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
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
421 409
422 410
423 411
424 412
425 413
426 414
427 415
428 416
429 417
430 418
< >
page |< < (362) 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-div703" type="section" level="3" n="35">
              <div xml:id="echoid-div703" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4331" xml:space="preserve">
                    <pb o="362" rhead="IO. BAPT. BENED." n="374" file="0374" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0374"/>
                  modifunis cum libramento triangulum ſcalenum conſtitueret.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4332" xml:space="preserve">Exempli gratia, ponamus lineam
                    <var>.d.b.c.</var>
                  eſſe libramentum .et
                    <var>.b.e.u.</var>
                  eius pedem,
                    <lb/>
                  funem autem, qui aliquando cum libramento facit triangulum iſocellum, & aliquan
                    <lb/>
                  do ſcalenum, eſſe
                    <var>.d.e.c.</var>
                  eſto etiam quod in figura
                    <var>.A.</var>
                  dictus triangulus
                    <var>.d.e.c.</var>
                  ſit iſo-
                    <lb/>
                  cellus, & in figura
                    <var>.B.</var>
                  ſcalenus. </s>
                  <s xml:id="echoid-s4333" xml:space="preserve">Tunc quæſiui à te an ſcires rationem, quare
                    <lb/>
                  funis
                    <var>.d.e.c.</var>
                  in figura
                    <var>.A.</var>
                  eſſet diſtenſus, & in figura
                    <var>.B.</var>
                  laxus quemadmodum vide-
                    <lb/>
                  bamus. </s>
                  <s xml:id="echoid-s4334" xml:space="preserve">cum mihireſponderis, neſcio quid, quod nunc memoria
                    <reg norm="non" type="context">nõ</reg>
                  teneo, ſed quia
                    <lb/>
                  pollicitus ſum metibi eam afferre, propterea nunc ad te mitto. </s>
                  <s xml:id="echoid-s4335" xml:space="preserve">Scias ergo huiuſ-
                    <lb/>
                  modirationem nihil aliud eſſe niſi quod in figura
                    <var>.A.</var>
                  duæ lineæ
                    <var>.c.e.</var>
                  et
                    <var>.d.e.</var>
                  ſimul è
                    <lb/>
                  directo iunctæ longiores ſint illis, quę reperiuntur in figura
                    <var>.B.</var>
                  ſed quia funis tam in
                    <lb/>
                  figura
                    <var>.B.</var>
                  quam in figura
                    <var>.A.</var>
                  vnus, & idem eſt, ideo in figura
                    <var>.B.</var>
                  laxatus eſt, & non in
                    <lb/>
                  tenſus, ut in figura
                    <var>.A</var>
                  . </s>
                  <s xml:id="echoid-s4336" xml:space="preserve">Sed vt huiuſmodi veritatis certam notitiam habeas, infraſcri
                    <lb/>
                  ptum circulum mente concipe
                    <var>.f.e.i.</var>
                  cuius ſemidiameter, æqualis ſit
                    <var>.b.e.</var>
                  & diame-
                    <lb/>
                  ter ſit
                    <var>.f.i.</var>
                  in quo imaginare eſſe tuum
                    <lb/>
                  libramentum
                    <var>.d.b.c.</var>
                  & figuras
                    <var>.A.</var>
                  et
                    <var>.B.</var>
                    <lb/>
                    <figure xlink:label="fig-0374-01" xlink:href="fig-0374-01a" number="413">
                      <image file="0374-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0374-01"/>
                    </figure>
                    <figure xlink:label="fig-0374-02" xlink:href="fig-0374-02a" number="414">
                      <image file="0374-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0374-02"/>
                    </figure>
                  & pr obabo lineas
                    <var>.d.e.c.</var>
                  figurę
                    <var>.A.</var>
                  lon
                    <lb/>
                  giores eſſe lineis
                    <var>.d.e.c.</var>
                  figuræ
                    <var>.B</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4337" xml:space="preserve">Imaginemur igitur lineam
                    <var>.b.e.</var>
                  eſſe
                    <lb/>
                  dimidium minoris axis
                    <reg norm="alicuius" type="simple">alicuiꝰ</reg>
                  ellipſis
                    <lb/>
                  cuius quidem figuræ ponamus
                    <var>.d.</var>
                  et
                    <var>.c.</var>
                    <lb/>
                  centra ipſius circunſcriptionis eſſe, cu
                    <lb/>
                  ius
                    <reg norm="circunferentia" type="context">circunferẽtia</reg>
                  , nullidubium eſt, quin
                    <lb/>
                  extra propoſitum circulum tranſitura,
                    <lb/>
                  & in vno tantummodo puncto ipſum
                    <lb/>
                  circulum tactura ſit, qui exiſtat
                    <var>.e.</var>
                    <lb/>
                  figuræ
                    <var>.A.</var>
                  ſeparatum tamen à puncto
                    <lb/>
                  e. figuræ
                    <var>.B</var>
                  . </s>
                  <s xml:id="echoid-s4338" xml:space="preserve">Tunc ſi protracta fue-
                    <lb/>
                  rit linea
                    <var>.d.e.</var>
                  figuræ
                    <var>.B.</var>
                  vſque ad gi
                    <lb/>
                    <figure xlink:label="fig-0374-03" xlink:href="fig-0374-03a" number="415">
                      <image file="0374-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0374-03"/>
                    </figure>
                  rum ellipticum in puncto
                    <var>.g.</var>
                  à quo
                    <lb/>
                  ad punctum
                    <var>.c.</var>
                  ducta etiam ſit linea
                    <lb/>
                    <var>g.c</var>
                  . </s>
                  <s xml:id="echoid-s4339" xml:space="preserve">tunc
                    <reg norm="manifeſtum" type="context">manifeſtũ</reg>
                  erit duas lineas
                    <lb/>
                    <var>d.e.</var>
                  et
                    <var>.e.c.</var>
                  figuræ
                    <var>.A.</var>
                  ſimul iunctas,
                    <lb/>
                  æquales eſſe duabus
                    <var>.d.g.</var>
                  et
                    <var>.g.c.</var>
                  ſi-
                    <lb/>
                  mul poſitis, vt etiam ex .52. tertij
                    <lb/>
                  Pergei facilè videre eſt, ſed ex .21.
                    <lb/>
                  primi Euclid. iam certò ſcimus
                    <var>.d.g.c.</var>
                  longiores eſſe
                    <var>.d.e.c.</var>
                  ſiguræ
                    <var>.B.</var>
                  ergo
                    <var>.d.e.c.</var>
                  figu-
                    <lb/>
                  ræ
                    <var>.A.</var>
                  longiores ſunt
                    <var>.d.e.c.</var>
                  figuræ
                    <var>.B.</var>
                  quod eſt propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4340" xml:space="preserve">Quod etiam mihinunc circa hoc ſuccurrit, tibi libenter ſignifico, hoc eſt, quod
                    <lb/>
                  ſicut in ellipſi duæ lineæ
                    <var>.d.e.e.c.</var>
                  figuræ
                    <var>.A.</var>
                  ſimul iunctæ, ſunt ſemper æquales duabus
                    <lb/>
                  lineis
                    <var>.d.g.g.c.</var>
                  in longitudine, ita in circulo duæ
                    <var>.d.e.e.c.</var>
                  figuræ
                    <var>.A.</var>
                  æquales ſunt in
                    <lb/>
                  potentia duabus
                    <var>.d.e.e.c.</var>
                  figurę
                    <var>.B</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4341" xml:space="preserve">Manifeſtum enim primum eſt ex penultima primi in figura
                    <var>.A.</var>
                  quadratum
                    <var>.e.c.</var>
                    <lb/>
                  æquale eſſe duobus quadratis ſcilicet
                    <var>.e.b.</var>
                  et
                    <var>.b.c.</var>
                  & quadratum
                    <var>.e.d.</var>
                  æquale duobus
                    <var>.
                      <lb/>
                    e.b.</var>
                  et
                    <var>.b.d</var>
                  . </s>
                  <s xml:id="echoid-s4342" xml:space="preserve">Quare quadrata
                    <var>.e.c.</var>
                  et
                    <var>.e.d.</var>
                  æqualia ſunt quadratis
                    <var>.e.b.</var>
                  figuræ
                    <var>.A.</var>
                  et
                    <var>.e.
                      <lb/>
                    b.</var>
                  figurę. B et
                    <var>.b.c.</var>
                  et
                    <var>.b.d.</var>
                  hoc eſt duplo quadrati
                    <var>.e.a.</var>
                  (ducta cum fuerit
                    <var>.e.a.</var>
                  perpen-
                    <lb/>
                  dicularis ad
                    <var>.c.b.d.a.</var>
                  ) duplo quadrati
                    <var>.a.b.</var>
                  ex penultima primi, & duplo quadrati
                    <var>.b.
                      <lb/>
                    c</var>
                  . </s>
                  <s xml:id="echoid-s4343" xml:space="preserve">Sed quadrata
                    <var>.d.e.</var>
                  et
                    <var>.e.c.</var>
                  figurę
                    <var>.B.</var>
                  æqualia ſunt duplo quadrati
                    <var>.a.e.</var>
                  & quadrato
                    <var>a.d.</var>
                  </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum