2" n="28">
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1664 <p>
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1665 <s xml:id="echoid-s117" xml:space="preserve">[<emph style="it">Note:
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1666 <p>
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1667 <s xml:id="echoid-s117" xml:space="preserve">
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1668 Some examples of Stevin's notation.
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1669 </s>
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1670 </p>
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1671 </emph>]
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1672 <lb/><lb/></s></p></div>
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1673 <pb file="add_6786_f389" o="389" n="777"/>
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1674 <pb file="add_6786_f389v" o="389v" n="778"/>
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1675 <pb file="add_6786_f390" o="390" n="779"/>
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1676 <pb file="add_6786_f390v" o="390v" n="780"/>
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1677 <pb file="add_6786_f391" o="391" n="781"/>
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1678 <pb file="add_6786_f391v" o="391v" n="782"/>
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1679 <pb file="add_6786_f392" o="392" n="783"/>
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1680 <pb file="add_6786_f392v" o="392v" n="784"/>
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1681 <pb file="add_6786_f393" o="393" n="785"/>
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1682 <pb file="add_6786_f393v" o="393v" n="786"/>
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1683 <pb file="add_6786_f394" o="394" n="787"/>
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1684 <div xml:id="echoid-div29" type="page_commentary" level="2" n="29">
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1685 <p>
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1686 <s xml:id="echoid-s119" xml:space="preserve">[<emph style="it">Note:
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1687 <p>
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1688 <s xml:id="echoid-s119" xml:space="preserve">
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1689 A set of Napier's bones, and some calculations.
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1690 </s>
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1691 </p>
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1692 </emph>]
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1693 <lb/><lb/></s></p></div>
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1694 <pb file="add_6786_f394v" o="394v" n="788"/>
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1695 <div xml:id="echoid-div30" type="page_commentary" level="2" n="30">
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1696 <p>
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1697 <s xml:id="echoid-s121" xml:space="preserve">[<emph style="it">Note:
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1698 <p>
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1699 <s xml:id="echoid-s121" xml:space="preserve">
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1700 Calculations using Napier's bones, continued from overleaf Add MS 6786, f. 394.
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1701 </s>
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1702 </p>
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1703 </emph>]
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1704 <lb/><lb/></s></p></div>
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1705 <pb file="add_6786_f395" o="395" n="789"/>
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1706 <pb file="add_6786_f395v" o="395v" n="790"/>
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1707 <pb file="add_6786_f396" o="396" n="791"/>
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1708 <pb file="add_6786_f396v" o="396v" n="792"/>
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1709 <pb file="add_6786_f397" o="397" n="793"/>
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1710 <pb file="add_6786_f397v" o="397v" n="794"/>
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1711 <pb file="add_6786_f398" o="398" n="795"/>
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1712 <p>
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1713 <s xml:id="echoid-s123" xml:space="preserve">
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1714 <sc>
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1715 One chain is 4 poles. One pole is 5.5 yards, or 198 inches.
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1716 </sc>
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1717 792 inches, 4 poles; the length of the chayne.
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1718 </s>
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1719 <lb/>
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1720 <s xml:id="echoid-s124" xml:space="preserve">
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1721 7920 tenths of an inch; 4 poles: or length of the chayne.
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1722 </s>
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1723 <lb/>
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1724 <s xml:id="echoid-s125" xml:space="preserve">
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1725 792 tenths or: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><mn>7</mn><mn>9</mn><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mrow></mstyle></math> inches or 6 foot 7 inches <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mstyle></math> of inches; is <lb/>
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1726 for one tenth parte of the chayne.
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1727 </s>
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1728 <lb/>
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1729 <s xml:id="echoid-s126" xml:space="preserve">
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1730 one of those partes must be divided into 10 <lb/>
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1731 other partes
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1732 </s>
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1733 </p>
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1734 <pb file="add_6786_f398v" o="398v" n="796"/>
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1735 <pb file="add_6786_f399" o="399" n="797"/>
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1736 <pb file="add_6786_f399v" o="399v" n="798"/>
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1737 <pb file="add_6786_f400" o="400" n="799"/>
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1738 <pb file="add_6786_f400v" o="400v" n="800"/>
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1739 <pb file="add_6786_f401" o="401" n="801"/>
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1740 <div xml:id="echoid-div31" type="page_commentary" level="2" n="31">
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1741 <p>
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1742 <s xml:id="echoid-s127" xml:space="preserve">[<emph style="it">Note:
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1743 <p>
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1744 <s xml:id="echoid-s127" xml:space="preserve">
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1745 This page referes to Stevin's <emph style="it">L 19arithmétique … aussi l 19algebre</emph>, page 306.
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1746 There Stevin solves the equation 1(3) = 6(1) + 40 (in modern notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo>=</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>4</mn><mn>0</mn></mstyle></math>),
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1747 leading to the cube roots writen down by Harriot at the top of the page.
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1748 </s>
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1749 </p>
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1750 </emph>]
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1751 <lb/><lb/></s></p></div>
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1752 <p>
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1753 <s xml:id="echoid-s129" xml:space="preserve">
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1754 √C.20 + √392 + √C.20 – √392. Stevin pag. <lb/>
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1755 306.
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1756 </s>
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1757 </p>
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1758 <pb file="add_6786_f401v" o="401v" n="802"/>
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1759 <pb file="add_6786_f402" o="402" n="803"/>
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1760 <pb file="add_6786_f402v" o="402v" n="804"/>
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1761 <pb file="add_6786_f403" o="403" n="805"/>
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1762 <pb file="add_6786_f403v" o="403v" n="806"/>
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1763 <pb file="add_6786_f404" o="404" n="807"/>
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1764 <pb file="add_6786_f404v" o="404v" n="808"/>
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1765 <pb file="add_6786_f405" o="405" n="809"/>
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1766 <p>
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1767 <s xml:id="echoid-s130" xml:space="preserve">
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1768 To set the elements of the doctrine of triangles <lb/>
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1769 as deviding of arke by the sines in <lb/>
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1770 datum rationum. &amp; doubling. <lb/>
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1771 The elements <emph style="super">by</emph> versed sines <lb/>
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1772 ut lat. ad lat. ita. signs aut. ad v. ang. <lb/>
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1773 &amp; the prosthephaeresis. <lb/>
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1774 in specie.
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1775 </s>
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1776 </p>
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1777 <p>
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1778 <s xml:id="echoid-s131" xml:space="preserve">
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1779 To set after the doctrine in species. <lb/>
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1780 &amp; in the forme of æquations, whereby <lb/>
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1781 the rules may be [???]: <lb/>
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1782 The compound numbers only <emph style="super">to be</emph> brought <lb/>
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1783 into one æquation.
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1784 </s>
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1785 </p>
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1786 <pb file="add_6786_f405v" o="405v" n="810"/>
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1787 <pb file="add_6786_f406" o="406" n="811"/>
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1788 <pb file="add_6786_f406v" o="406v" n="812"/>
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1789 <pb file="add_6786_f407" o="407" n="813"/>
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1790 <pb file="add_6786_f407v" o="407v" n="814"/>
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1791 <pb file="add_6786_f408" o="408" n="815"/>
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1792 <div xml:id="echoid-div32" type="page_commentary" level="2" n="32">
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1793 <p>
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1794 <s xml:id="echoid-s132" xml:space="preserve">[<emph style="it">Note:
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1795 <p>
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1796 <s xml:id="echoid-s132" xml:space="preserve">
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1797 The reference to Pappus is to Commandino's edition of Books III to VIII,
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1798 <emph style="it">Mathematicae collecitones</emph> (1558).
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1799 The proposition on page 47 is Proposition IV.14.
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1800 </s>
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1801 <lb/>
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1802 <quote xml:lang="lat">
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1803 Theorema XIIII. Propositio XIIII. <lb/>
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1804 Sint duo semicirculi BGC BED: &amp; ipsos contingat circulus EFGH: a cuius centro A ad BC basim semicirculorum
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1805 perpendicularis ducatur AM. Dico ut BM as eam, quæ ex centro circuli EFGH,
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1806 ita esse in prima figura vtramque simul CB BD ad earum excessum CD;
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1807 in secunda vero, &amp; tertia figura, ita esse excessum CB BD ad vtramque ipsarum CB BD.
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1808 </quote>
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1809 <lb/>
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1810 <quote>
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1811 Let there be two semicircles BGC and BED, and their touching circle EFGH, from whose centre A to BC,
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1812 the base of the semicircle, there is drawn the perpendicular AM.
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1813 I say that as BM is to that line from the centre of the circle EFGH,
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1814 inthe first figure will be CB and BD togher to their excess, CD;
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1815 but in the second and third figure, it will be as the excess of CB over BD to both of CB and BD together.
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1816 </quote>
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1817 <lb/>
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1818 <s xml:id="echoid-s133" xml:space="preserve">
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1819 For Harriot's diagrams for this proposition, see Add MS 6784, f. 203 and f. 204;
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1820 this page shows only calculations of ratios.
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1821 </s>
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1822 </p>
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1823 </emph>]
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1824 <lb/><lb/></s></p></div>
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1825 <head xml:id="echoid-head9" xml:space="preserve">
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1826 1) Pappus pag. 47
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1827 </head>
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1828 <pb file="add_6786_f408v" o="408v" n="816"/>
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1829 <pb file="add_6786_f409" o="409" n="817"/>
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1830 <pb file="add_6786_f409v" o="409v" n="818"/>
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1831 <pb file="add_6786_f410" o="410" n="819"/>
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1832 <div xml:id="echoid-div33" type="page_commentary" level="2" n="33">
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1833 <p>
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1834 <s xml:id="echoid-s135" xml:space="preserve">[<emph style="it">Note:
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1835 <p>
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1836 <s xml:id="echoid-s135" xml:space="preserve">
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1837 Rough working, similar to page 14 of the 'Magisteria' (Add MS 6782, f. 121).
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1838 </s>
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1839 </p>
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1840 </emph>]
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1841 <lb/><lb/></s></p></div>
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1842 <pb file="add_6786_f410v" o="410v" n="820"/>
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1843 <pb file="add_6786_f411" o="411" n="821"/>
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1844 <pb file="add_6786_f411v" o="411v" n="822"/>
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1845 <pb file="add_6786_f412" o="412" n="823"/>
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1846 <pb file="add_6786_f412v" o="412v" n="824"/>
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1847 <pb file="add_6786_f413" o="413" n="825"/>
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1848 <pb file="add_6786_f413v" o="413v" n="826"/>
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1849 <pb file="add_6786_f414" o="414" n="827"/>
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1850 <pb file="add_6786_f414v" o="414v" n="828"/>
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1851 <pb file="add_6786_f415" o="415" n="829"/>
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1852 <c>
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1853 Work on eliminating the linear term from an equation of degree 5.
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1854 </c>
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1855 <head xml:id="echoid-head10" xml:space="preserve">
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1856 bb<emph style="super">2</emph>
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1857 </head>
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1858 <pb file="add_6786_f415v" o="415v" n="830"/>
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1859 <pb file="add_6786_f416" o="416" n="831"/>
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1860 <pb file="add_6786_f416v" o="416v" n="832"/>
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1861 <pb file="add_6786_f417" o="417" n="833"/>
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1862 <div xml:id="echoid-div34" type="page_commentary" level="2" n="34">
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1863 <p>
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1864 <s xml:id="echoid-s137" xml:space="preserve">[<emph style="it">Note:
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1865 <p>
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1866 <s xml:id="echoid-s137" xml:space="preserve">
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1867 The numbers in the table at the top of the page are, from left to right:
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1868 units, lengths, triangular numbers, triangular-pyramidal numbers, and so on. <lb/>
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1869 The table in the centre of the page repeats the first and third columns from the table at the top,
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1870 but now the triangular numbers are written in multiplicative form, thus,
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1871 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>6</mn><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><mn>4</mn></mrow><mrow><mn>1</mn><mo>×</mo><mn>2</mn></mrow></mfrac></mstyle></math>. <lb/>
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1872 The third table gives all the rows in multiplicative form, thus in the seventh row,
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1873 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>8</mn><mn>4</mn><mo>=</mo><mfrac><mrow><mn>7</mn><mo>×</mo><mn>8</mn><mo>×</mo><mn>9</mn></mrow><mrow><mn>1</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>3</mn></mrow></mfrac></mstyle></math>. <lb/>
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1874 The final row gives general formulae for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>n</mi></mstyle></math>th row. <lb/>
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1875 See also page 1 of the 'Magisteria' (Add MS 6782, f. 108), for which this is possibly a draft.
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1876 </s>
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1877 </p>
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1878 </emph>]
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1879 <lb/><lb/></s></p></div>
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1880 <head xml:id="echoid-head11" xml:space="preserve" xml:lang="lat">
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1881 De numeris triangularibus.
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1882 </head>
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1883 <pb file="add_6786_f417v" o="417v" n="834"/>
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1884 <pb file="add_6786_f418" o="418" n="835"/>
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1885 <pb file="add_6786_f418v" o="418v" n="836"/>
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1886 <pb file="add_6786_f419" o="419" n="837"/>
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1887 <pb file="add_6786_f419v" o="419v" n="838"/>
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1888 <pb file="add_6786_f420" o="420" n="839"/>
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1889 <pb file="add_6786_f420v" o="420v" n="840"/>
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1890 <div xml:id="echoid-div35" type="page_commentary" level="2" n="35">
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1891 <p>
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1892 <s xml:id="echoid-s139" xml:space="preserve">[<emph style="it">Note:
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1893 <p>
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1894 <s xml:id="echoid-s139" xml:space="preserve">
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1895 Calulation of the number of days and hours in
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1896 (i) 235 lunar months; (ii) 19 solar years; (iii) Julian years,
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1897 and the differences between them.
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1898 </s>
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1899 </p>
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1900 </emph>]
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1901 <lb/><lb/></s></p></div>
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1902 <p xml:lang="lat">
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1903 <s xml:id="echoid-s141" xml:space="preserve">
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1904 235. Menses.
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1905 <lb/>[<emph style="it">tr:
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1906 235 lunar months.
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1907 </emph>]<lb/>
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1908 </s>
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1909 </p>
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1910 <p xml:lang="lat">
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1911 <s xml:id="echoid-s142" xml:space="preserve">
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1912 19. Solares.
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1913 <lb/>[<emph style="it">tr:
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1914 19 solar years.
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1915 </emph>]<lb/>
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1916 </s>
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1917 </p>
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1918 <p xml:lang="lat">
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1919 <s xml:id="echoid-s143" xml:space="preserve">
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1920 19. Juliani.
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1921 <lb/>[<emph style="it">tr:
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1922 19 Julian years.
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1923 </emph>]<lb/>
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1924 </s>
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1925 </p>
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1926 <pb file="add_6786_f421" o="421" n="841"/>
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1927 <div xml:id="echoid-div36" type="page_commentary" level="2" n="36">
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1928 <p>
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1929 <s xml:id="echoid-s144" xml:space="preserve">[<emph style="it">Note:
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1930 <p>
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1931 <s xml:id="echoid-s144" xml:space="preserve">
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1932 Further calculations relating lunar months to solar years.
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1933 </s>
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1934 </p>
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1935 </emph>]
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1936 <lb/><lb/></s></p></div>
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1937 <pb file="add_6786_f421v" o="421v" n="842"/>
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1938 <pb file="add_6786_f422" o="422" n="843"/>
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1939 <head xml:id="echoid-head12" xml:space="preserve">
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1940 Mercators map
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1941 </head>
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1942 <p>
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1943 <s xml:id="echoid-s146" xml:space="preserve">
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1944 Babilon
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1945 </s>
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1946 <lb/>
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1947 <s xml:id="echoid-s147" xml:space="preserve">
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1948 Alexandria
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1949 </s>
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1950 <lb/>
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1951 <s xml:id="echoid-s148" xml:space="preserve">
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1952 Jerusalem
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1953 </s>
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1954 </p>
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1955 <p>
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1956 <s xml:id="echoid-s149" xml:space="preserve">
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1957 London
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1958 </s>
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1959 <lb/>
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1960 <s xml:id="echoid-s150" xml:space="preserve">
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1961 Huena
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1962 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1963 <lb/>
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1964 <s xml:id="echoid-s151" xml:space="preserve">
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1965 Venetia
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1966 </s>
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1967 <lb/>
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1968 <s xml:id="echoid-s152" xml:space="preserve">
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1969 Praga
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1970 </s>
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1971 <lb/>
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1972 <s xml:id="echoid-s153" xml:space="preserve">
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1973 Roma
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1974 </s>
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1975 </p>
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1976 <p>
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1977 <s xml:id="echoid-s154" xml:space="preserve">
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1978 Ptol: geogr:
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1979 <lb/>[<emph style="it">tr:
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1980 Prolemy's geography
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1981 </emph>]<lb/>
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1982 </s>
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1983 <lb/>
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1984 <s xml:id="echoid-s155" xml:space="preserve">
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1985 Hierosolyma. long.
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1986 <lb/>[<emph style="it">tr:
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1987 Longitude of Jersualem
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1988 </emph>]<lb/>
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1989 </s>
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1990 <lb/>
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1991 <s xml:id="echoid-s156" xml:space="preserve">
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1992 Alexandria. long.
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1993 </s>
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1994 <lb/>
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1995 <s xml:id="echoid-s157" xml:space="preserve">
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1996 Babilon. long.
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1997 </s>
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1998 <lb/>
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1999 <s xml:id="echoid-s158" xml:space="preserve">
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2000 Roma. long.
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2001 </s>
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2002 <lb/>
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2003 <s xml:id="echoid-s159" xml:space="preserve">
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2004 Londinium. long.
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2005 </s>
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2006 </p>
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2007 <p>
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2008 <s xml:id="echoid-s160" xml:space="preserve">
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2009 Huena <lb/>
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2010 ab Alex:
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2011 </s>
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2012 </p>
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2013 <p>
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2014 <s xml:id="echoid-s161" xml:space="preserve">
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2015 Huena ab <lb/>
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2016 Alexand.
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2017 </s>
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2018 </p>
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2019 <p>
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2020 <s xml:id="echoid-s162" xml:space="preserve">
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2021 Huena <lb/>
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2022 ab Alex.
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2023 </s>
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2024 </p>
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2025 <p>
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2026 <s xml:id="echoid-s163" xml:space="preserve">
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2027 Huena a Londino
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2028 </s>
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2029 </p>
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2030 <p>
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2031 <s xml:id="echoid-s164" xml:space="preserve">
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2032 Huena <lb/>
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2033 ab Alex:
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2034 </s>
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diff changeset
2035 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2036 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2037 <s xml:id="echoid-s165" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2038 Tycho habet 1.35. diff. long <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2039 Huenæ ab Alex.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2040 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2041 Tycho has 1.35. as the difference in longitude betweeh Huena and Alexandria.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2042 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2043 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2044 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2045 <pb file="add_6786_f422v" o="422v" n="844"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2046 <pb file="add_6786_f423" o="423" n="845"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2047 <div xml:id="echoid-div37" type="page_commentary" level="2" n="37">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2048 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2049 <s xml:id="echoid-s166" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2050 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2051 <s xml:id="echoid-s166" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2052 Calculations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>7</mn><mo>.</mo><mn>8</mn><mn>6</mn><mn>9</mn><mn>6</mn><mn>0</mn><mn>4</mn><mn>4</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>=</mo><msqrt><mrow><mo maxsize="1">(</mo><mi>Ï€</mi><mrow><msup><mo maxsize="1">)</mo><mn>2</mn></msup></mrow><mo>-</mo><mn>2</mn></mrow></msqrt></mrow></msqrt></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2053 and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>5</mn><mo>.</mo><mn>8</mn><mn>6</mn><mn>9</mn><mn>6</mn><mn>0</mn><mn>4</mn><mn>4</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>=</mo><msqrt><mrow><mo maxsize="1">(</mo><mi>Ï€</mi><mrow><msup><mo maxsize="1">)</mo><mn>2</mn></msup></mrow><mo>-</mo><mn>4</mn></mrow></msqrt></mrow></msqrt></mstyle></math>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2054 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2055 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2056 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2057 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2058 <pb file="add_6786_f423v" o="423v" n="846"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2059 <div xml:id="echoid-div38" type="page_commentary" level="2" n="38">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2060 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2061 <s xml:id="echoid-s168" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2062 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2063 <s xml:id="echoid-s168" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2064 Calculations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>5</mn><mo>.</mo><mn>9</mn><mn>3</mn><mn>4</mn><mn>8</mn><mn>0</mn><mn>2</mn><mn>2</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>=</mo><msqrt><mrow><mfrac><mrow><mo maxsize="1">(</mo><mi>Ï€</mi><mrow><msup><mo maxsize="1">)</mo><mn>2</mn></msup></mrow><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msqrt></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2065 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2066 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2067 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2068 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2069 <pb file="add_6786_f424" o="424" n="847"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2070 <div xml:id="echoid-div39" type="page_commentary" level="2" n="39">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2071 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2072 <s xml:id="echoid-s170" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2073 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2074 <s xml:id="echoid-s170" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2075 Note that <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>9</mn><mo>.</mo><mn>8</mn><mn>6</mn><mn>9</mn><mn>6</mn><mn>0</mn><mn>4</mn><mn>4</mn><mo>=</mo><mo maxsize="1">(</mo><mi>Ï€</mi><mrow><msup><mo maxsize="1">)</mo><mn>2</mn></msup></mrow></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2076 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2077 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2078 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2079 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2080 <pb file="add_6786_f424v" o="424v" n="848"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2081 <div xml:id="echoid-div40" type="page_commentary" level="2" n="40">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2082 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2083 <s xml:id="echoid-s172" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2084 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2085 <s xml:id="echoid-s172" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2086 Calculations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mn>2</mn><mn>1</mn><mn>9</mn><mn>2</mn><mo>.</mo><mo>.</mo><mo>.</mo></mrow></msqrt></mstyle></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><msqrt><mrow><mn>2</mn><mn>5</mn><mo>.</mo><mn>9</mn><mn>3</mn><mn>5</mn><mn>2</mn><mn>7</mn><mo>.</mo><mo>.</mo><mo>.</mo></mrow></msqrt></mstyle></math>.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2087 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2088 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2089 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2090 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2091 <pb file="add_6786_f425" o="425" n="849"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2092 <pb file="add_6786_f425v" o="425v" n="850"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2093 <pb file="add_6786_f426" o="426" n="851"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2094 <pb file="add_6786_f426v" o="426v" n="852"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2095 <pb file="add_6786_f427" o="427" n="853"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2096 <pb file="add_6786_f427v" o="427v" n="854"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2097 <pb file="add_6786_f428" o="428" n="855"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2098 <pb file="add_6786_f428v" o="428v" n="856"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2099 <pb file="add_6786_f429" o="429" n="857"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2100 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2101 <s xml:id="echoid-s174" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2102 These wordes are written <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2103 with China inke. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2104 so likewise are these: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2105 But these are written with London inke.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2106 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2107 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2108 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2109 <s xml:id="echoid-s175" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2110 With China inke these wordes. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2111 With China inke these wordes. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2112 were written with thick <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2113 inke &amp;c.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2114 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2115 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2116 <pb file="add_6786_f429v" o="429v" n="858"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2117 <pb file="add_6786_f430" o="430" n="859"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2118 <pb file="add_6786_f430v" o="430v" n="860"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2119 <pb file="add_6786_f431" o="431" n="861"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2120 <pb file="add_6786_f431v" o="431v" n="862"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2121 <pb file="add_6786_f432" o="432" n="863"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2122 <pb file="add_6786_f432v" o="432v" n="864"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2123 <pb file="add_6786_f433" o="433" n="865"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2124 <pb file="add_6786_f433v" o="433v" n="866"/>
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diff changeset
2125 <pb file="add_6786_f434" o="434" n="867"/>
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diff changeset
2126 <pb file="add_6786_f434v" o="434v" n="868"/>
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diff changeset
2127 <pb file="add_6786_f435" o="435" n="869"/>
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diff changeset
2128 <pb file="add_6786_f435v" o="435v" n="870"/>
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diff changeset
2129 <pb file="add_6786_f436" o="436" n="871"/>
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diff changeset
2130 <pb file="add_6786_f436v" o="436v" n="872"/>
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diff changeset
2131 <pb file="add_6786_f437" o="437" n="873"/>
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diff changeset
2132 <pb file="add_6786_f437v" o="437v" n="874"/>
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diff changeset
2133 <pb file="add_6786_f438" o="438" n="875"/>
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diff changeset
2134 <pb file="add_6786_f438v" o="438v" n="876"/>
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diff changeset
2135 <pb file="add_6786_f439" o="439" n="877"/>
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diff changeset
2136 <pb file="add_6786_f439v" o="439v" n="878"/>
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2137 <pb file="add_6786_f440" o="440" n="879"/>
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diff changeset
2138 <div xml:id="echoid-div41" type="page_commentary" level="2" n="41">
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diff changeset
2139 <p>
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diff changeset
2140 <s xml:id="echoid-s176" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2141 <p>
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diff changeset
2142 <s xml:id="echoid-s176" xml:space="preserve">This sheet contains Harriot's exploration of Proposition 2, Lemma 4, from the
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diff changeset
2143 <emph style="it">Sphaerica Menelai</emph> of Menelaus, as translated by Maurolico (1558).
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diff changeset
2144 The text includes a supplement by Thabit ibn Qurra (see Add MS 6787, f. 306v to f. 308 and f. 309v). <lb/>
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2145 For Harriot's copy of Propositions 1 and 2 see Add MS 6787, f. 306 to f. 309v.
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diff changeset
2146 The pages relevant to Proposition 2, Lemma 4, are f. 307, f. 307v, and f. 308.
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2147 </s>
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2148 </p>
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2149 </emph>]
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2150 <lb/><lb/></s></p></div>
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2151 <p xml:lang="lat">
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2152 <s xml:id="echoid-s178" xml:space="preserve">
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2153 Si fuerint sex quantitates, quorum ratio primæ ad secundum: componatur ex rationibus, <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2154 tertia ad quartam, et quintæ ad sextam. Tum solidum sub prima quarta et sexta <lb/>
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diff changeset
2155 contentum, æquale erit solido sub secundo tertia et quinta comprehenso.
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2156 <lb/>[<emph style="it">tr:
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2157 If there are six quantities, where the ratio of the first to the second is composed of
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2158 the ratio of the third to the fourth and of the fifth to the sixth,
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2159 then the solid content of the first, fourth, and sixth will be equal to
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2160 the solid composed of the second, third, and fifth.
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2161 </emph>]<lb/>
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2162 </s>
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2163 </p>
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2164 <p xml:lang="lat">
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2165 <s xml:id="echoid-s179" xml:space="preserve">
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2166 Sex quantitates.
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2167 <lb/>[<emph style="it">tr:
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2168 The six quantities
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2169 </emph>]<lb/>
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2170 </s>
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2171 </p>
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2172 <p xml:lang="lat">
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2173 <s xml:id="echoid-s180" xml:space="preserve">
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2174 Ergo solidum <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi><mi>z</mi><mo>=</mo><mi>b</mi><mi>g</mi><mi>e</mi></mstyle></math>.
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2175 <lb/>[<emph style="it">tr:
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2176 Therefore the solid <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>d</mi><mi>z</mi><mo>=</mo><mi>b</mi><mi>g</mi><mi>e</mi></mstyle></math>.
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2177 </emph>]<lb/>
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2178 </s>
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2179 </p>
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2180 <p xml:lang="lat">
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2181 <s xml:id="echoid-s181" xml:space="preserve">
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2182 Varia transpositio utrinque <emph style="st">solilidi</emph> solidi terminorum.
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2183 <lb/>[<emph style="it">tr:
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2184 Various transpositions of the terms of both solids.
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2185 </emph>]<lb/>
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2186 </s>
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2187 </p>
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2188 <p xml:lang="lat">
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2189 <s xml:id="echoid-s182" xml:space="preserve">
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2190 Habitudines æqualium solidorum. <lb/>[<emph style="it">tr:
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2191 Forms of equal solids
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2192 </emph>]<lb/>
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2193 </s>
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2194 </p>
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2195 <p xml:lang="lat">
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2196 <s xml:id="echoid-s183" xml:space="preserve">
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2197 Thebit ben Corat. <lb/>
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2198 et Ma<emph style="super">u</emph>rolicus.
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2199 <lb/>[<emph style="it">tr:
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2200 Thabit ibn Qurra and Maurolico.
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2201 </emph>]<lb/>
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2202 </s>
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2203 </p>
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2204 <p xml:lang="lat">
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2205 <s xml:id="echoid-s184" xml:space="preserve">
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2206 compositiones
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2207 <lb/>[<emph style="it">tr:
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2208 compositions
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2209 </emph>]<lb/>
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2210 </s>
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2211 </p>
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2212 <p xml:lang="lat">
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2213 <s xml:id="echoid-s185" xml:space="preserve">
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2214 componentes rationes transpositæ
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2215 <lb/>[<emph style="it">tr:
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2216 components of the transposed ratios
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2217 </emph>]<lb/>
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2218 </s>
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2219 </p>
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2220 <p xml:lang="lat">
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2221 <s xml:id="echoid-s186" xml:space="preserve">
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2222 Si consequentes fiant antecedentes <lb/>
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diff changeset
2223 et antecedentes consequentes; sunt alia <lb/>
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diff changeset
2224 36 compositiones.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2225 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2226 If the consequents become antecedents and antecedents consequents, there are another 36 compositions.
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diff changeset
2227 </emph>]<lb/>
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2228 </s>
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2229 </p>
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diff changeset
2230 <pb file="add_6786_f440v" o="440v" n="880"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2231 <pb file="add_6786_f441" o="441" n="881"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2232 <head xml:id="echoid-head13" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2233 In ptolomaicam propositione
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2234 <lb/>[<emph style="it">tr:
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diff changeset
2235 On a proposition of Ptolemy
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2236 </emph>]<lb/>
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2237 </head>
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2238 <pb file="add_6786_f441v" o="441v" n="882"/>
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2239 <pb file="add_6786_f442" o="442" n="883"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2240 <p xml:lang="lat">
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2241 <s xml:id="echoid-s187" xml:space="preserve">
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diff changeset
2242 Data magnitudine
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2243 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2244 given magnitude
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2245 </emph>]<lb/>
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2246 </s>
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2247 </p>
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2248 <p xml:lang="lat">
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2249 <s xml:id="echoid-s188" xml:space="preserve">
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2250 Data ratione
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2251 <lb/>[<emph style="it">tr:
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2252 Gien ratio
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2253 </emph>]<lb/>
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2254 </s>
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2255 </p>
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2256 <p xml:lang="lat">
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2257 <s xml:id="echoid-s189" xml:space="preserve">
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2258 Quæruntur magnitudines
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2259 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2260 Magnitudes sought
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2261 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2262 </s>
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2263 <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2264 <s xml:id="echoid-s190" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2265 vel cuiuslibet alterius
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2266 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2267 or any others one wishes
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2268 </emph>]<lb/>
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2269 </s>
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2270 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2271 <pb file="add_6786_f442v" o="442v" n="884"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2272 <pb file="add_6786_f443" o="443" n="885"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2273 <pb file="add_6786_f443v" o="443v" n="886"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2274 <div xml:id="echoid-div42" type="page_commentary" level="2" n="42">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2275 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2276 <s xml:id="echoid-s191" xml:space="preserve">[<emph style="it">Note:
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2277 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2278 <s xml:id="echoid-s191" xml:space="preserve">For the proposition referred to here, see Add MS 6785, f. 179.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2279 See also Add MS 6786, f. 441 to f. 444.
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2280 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2281 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2282 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2283 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2284 <head xml:id="echoid-head14" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2285 In prop. ptolomaica initio Finkij
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2286 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2287 On a proposition of Ptolemy from the beginning of Finck
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2288 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2289 </head>
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2290 <pb file="add_6786_f444" o="444" n="887"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2291 <pb file="add_6786_f444v" o="444v" n="888"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2292 <pb file="add_6786_f445" o="445" n="889"/>
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2293 <pb file="add_6786_f445v" o="445v" n="890"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2294 <pb file="add_6786_f446" o="446" n="891"/>
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2295 <pb file="add_6786_f446v" o="446v" n="892"/>
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2296 <pb file="add_6786_f447" o="447" n="893"/>
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2297 <pb file="add_6786_f447v" o="447v" n="894"/>
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2298 <pb file="add_6786_f448" o="448" n="895"/>
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2299 <p xml:lang="lat">
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2300 <s xml:id="echoid-s193" xml:space="preserve">
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2301 Ex Stigelij lib. de circulis <lb/>
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2302 calistibus. et Doctrina <lb/>
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2303 [???]
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2304 </s>
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2305 </p>
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2306 <p xml:lang="lat">
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2307 <s xml:id="echoid-s194" xml:space="preserve">
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2308 nostra
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2309 </s>
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2310 </p>
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2311 <p xml:lang="lat">
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2312 <s xml:id="echoid-s195" xml:space="preserve">
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2313 invertibus
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2314 </s>
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2315 </p>
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2316 <pb file="add_6786_f448v" o="448v" n="896"/>
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2317 <pb file="add_6786_f449" o="449" n="897"/>
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2318 <pb file="add_6786_f449v" o="449v" n="898"/>
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2319 <pb file="add_6786_f450" o="450" n="899"/>
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2320 <div xml:id="echoid-div43" type="page_commentary" level="2" n="43">
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2321 <p>
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2322 <s xml:id="echoid-s196" xml:space="preserve">[<emph style="it">Note:
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2323 <p>
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2324 <s xml:id="echoid-s196" xml:space="preserve">
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2325 One of several pages containing a mnemonic for the digits of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>Ï€</mi></mstyle></math>,
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2326 by making <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mn>1</mn><mo>=</mo><mi>a</mi></mstyle></math>, 2 = b <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>,</mo></mstyle></math> 3 = c <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>,</mo><mi>a</mi><mi>n</mi><mi>d</mi><mi>s</mi><mi>o</mi><mi>o</mi><mi>n</mi><mo>.</mo></mstyle></math></s>
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2327 </p>
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2328 </emph>]
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2329 <lb/><lb/></s></p></div>
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2330 <p>
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2331 <s xml:id="echoid-s198" xml:space="preserve">
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2332 cadaeibf <lb/>
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2333 31415926
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2334 </s>
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2335 </p>
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2336 <pb file="add_6786_f450v" o="450v" n="900"/>
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2337 <pb file="add_6786_f451" o="451" n="901"/>
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2338 <pb file="add_6786_f451v" o="451v" n="902"/>
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2339 <pb file="add_6786_f452" o="452" n="903"/>
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2340 <pb file="add_6786_f452v" o="452v" n="904"/>
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2341 <pb file="add_6786_f453" o="453" n="905"/>
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2342 <pb file="add_6786_f453v" o="453v" n="906"/>
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2343 <div xml:id="echoid-div44" type="page_commentary" level="2" n="44">
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2344 <p>
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2345 <s xml:id="echoid-s199" xml:space="preserve">[<emph style="it">Note:
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2346 <p>
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2347 <s xml:id="echoid-s199" xml:space="preserve">
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2348 The reference on this page is to Viète's
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2349 <emph style="it">Variorum responsorum liber VIII</emph>, Chapter 17.
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2350 </s>
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2351 <lb/>
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2352 <quote xml:lang="lat">
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2353 Theorema. <lb/>
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2354 Si fuerint magnitudines continue proportionales: erit ut terminus rationis major ad terminum rationis minorem,
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2355 ita differentia compositæ ex ombinbus &amp; minimæ ad differentiam compositæ ex omnibus &amp; maximæ.
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2356 </quote>
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2357 <lb/>
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2358 <quote>
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2359 If there are magnitudes in continued proportion, then the ratio of the greatest term to the least will be
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2360 as the difference between the sum of all and the minimum to the difference between the sum of all and the maximum.
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2361 </quote>
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2362 <lb/>
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2363 <s xml:id="echoid-s200" xml:space="preserve">
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2364 Harriot's notation here is the same as Viète's.
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2365 </s>
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2366 </p>
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2367 </emph>]
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2368 <lb/><lb/></s></p></div>
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2369 <head xml:id="echoid-head15" xml:space="preserve" xml:lang="lat">
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2370 In Cap. 17. Resp. pag. 29.
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2371 Vieta
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2372 <lb/>[<emph style="it">tr:
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2373 From Chapter 17, Responsorum, page 29, Viète
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2374 </emph>]<lb/>
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2375 </head>
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2376 <p xml:lang="lat">
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2377 <s xml:id="echoid-s202" xml:space="preserve">
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2378 Si fuerint magnitudines continue proportionales: Erit ut terminus <lb/>
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2379 rationis major ad terminum rationis minorem; ita differentia <lb/>
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2380 compositæ ex ombinbus et minimæ ad differentiam compositæ ex <lb/>
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2381 omnibus et maximæ.
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2382 <lb/>[<emph style="it">tr:
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2383 If there are magnitudes in continued proportion, then the ratio of the greatest term to the least will be
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2384 as the difference between the sum of all and the minimum to the difference between the sum of all and the maximum.
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2385 </emph>]<lb/>
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2386 </s>
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2387 </p>
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2388 <p xml:lang="lat">
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2389 <s xml:id="echoid-s203" xml:space="preserve">
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2390 Sit maxima. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>. <lb/>
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2391 minima. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>X</mi></mstyle></math>. <lb/>
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2392 composita ex omnibus. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math> <lb/>
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2393 ratio Maioris ad minore. <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>B</mi></mstyle></math>.
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2394 <lb/>[<emph style="it">tr:
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2395 Let the greatest be <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi></mstyle></math>, <lb/>
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2396 the least <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>X</mi></mstyle></math>, <lb/>
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2397 the sum of all <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>F</mi></mstyle></math>, <lb/>
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2398 the ratio of a greater to the lesser <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>D</mi><mo>:</mo><mi>B</mi></mstyle></math>.
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2399 </emph>]<lb/>
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2400 </s>
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2401 </p>
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2402 <p xml:lang="lat">
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2403 <s xml:id="echoid-s204" xml:space="preserve">
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2404 Alius sic: si fuerint magnitudes continue proportionales: <lb/>
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2405 ut prima ad secundam: ita omnes antecedentes ad omnes consequentes.
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2406 <lb/>[<emph style="it">tr:
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2407 Otherwise thusL if there are magnitudes in continued proportion, as the first is to the second,
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2408 so are all the antecedents to all the consequents.
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2409 </emph>]<lb/>
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2410 </s>
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2411 </p>
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2412 <pb file="add_6786_f454" o="454" n="907"/>
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2413 <pb file="add_6786_f454v" o="454v" n="908"/>
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2414 <pb file="add_6786_f455" o="455" n="909"/>
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2415 <p>
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2416 <s xml:id="echoid-s205" xml:space="preserve">
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2417 12£ sterling. = 1£ gold angel
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2418 </s>
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2419 </p>
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diff changeset
2420 <pb file="add_6786_f455v" o="455v" n="910"/>
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diff changeset
2421 <pb file="add_6786_f456" o="456" n="911"/>
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diff changeset
2422 <pb file="add_6786_f456v" o="456v" n="912"/>
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diff changeset
2423 <pb file="add_6786_f457" o="457" n="913"/>
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2424 <div xml:id="echoid-div45" type="page_commentary" level="2" n="45">
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2425 <p>
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diff changeset
2426 <s xml:id="echoid-s206" xml:space="preserve">[<emph style="it">Note:
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diff changeset
2427 <p>
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diff changeset
2428 <s xml:id="echoid-s206" xml:space="preserve">
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diff changeset
2429 Powers of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo maxsize="1">)</mo></mstyle></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo maxsize="1">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mrow><msup><mo maxsize="1">)</mo><mn>5</mn></msup></mrow></mstyle></math>.
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diff changeset
2430 Each power is calculated from the previous one by multiplication. <lb/>
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diff changeset
2431 Note the use of cossist notation:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2432 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>r</mi></mstyle></math> for a first power, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi></mstyle></math> for a square, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math> for a cube, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>z</mi></mstyle></math> for a square-suare or fourth power,
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diff changeset
2433 <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mo>ß</mo></mstyle></math> for a sursolid or fifth power. <lb/>
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diff changeset
2434 Below the main table is a list of the final sums, including the sixth power (<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>z</mi><mi>c</mi></mstyle></math>),
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2435 which has not been calculated on this page but which can be deduced from the pattern for the previous cases. <lb/>
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2436 For a similar table see Add MS 6782, f. 276. <lb/>
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2437 This table underpins the method of root extraction taught by Francois Viete
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2438 in <emph style="it">De numerosa potestatum resolutione</emph> (1600).
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2439 </s>
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2440 </p>
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2441 </emph>]
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2442 <lb/><lb/></s></p></div>
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2443 <p xml:lang="lat">
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2444 <s xml:id="echoid-s208" xml:space="preserve">
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2445 species figuratorum <lb/>
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2446 ex binomia radice
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2447 <lb/>[<emph style="it">tr:
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2448 terms of figurate numbers from binomial roots
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2449 </emph>]<lb/>
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2450 </s>
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2451 </p>
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2452 <p xml:lang="lat">
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2453 <s xml:id="echoid-s209" xml:space="preserve">
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2454 (sunt canones pro <lb/>
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2455 extractione radicum.)
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2456 <lb/>[<emph style="it">tr:
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2457 (these are the canons for the extraction of roots.)
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2458 </emph>]<lb/>
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2459 </s>
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2460 </p>
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2461 <p xml:lang="lat">
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2462 <s xml:id="echoid-s210" xml:space="preserve">
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2463 (Demptis numeris sunt species <lb/>
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2464 continue proportionalium, <lb/>
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2465 in minimis terminis <lb/>
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2466 ut <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math>, ad <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>.)
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2467 <lb/>[<emph style="it">tr:
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2468 (Without the numbers, the terms are in continual proportion, in the ratio expressed in lowest terms as <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>b</mi></mstyle></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>c</mi></mstyle></math>).
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2469 </emph>]<lb/>
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2470 </s>
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2471 </p>
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2472 <pb file="add_6786_f457v" o="457v" n="914"/>
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2473 <pb file="add_6786_f458" o="458" n="915"/>
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2474 <p xml:lang="lat">
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2475 <s xml:id="echoid-s211" xml:space="preserve">
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2476 vale vale cane ne titules mandataque frangas
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2477 </s>
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2478 </p>
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2479 <pb file="add_6786_f458v" o="458v" n="916"/>
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2480 <pb file="add_6786_f459" o="459" n="917"/>
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2481 <pb file="add_6786_f459v" o="459v" n="918"/>
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2482 <pb file="add_6786_f460" o="460" n="919"/>
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2483 <pb file="add_6786_f460v" o="460v" n="920"/>
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2484 <pb file="add_6786_f461" o="461" n="921"/>
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2485 <pb file="add_6786_f461v" o="461v" n="922"/>
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2486 <pb file="add_6786_f462" o="462" n="923"/>
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2487 <pb file="add_6786_f462v" o="462v" n="924"/>
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2488 <pb file="add_6786_f463" o="463" n="925"/>
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2489 <pb file="add_6786_f463v" o="463v" n="926"/>
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2490 <pb file="add_6786_f464" o="464" n="927"/>
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2491 <pb file="add_6786_f464v" o="464v" n="928"/>
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2492 <pb file="add_6786_f465" o="465" n="929"/>
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2493 <pb file="add_6786_f465v" o="465v" n="930"/>
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2494 <pb file="add_6786_f466" o="466" n="931"/>
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2495 <pb file="add_6786_f466v" o="466v" n="932"/>
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2496 <pb file="add_6786_f467" o="467" n="933"/>
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2497 <pb file="add_6786_f467v" o="467v" n="934"/>
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2498 <pb file="add_6786_f468" o="468" n="935"/>
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2499 <pb file="add_6786_f468v" o="468v" n="936"/>
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2500 <pb file="add_6786_f469" o="469" n="937"/>
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2501 <pb file="add_6786_f469v" o="469v" n="938"/>
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2502 <pb file="add_6786_f470" o="470" n="939"/>
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2503 <pb file="add_6786_f470v" o="470v" n="940"/>
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2504 <pb file="add_6786_f471" o="471" n="941"/>
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2505 <pb file="add_6786_f471v" o="471v" n="942"/>
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2506 <pb file="add_6786_f472" o="472" n="943"/>
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2507 <head xml:id="echoid-head16" xml:space="preserve" xml:lang="lat">
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2508 Ratio æqualitatis in infinitum.
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2509 <lb/>[<emph style="it">tr:
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2510 A ratio of equality at infinity.
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diff changeset
2511 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2512 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2513 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2514 <s xml:id="echoid-s212" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2515 A cipher being the last of this lower progression what wilbe <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2516 over it, of the hyer, proceeding &amp; continuing, as it is <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2517 before?
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2518 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2519 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2520 <pb file="add_6786_f472v" o="472v" n="944"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2521 <pb file="add_6786_f473" o="473" n="945"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2522 <pb file="add_6786_f473v" o="473v" n="946"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2523 <pb file="add_6786_f474" o="474" n="947"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2524 <pb file="add_6786_f474v" o="474v" n="948"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2525 <pb file="add_6786_f475" o="475" n="949"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2526 <pb file="add_6786_f475v" o="475v" n="950"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2527 <pb file="add_6786_f476" o="476" n="951"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2528 <pb file="add_6786_f476v" o="476v" n="952"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2529 <pb file="add_6786_f477" o="477" n="953"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2530 <pb file="add_6786_f477v" o="477v" n="954"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2531 <pb file="add_6786_f478" o="478" n="955"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2532 <pb file="add_6786_f478v" o="478v" n="956"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2533 <pb file="add_6786_f479" o="479" n="957"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2534 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2535 <s xml:id="echoid-s213" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2536 William Yates William Yates. Christopher Tooke.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2537 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2538 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2539 <pb file="add_6786_f479v" o="479v" n="958"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2540 <pb file="add_6786_f480" o="480" n="959"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2541 <pb file="add_6786_f480v" o="480v" n="960"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2542 <pb file="add_6786_f481" o="481" n="961"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2543 <pb file="add_6786_f481v" o="481v" n="962"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2544 <pb file="add_6786_f482" o="482" n="963"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2545 <pb file="add_6786_f482v" o="482v" n="964"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2546 <pb file="add_6786_f483" o="483" n="965"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2547 <pb file="add_6786_f483v" o="483v" n="966"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2548 <pb file="add_6786_f484" o="484" n="967"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2549 <pb file="add_6786_f484v" o="484v" n="968"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2550 <pb file="add_6786_f485" o="485" n="969"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2551 <head xml:id="echoid-head17" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2552 Ex bin: med: 4.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2553 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2554 From a fourth bimedial.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2555 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2556 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2557 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2558 <s xml:id="echoid-s214" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2559 bin. 6
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2560 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2561 A sixth binome.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2562 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2563 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2564 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2565 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2566 <s xml:id="echoid-s215" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2567 bin. 5 ex bin: med. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2568 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2569 A fifth binome from a first bimedial.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2570 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2571 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2572 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2573 <head xml:id="echoid-head18" xml:space="preserve" xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2574 Ex bin: med: 5.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2575 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2576 From fifth bimedials.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2577 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2578 </head>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2579 <p xml:lang="lat">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2580 <s xml:id="echoid-s216" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2581 bin. 5 ex bin: med. 1.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2582 <lb/>[<emph style="it">tr:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2583 A fifth binome from a first bimedial.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2584 </emph>]<lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2585 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2586 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2587 <pb file="add_6786_f485v" o="485v" n="970"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2588 <pb file="add_6786_f486" o="486" n="971"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2589 <pb file="add_6786_f486v" o="486v" n="972"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2590 <pb file="add_6786_f487" o="487" n="973"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2591 <pb file="add_6786_f487v" o="487v" n="974"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2592 <pb file="add_6786_f488" o="488" n="975"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2593 <pb file="add_6786_f488v" o="488v" n="976"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2594 <pb file="add_6786_f489" o="489" n="977"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2595 <pb file="add_6786_f489v" o="489v" n="978"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2596 <pb file="add_6786_f490" o="490" n="979"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2597 <pb file="add_6786_f490v" o="490v" n="980"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2598 <div xml:id="echoid-div46" type="page_commentary" level="2" n="46">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2599 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2600 <s xml:id="echoid-s217" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2601 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2602 <s xml:id="echoid-s217" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2603 The author of this fragment is unkown.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2604 However, the same form of address was used by Harriot's friend Nathaniel Trporley, see Add MS 67888, f. 117.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2605 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2606 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2607 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2608 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
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2609 <p>
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2610 <s xml:id="echoid-s219" xml:space="preserve">
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2611 TO HIS VERY LOVING FRENDE <lb/>
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2612 MASTER THOMAS HARRIOT <lb/>
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2613 GEVE THESE AT SION.
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2614 </s>
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2615 </p>
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2616 <pb file="add_6786_f491" o="491" n="981"/>
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2617 <pb file="add_6786_f491v" o="491v" n="982"/>
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2618 <pb file="add_6786_f492" o="492" n="983"/>
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2619 <pb file="add_6786_f492v" o="492v" n="984"/>
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2620 <pb file="add_6786_f493" o="493" n="985"/>
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2621 <pb file="add_6786_f493v" o="493v" n="986"/>
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2622 <pb file="add_6786_f494" o="494" n="987"/>
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2623 <pb file="add_6786_f494v" o="494v" n="988"/>
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2624 <pb file="add_6786_f495" o="495" n="989"/>
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2625 <pb file="add_6786_f495v" o="495v" n="990"/>
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2626 <pb file="add_6786_f496" o="496" n="991"/>
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2627 <pb file="add_6786_f496v" o="496v" n="992"/>
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2628 <pb file="add_6786_f497" o="497" n="993"/>
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2629 <pb file="add_6786_f497v" o="497v" n="994"/>
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2630 <pb file="add_6786_f498" o="498" n="995"/>
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2631 <pb file="add_6786_f498v" o="498v" n="996"/>
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2632 <pb file="add_6786_f499" o="499" n="997"/>
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2633 <pb file="add_6786_f499v" o="499v" n="998"/>
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2634 <pb file="add_6786_f500" o="500" n="999"/>
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2635 <pb file="add_6786_f500v" o="500v" n="1000"/>
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2636 <pb file="add_6786_f501" o="501" n="1001"/>
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2637 <pb file="add_6786_f501v" o="501v" n="1002"/>
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2638 <pb file="add_6786_f502" o="502" n="1003"/>
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2639 <pb file="add_6786_f502v" o="502v" n="1004"/>
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2640 <pb file="add_6786_f503" o="503" n="1005"/>
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2641 <pb file="add_6786_f503v" o="503v" n="1006"/>
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2642 <pb file="add_6786_f504" o="504" n="1007"/>
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2643 <pb file="add_6786_f504v" o="504v" n="1008"/>
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2644 <pb file="add_6786_f505" o="505" n="1009"/>
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2645 <pb file="add_6786_f505v" o="505v" n="1010"/>
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2646 <pb file="add_6786_f506" o="506" n="1011"/>
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2647 <pb file="add_6786_f506v" o="506v" n="1012"/>
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2648 <pb file="add_6786_f507" o="507" n="1013"/>
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2649 <pb file="add_6786_f507v" o="507v" n="1014"/>
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2650 <pb file="add_6786_f508" o="508" n="1015"/>
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2651 <pb file="add_6786_f508v" o="508v" n="1016"/>
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2652 <c>
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2653 See also Add MS 6783, f. 174 (d.10) where the same quadratic equation is solved for <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>d</mi></mstyle></math>.
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2654 </c>
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2655 <head xml:id="echoid-head19" xml:space="preserve">
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2656 as<emph style="super">2</emph>)
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2657 </head>
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2658 <p xml:lang="lat">
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2659 <s xml:id="echoid-s220" xml:space="preserve">
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2660 ad expurgandam <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi></mstyle></math>
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2661 <lb/>[<emph style="it">tr:
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2662 for the removal of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle><mi>a</mi><mi>a</mi></mstyle></math>.
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2663 </emph>]<lb/>
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2664 </s>
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2665 </p>
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2666 <pb file="add_6786_f509" o="509" n="1017"/>
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2667 <pb file="add_6786_f509v" o="509v" n="1018"/>
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2668 <pb file="add_6786_f510" o="510" n="1019"/>
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2669 <div xml:id="echoid-div47" type="page_commentary" level="2" n="47">
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2670 <p>
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2671 <s xml:id="echoid-s221" xml:space="preserve">[<emph style="it">Note:
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2672 <p>
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2673 <s xml:id="echoid-s221" xml:space="preserve">
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2674 Examples of arithmetic, geometric, and harmonic porgressions, and rules for their general terms.
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2675 (The terms of a harmonic progression are the reciprocals of an arithmetic porgression.)
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2676 </s>
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2677 </p>
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2678 </emph>]
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2679 <lb/><lb/></s></p></div>
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2680 <p xml:lang="lat">
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2681 <s xml:id="echoid-s223" xml:space="preserve">
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2682 <reg norm="Arithmetica" type="abbr">Arith</reg>. 3. 6. 9.
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2683 </s>
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2684 <lb/>
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2685 <s xml:id="echoid-s224" xml:space="preserve">
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2686 <reg norm="Geometrica" type="abbr">Geo</reg>. 3. 6. 12.
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2687 </s>
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2688 <lb/>
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2689 <s xml:id="echoid-s225" xml:space="preserve">
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2690 <reg norm="Harmonica" type="abbr">Har</reg>. 6. 3. 2.
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2691 </s>
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2692 </p>
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2693 <pb file="add_6786_f510v" o="510v" n="1020"/>
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2694 <pb file="add_6786_f511" o="511" n="1021"/>
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2695 <pb file="add_6786_f511v" o="511v" n="1022"/>
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2696 <pb file="add_6786_f512" o="512" n="1023"/>
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2697 <pb file="add_6786_f512v" o="512v" n="1024"/>
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2698 <pb file="add_6786_f513" o="513" n="1025"/>
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2699 <pb file="add_6786_f513v" o="513v" n="1026"/>
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2700 <pb file="add_6786_f514" o="514" n="1027"/>
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2701 <pb file="add_6786_f514v" o="514v" n="1028"/>
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2702 <pb file="add_6786_f515" o="515" n="1029"/>
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2703 <pb file="add_6786_f515v" o="515v" n="1030"/>
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2704 <pb file="add_6786_f516" o="516" n="1031"/>
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2705 <pb file="add_6786_f516v" o="516v" n="1032"/>
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2706 <div xml:id="echoid-div48" type="page_commentary" level="2" n="48">
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2707 <p>
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2708 <s xml:id="echoid-s226" xml:space="preserve">[<emph style="it">Note:
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2709 <p>
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2710 <s xml:id="echoid-s226" xml:space="preserve">
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2711 This page contains jottings on both binary and ternary arithmetic. <lb/>
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2712 The calculation on the left shows 101101 (= 45) multiplied by 1011 (= 11);
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diff changeset
2713 the answer, 111,101,111 (= 495), is then divided by 1011 (= 11) to recover 101101 (= 45).
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2714 </s>
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2715 </p>
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2716 </emph>]
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diff changeset
2717 <lb/><lb/></s></p></div>
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2718 <p xml:lang="lat">
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2719 <s xml:id="echoid-s228" xml:space="preserve">
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2720 ternaria <lb/>
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2721 <lb/>[<emph style="it">tr:
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2722 ternary
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2723 </emph>]<lb/>
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2724 </s>
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2725 </p>
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2726 <p xml:lang="lat">
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2727 <s xml:id="echoid-s229" xml:space="preserve">
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2728 binaria <lb/>
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2729 <lb/>[<emph style="it">tr:
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2730 binary
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2731 </emph>]<lb/>
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2732 </s>
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2733 </p>
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2734 <pb file="add_6786_f517" o="517" n="1033"/>
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2735 <pb file="add_6786_f517v" o="517v" n="1034"/>
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2736 <pb file="add_6786_f518" o="518" n="1035"/>
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2737 <div xml:id="echoid-div49" type="page_commentary" level="2" n="49">
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2738 <p>
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2739 <s xml:id="echoid-s230" xml:space="preserve">[<emph style="it">Note:
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2740 <p>
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2741 <s xml:id="echoid-s230" xml:space="preserve">
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2742 The beginning of a page 34.3 for the 'Magisteria',
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2743 not used in the final version which has only pages 34.1 and 34.2 (see Add MS 6782, f. 141 and f. 142).
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2744 </s>
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2745 </p>
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2746 </emph>]
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2747 <lb/><lb/></s></p></div>
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2748 <pb file="add_6786_f518v" o="518v" n="1036"/>
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2749 <pb file="add_6786_f519" o="519" n="1037"/>
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2750 <pb file="add_6786_f519v" o="519v" n="1038"/>
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2751 <pb file="add_6786_f520" o="520" n="1039"/>
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2752 <pb file="add_6786_f520v" o="520v" n="1040"/>
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2753 <pb file="add_6786_f521" o="521" n="1041"/>
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2754 <pb file="add_6786_f521v" o="521v" n="1042"/>
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2755 <pb file="add_6786_f522" o="522" n="1043"/>
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2756 <pb file="add_6786_f522v" o="522v" n="1044"/>
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2757 <pb file="add_6786_f523" o="523" n="1045"/>
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2758 <pb file="add_6786_f523v" o="523v" n="1046"/>
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2759 <pb file="add_6786_f524" o="524" n="1047"/>
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2760 <pb file="add_6786_f524v" o="524v" n="1048"/>
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2761 <pb file="add_6786_f525" o="525" n="1049"/>
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2762 <pb file="add_6786_f525v" o="525v" n="1050"/>
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2763 <pb file="add_6786_f526" o="526" n="1051"/>
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2764 <pb file="add_6786_f526v" o="526v" n="1052"/>
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2765 <pb file="add_6786_f527" o="527" n="1053"/>
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2766 <pb file="add_6786_f527v" o="527v" n="1054"/>
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2767 <pb file="add_6786_f528" o="528" n="1055"/>
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2768 <pb file="add_6786_f528v" o="528v" n="1056"/>
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2769 <pb file="add_6786_f529" o="529" n="1057"/>
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2770 <pb file="add_6786_f529v" o="529v" n="1058"/>
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2771 <pb file="add_6786_f530" o="530" n="1059"/>
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2772 <pb file="add_6786_f530v" o="530v" n="1060"/>
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2773 <pb file="add_6786_f531" o="531" n="1061"/>
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2774 <pb file="add_6786_f531v" o="531v" n="1062"/>
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2775 <pb file="add_6786_f532" o="532" n="1063"/>
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2776 <pb file="add_6786_f532v" o="532v" n="1064"/>
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2777 <pb file="add_6786_f533" o="533" n="1065"/>
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2778 <pb file="add_6786_f533v" o="533v" n="1066"/>
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2779 <pb file="add_6786_f534" o="534" n="1067"/>
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2780 <pb file="add_6786_f534v" o="534v" n="1068"/>
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2781 <pb file="add_6786_f535" o="535" n="1069"/>
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2782 <pb file="add_6786_f535v" o="535v" n="1070"/>
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2783 <pb file="add_6786_f536" o="536" n="1071"/>
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2784 <pb file="add_6786_f536v" o="536v" n="1072"/>
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2785 <pb file="add_6786_f537" o="537" n="1073"/>
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2786 <pb file="add_6786_f537v" o="537v" n="1074"/>
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2787 <pb file="add_6786_f538" o="538" n="1075"/>
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2788 <pb file="add_6786_f538v" o="538v" n="1076"/>
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2789 <pb file="add_6786_f539" o="539" n="1077"/>
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2790 <pb file="add_6786_f539v" o="539v" n="1078"/>
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2791 <pb file="add_6786_f540" o="540" n="1079"/>
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2792 <pb file="add_6786_f540v" o="540v" n="1080"/>
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2793 <pb file="add_6786_f541" o="541" n="1081"/>
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2794 <pb file="add_6786_f541v" o="541v" n="1082"/>
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2795 <pb file="add_6786_f542" o="542" n="1083"/>
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2796 <pb file="add_6786_f542v" o="542v" n="1084"/>
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diff changeset
2797 <pb file="add_6786_f543" o="543" n="1085"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2798 <pb file="add_6786_f543v" o="543v" n="1086"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2799 <pb file="add_6786_f544" o="544" n="1087"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2800 <pb file="add_6786_f544v" o="544v" n="1088"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2801 <pb file="add_6786_f545" o="545" n="1089"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2802 <pb file="add_6786_f545v" o="545v" n="1090"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2803 <pb file="add_6786_f546" o="546" n="1091"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2804 <pb file="add_6786_f546v" o="546v" n="1092"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2805 <pb file="add_6786_f547" o="547" n="1093"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2806 <pb file="add_6786_f547v" o="547v" n="1094"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2807 <pb file="add_6786_f548" o="548" n="1095"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2808 <pb file="add_6786_f548v" o="548v" n="1096"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2809 <pb file="add_6786_f549" o="549" n="1097"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2810 <pb file="add_6786_f549v" o="549v" n="1098"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2811 <pb file="add_6786_f550" o="550" n="1099"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2812 <pb file="add_6786_f550v" o="550v" n="1100"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2813 <pb file="add_6786_f551" o="551" n="1101"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2814 <pb file="add_6786_f551v" o="551v" n="1102"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2815 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2816 <s xml:id="echoid-s232" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2817 red sage. 624. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2818 une. 1073. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2819 cummin. 908. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2820 cammomill. 616. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2821 otes. 69. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2822 wall une. 984.i.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2823 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2824 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2825 <pb file="add_6786_f552" o="552" n="1103"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2826 <pb file="add_6786_f552v" o="552v" n="1104"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2827 <pb file="add_6786_f553" o="553" n="1105"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2828 <pb file="add_6786_f553v" o="553v" n="1106"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2829 <pb file="add_6786_f554" o="554" n="1107"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2830 <pb file="add_6786_f554v" o="554v" n="1108"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2831 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2832 <s xml:id="echoid-s233" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2833 poles <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2834 London <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2835 Syon <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2836 London Durham house <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2837 The East <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2838 Syon
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2839 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2840 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2841 <pb file="add_6786_f555" o="555" n="1109"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2842 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2843 <s xml:id="echoid-s234" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2844 Brought by Mr Alisbury from Bristow <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2845 Avacardus <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2846 The kernel <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2847 good to eat. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2848 The ioyce of the vine <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2849 good for tetters. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2850 quod de Loan. <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2851 The Apot: <lb/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2852 in Blackfriars.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2853 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2854 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2855 <pb file="add_6786_f555v" o="555v" n="1110"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2856 <pb file="add_6786_f556" o="556" n="1111"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2857 <pb file="add_6786_f556v" o="556v" n="1112"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2858 <div xml:id="echoid-div50" type="page_commentary" level="2" n="50">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2859 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2860 <s xml:id="echoid-s235" xml:space="preserve">[<emph style="it">Note:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2861 <p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2862 <s xml:id="echoid-s235" xml:space="preserve">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2863 Pythagoreadn triples with hypotenuse 65, 85, 221, and 1105.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2864 </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2865 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2866 </emph>]
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2867 <lb/><lb/></s></p></div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2868 <pb file="add_6786_f557" o="557" n="1113"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2869 <pb file="add_6786_f557v" o="557v" n="1114"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2870 <pb file="add_6786_f558" o="558" n="1115"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2871 <pb file="add_6786_f558v" o="558v" n="1116"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2872 <pb file="add_6786_f559" o="559" n="1117"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2873 <pb file="add_6786_f559v" o="559v" n="1118"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2874 <pb file="add_6786_f560" o="560" n="1119"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2875 <pb file="add_6786_f560v" o="560v" n="1120"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2876 <pb file="add_6786_f561" o="561" n="1121"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2877 <pb file="add_6786_f561v" o="561v" n="1122"/>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2878 </div>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2879 </text>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2880 </echo>