Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Page concordance

< >
Scan Original
391 379
392 380
393 381
394 382
395 383
396 384
397 385
398 386
399 387
400 388
401 389
402 390
403 391
404 392
405 393
406 394
407 395
408 396
409 397
410 398
411 399
412 400
413 401
414 402
415 403
416 404
417 405
418 406
419 407
420 408
< >
page |< < (386) of 445 > >|
IO. BAPT. BENED.
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div737" type="section" level="3" n="42">
              <div xml:id="echoid-div737" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4580" xml:space="preserve">
                    <pb o="386" rhead="IO. BAPT. BENED." n="398" file="0398" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0398"/>
                  ipſius
                    <var>.b.e.</var>
                  ad compoſitum quintupli ipſius
                    <var>.a.b.</var>
                  cum decuplo ipſius
                    <var>.c.b.</var>
                  cum decuplo
                    <lb/>
                  ipſius
                    <var>.b.d.</var>
                  cum quintuplo ipſius
                    <var>.b.e.</var>
                  eadem ſit quæ ipſius
                    <var>.g.h.</var>
                  ad
                    <var>.a.d.</var>
                  & vult proba-
                    <lb/>
                  re
                    <var>.f.h.</var>
                  eſſe duas quintas ipſius
                    <var>.a.b</var>
                  .</s>
                </p>
                <div xml:id="echoid-div740" type="float" level="5" n="4">
                  <figure xlink:label="fig-0397-01" xlink:href="fig-0397-01a">
                    <image file="0397-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0397-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4581" xml:space="preserve">Cum autem dicit proportionem ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.c.d.</var>
                  & ipſius
                    <var>.c.d.</var>
                  ad
                    <var>.d.e.</var>
                  eſſe vt ipſius
                    <lb/>
                    <var>a.b.</var>
                  a
                    <unsure/>
                  d.b.c. & cętera, verum dicit ex .19. quinti Eucli. eo quod cum ex hypotheſi ſit
                    <lb/>
                  ipſius,
                    <var>a.b.</var>
                  totalis ad
                    <var>.c.b.</var>
                  totalom vt ipſius
                    <var>.c.b.</var>
                  partialis (ſumptæ vt pars abſciſa ab
                    <var>.a.
                      <lb/>
                    b.</var>
                  pro nunc) ad
                    <var>.d.b.</var>
                  partialem (abſciſam ab
                    <var>.c.b.</var>
                  ) erit ex .19. dicta ipſius
                    <var>.a.c.</var>
                  (reſidui
                    <lb/>
                  ex
                    <var>.a.b.</var>
                  ) ad
                    <var>.c.d.</var>
                  (reſiduum ex
                    <var>.c.b.</var>
                  ) vt ipſius
                    <var>.a.b.</var>
                  ad
                    <var>.c.b.</var>
                  & ita probabitur de pro-
                    <lb/>
                  portione ipſiuas
                    <var>.c.d.</var>
                  ad
                    <var>.d.e.</var>
                  eadem ratione.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4582" xml:space="preserve">Cum verò ex .18. quinti ſit ipſius
                    <var>.a.b.</var>
                  cum
                    <var>.c.b.</var>
                  ad
                    <var>.c.b.</var>
                  vt ipſius
                    <var>.a.d.</var>
                  ad
                    <var>.d.e.</var>
                  ergo ex
                    <lb/>
                  22. eiuſdem, ita erit ipſius
                    <var>.a.b.</var>
                  cum
                    <var>.c.b.</var>
                  ad
                    <var>.d.b.</var>
                  vt
                    <var>.a.d.</var>
                  ad
                    <var>.d.e.</var>
                  & exijſdem rationibus
                    <lb/>
                  eadem proportio erit ipſius
                    <var>.c.b.</var>
                  cum
                    <var>.d.b.</var>
                  ad
                    <var>.b.e.</var>
                  vt
                    <var>.a.d.</var>
                  ad
                    <var>.d.e.</var>
                  quod inquit Archi.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4583" xml:space="preserve">Verum etiam erit (ex .13. quinti) cum dicit eandem proportionem eſſe ipſius
                    <var>.a.d.</var>
                    <lb/>
                  ad
                    <var>.d.e.</var>
                  quę dupli primi antecedentis cum ſimplo ſecundi antecedentis ad duplum
                    <lb/>
                  primi conſequentis cum ſimplo ſecundi conſequentis, hoc eſt dupli ipſius
                    <var>.a.b.c.</var>
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  ſimplo
                    <var>.c.b.d.</var>
                  ad duplum ipſius
                    <var>.d.b.</var>
                  cum ſimplo
                    <var>.e.b.</var>
                  hoc eft dupli
                    <var>.a.b.</var>
                  cum triplo ip-
                    <lb/>
                  ſius
                    <var>.b.c.</var>
                  cum ſimplo
                    <var>.d.b.</var>
                  ad duplum ipſius
                    <var>.d.b.</var>
                  cum ſimplo
                    <var>.e.b</var>
                  . </s>
                  <s xml:id="echoid-s4584" xml:space="preserve">Nunc duplum
                    <var>.a.b.</var>
                    <lb/>
                  cum triplo
                    <var>.b.c.</var>
                  cum ſimplo
                    <var>.b.d.</var>
                  ſignatum ſit charactere
                    <var>.D.</var>
                  ſuum verò conſequens,
                    <lb/>
                  hoc eſt duplum
                    <var>.d.b.</var>
                    <reg norm="cum" type="context">cũ</reg>
                  ſimplo
                    <var>.e.b.</var>
                  ſignificetur à charactere
                    <var>.B.</var>
                  hinc proportio ipſius
                    <lb/>
                    <anchor type="note" xlink:label="note-0398-01a" xlink:href="note-0398-01"/>
                    <var>a.d.</var>
                  ad
                    <var>.d.e.</var>
                  erit vt
                    <var>.D.</var>
                  ad
                    <var>.B</var>
                  .</s>
                </p>
                <div xml:id="echoid-div741" type="float" level="5" n="5">
                  <note xlink:label="note-0398-01" xlink:href="note-0398-01a" position="left" xml:space="preserve">M</note>
                </div>
                <p>
                  <s xml:id="echoid-s4585" xml:space="preserve">Inquit nunc Archimedes, ſi quis ſumeret aliquod maius antecedens æquale ſci-
                    <lb/>
                  licet duplo ipſius
                    <var>.a.b.</var>
                  cum quadruplo ipſius
                    <var>.b.e.</var>
                  cum quadruplo ipſius
                    <var>.b.d.</var>
                  cum du-
                    <lb/>
                  plo ipſius
                    <var>.b.e.</var>
                    <reg norm="compararetque" type="simple">compararetq́;</reg>
                  illud cum
                    <reg norm="conſequente" type="context">cõſequente</reg>
                    <var>.B.</var>
                  clarum eſſet ex .8. quinti quod
                    <lb/>
                  tale antecedens maiorem proportionem haberet ad
                    <var>.B.</var>
                  quam ad
                    <var>.D.</var>
                  hoc eſt maiorem
                    <lb/>
                  quàm ipſius
                    <var>.a.d.</var>
                  ad
                    <var>.d.e.</var>
                  ex .12. quinti.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4586" xml:space="preserve">Nunc ſi ſumpta fuerit aliqua linea, puta
                    <var>.d.o.</var>
                  cui
                    <var>.a.d.</var>
                    <reg norm="dictam" type="context">dictã</reg>
                  habeat proportionem
                    <lb/>
                  maiorem, larum erit ex ſecunda parte decimę quinti quod
                    <var>.d.o.</var>
                  minor erit ipſa
                    <var>.d.e.</var>
                    <lb/>
                  Corrige igitur impreſſionem Baſileę locando characterem
                    <var>.o.</var>
                  inter
                    <var>.d.</var>
                  et
                    <var>.e.</var>
                  eo quod
                    <lb/>
                  ibi poſitum non fuit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4587" xml:space="preserve">Volo nunc quod dictum maius antecedens æquale ſcilicet duplo ipſius
                    <var>.a.b.</var>
                  cum
                    <lb/>
                  quadruplo ipſius
                    <var>.b.c.</var>
                  cum quadruplo ipſius
                    <var>.b.d.</var>
                  cum duplo ipſius
                    <var>.b.c.</var>
                  ſignificetur à
                    <lb/>
                  charactere
                    <var>.A</var>
                  . </s>
                  <s xml:id="echoid-s4588" xml:space="preserve">Hinc habebimus proportionem ipſius
                    <var>.a.d.</var>
                  ad
                    <var>.d.o.</var>
                  ut
                    <var>.A.</var>
                  ad
                    <var>.B</var>
                  .</s>
                </p>
                <note position="left" xml:space="preserve">β</note>
                <p>
                  <s xml:id="echoid-s4589" xml:space="preserve">Ex .18. quinti poſtea habebimus
                    <var>.A.B.</var>
                  ad
                    <var>.B.</var>
                  vt
                    <var>.a.o.</var>
                  ad
                    <var>.d.o.</var>
                  & proportionalitate
                    <lb/>
                  euerſa in .19. dicti ita erit
                    <var>.A.B.</var>
                  ad
                    <var>.A.</var>
                  vt
                    <var>.a.o.</var>
                  ad
                    <var>.a.d</var>
                  . </s>
                  <s xml:id="echoid-s4590" xml:space="preserve">Sed hoc vltimum antecedens in
                    <lb/>
                    <anchor type="note" xlink:label="note-0398-03a" xlink:href="note-0398-03"/>
                  ſe continet id quod Archimedes ſcribit, hoc eſt duplum ipſius
                    <var>.a.b.</var>
                    <reg norm="quadruplum" type="context">quadruplũ</reg>
                  ipſius
                    <lb/>
                    <var>b.c.</var>
                  ſexcuplum ipſius
                    <var>.b.d.</var>
                  & triplum ipſius
                    <var>.b.e</var>
                  . </s>
                  <s xml:id="echoid-s4591" xml:space="preserve">Conſequens verò
                    <var>.A.</var>
                  continet du
                    <lb/>
                  plum ipſius
                    <var>.a.b.</var>
                  quadruplum ipſius
                    <var>.b.c.</var>
                  quadruplum ipſius
                    <var>.b.d.</var>
                  & duplum ipſius
                    <var>.b.e</var>
                  .</s>
                </p>
                <div xml:id="echoid-div742" type="float" level="5" n="6">
                  <note xlink:label="note-0398-03" xlink:href="note-0398-03a" position="left" xml:space="preserve">T</note>
                </div>
                <p>
                  <s xml:id="echoid-s4592" xml:space="preserve">Ex ſuppoſito deinde ipſius Archimedis & ex conuerſa proportionalitate in .19.
                    <lb/>
                  dicta, verum eſt id quod dicit Archimedes, videlicet quod eadem proportio eſt
                    <lb/>
                  ipſius
                    <var>.a.d.</var>
                  ad
                    <var>.g.h.</var>
                  quod quintupli ipſius
                    <var>.a.b.</var>
                  cum quintuplo ipſius
                    <var>.b.e.</var>
                  cum decuplo
                    <lb/>
                  ipſius
                    <var>.b.c.</var>
                  cum decuplo ipſius
                    <var>.b.d.</var>
                  (quod quidem antecedens ſignificetur per
                    <var>.V.</var>
                  )
                    <lb/>
                  ad duplum ipſius
                    <var>.a.b.</var>
                  cum quadruplo ipſius
                    <var>.b.c.</var>
                  cum ſexcuplo ipſius
                    <var>.b.d.</var>
                  cum triplo
                    <lb/>
                  ipſius
                    <var>.b.e.</var>
                  hoc eſt ad
                    <var>.A.B</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4593" xml:space="preserve">Erit igitur
                    <var>.V.</var>
                  ad
                    <var>.A.B.</var>
                  vt ipſius
                    <var>.a.d.</var>
                  ad
                    <var>.g.h.</var>
                  ſed ſuperius vbi ſignatum eſt
                    <var>.T.</var>
                  iam
                    <lb/>
                  probatum fuit ita eſſe
                    <var>.A.B.</var>
                  ad
                    <var>.A.</var>
                  vt ipſius
                    <var>.a.o.</var>
                  ad
                    <var>.a.d</var>
                  . </s>
                  <s xml:id="echoid-s4594" xml:space="preserve">Ergò ex .23. quinti Archime
                    <lb/>
                  des verum ſcribit, hoc eſt quod ita erit ipſius
                    <var>.V.</var>
                  ad
                    <var>.A.</var>
                  vt ipſius
                    <var>.a.o.</var>
                  ad
                    <var>.g.h</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4595" xml:space="preserve">Clarum per ſe etiam eſt, id quod Archimed. dicit hoc eſt quod
                    <var>.V.</var>
                  ad
                    <var>.A.</var>
                  eſt vt
                    <lb/>
                    <anchor type="note" xlink:label="note-0398-04a" xlink:href="note-0398-04"/>
                  </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>