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]

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        <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>
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