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
371 359
372 360
373 361
374 362
375 363
376 364
377 365
378 366
379 367
380 368
381 369
382 370
383 371
384 372
385 373
386 374
387 375
388 376
389 377
390 378
391 379
392 380
393 381
394 382
395 383
396 384
397 385
398 386
399 387
400 388
< >
page |< < (386) of 445 > >|
    <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>
                <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/>
                    <note xlink:label="note-0398-01" xlink:href="note-0398-01a" position="left" xml:space="preserve">M</note>
                    <var>a.d.</var>
                  ad
                    <var>.d.e.</var>
                  erit vt
                    <var>.D.</var>
                  ad
                    <var>.B</var>
                  .</s>
                </p>
                <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/>
                    <note xlink:label="note-0398-03" xlink:href="note-0398-03a" position="left" xml:space="preserve">T</note>
                  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>
                <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/>
                    <note xlink:label="note-0398-04" xlink:href="note-0398-04a" position="left" xml:space="preserve">ω</note>
                  </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>