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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div591" type="section" level="3" n="22">
              <div xml:id="echoid-div594" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s3775" xml:space="preserve">
                    <pb o="306" rhead="IO. BAPT. BENED." n="318" file="0318" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0318"/>
                  ſcientia. </s>
                  <s xml:id="echoid-s3776" xml:space="preserve">Quare ex .9. quinti, ita erit
                    <var>.s.d.</var>
                  ad dictum
                    <var>.d.u.</var>
                  vt ad quadrilaterum
                    <var>.e.q.u.
                      <lb/>
                    x.</var>
                  hoc eſt vt
                    <var>.A.</var>
                  ad
                    <var>.B.</var>
                  ex .11. eiuſdem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3777" xml:space="preserve">Sed ſi punctum
                    <var>.q.</var>
                  fuerit extra ut in .2. figura videre eſt. </s>
                  <s xml:id="echoid-s3778" xml:space="preserve">tunc manifeſtum erit,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  triangulus
                    <var>.e.x.t.</var>
                  maior erit pa-
                    <lb/>
                  rallelogrammo
                    <var>.d.u.</var>
                  per triangu
                    <lb/>
                    <figure xlink:label="fig-0318-01" xlink:href="fig-0318-01a" number="340">
                      <image file="0318-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0318-01"/>
                    </figure>
                  lum
                    <var>.q.t.u.</var>
                  cum triangulus
                    <var>.q.i.p.</var>
                    <lb/>
                  æqualis triangulo
                    <var>.d.i.e.</var>
                  excedat
                    <lb/>
                  quadrilaterum
                    <var>.i.t.u.p.</var>
                  per trian
                    <lb/>
                  gulum
                    <reg norm="dictum" type="context">dictũ</reg>
                    <var>.q.t.u.</var>
                  quapropter
                    <lb/>
                  cum diuiſus fuerit triangulus
                    <var>.e.
                      <lb/>
                    x.t.</var>
                  mediante linea
                    <var>.o.n.K.</var>
                  ita
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                    <reg norm="quadrilaterum" type="context">quadrilaterũ</reg>
                    <var>.e.n.K.t.</var>
                  ſit æquale
                    <lb/>
                  triangulo
                    <var>.q.t.u.</var>
                  ex doctrina præ
                    <lb/>
                  cedenti, habebimus propoſitum.</s>
                </p>
              </div>
              <div xml:id="echoid-div597" type="letter" level="4" n="3">
                <head xml:id="echoid-head461" style="it" xml:space="preserve">Idem de frusto trianguli.</head>
                <head xml:id="echoid-head462" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3779" xml:space="preserve">SEd ſi quadrilaterum dictum eſſet fruſtum alicuius
                    <reg norm="trianguli" type="context">triãguli</reg>
                  ut in figura
                    <var>.A.</var>
                  hic ſub
                    <lb/>
                  ſcripta videre eſt, ſuppoſita,
                    <var>b.d.</var>
                  parallela ad
                    <var>.u.p.</var>
                  ita faciendum eſſet, ducendo
                    <lb/>
                  ſcilicet parallelam
                    <var>.u.x.</var>
                  ad
                    <var>.b.p.</var>
                  quæ producatur vſque ad concurſum cum
                    <var>.b.d.</var>
                    <lb/>
                  in puncto
                    <var>.x.</var>
                    <reg norm="ſitque" type="simple">ſitq́;</reg>
                  proportio data inter
                    <var>.t.a.</var>
                  et
                    <var>.a.e.</var>
                  quas duas lineas cogitemus inuicem
                    <lb/>
                  directè coniunctas, </s>
                  <s xml:id="echoid-s3780" xml:space="preserve">tunc diuidatur tota
                    <var>.t.e.</var>
                    <lb/>
                    <figure xlink:label="fig-0318-02" xlink:href="fig-0318-02a" number="341">
                      <image file="0318-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0318-02"/>
                    </figure>
                  in puncto
                    <var>.i.</var>
                  ita vt
                    <var>.t.i.</var>
                  ad
                    <var>.i.e.</var>
                  ſit vt quadrilate
                    <lb/>
                  ri
                    <var>.p.d.</var>
                  ad trigonum
                    <var>.u.d.x</var>
                  . </s>
                  <s xml:id="echoid-s3781" xml:space="preserve">deinde diuidatur
                    <lb/>
                    <var>t.i.</var>
                  in puncto r. tali modo vt
                    <var>.t.r.</var>
                  ad
                    <var>.r.i.</var>
                  ſe ha-
                    <lb/>
                  beat vt
                    <var>.t.a.</var>
                  ad
                    <var>.a.e.</var>
                  quo facto ex doctrina
                    <reg norm="prae­ cedenti" type="simple">prę­
                      <lb/>
                    cedenti</reg>
                  diuidatur totum parallelogram--
                    <lb/>
                  mum
                    <var>.p.x.</var>
                  mediante linea
                    <var>.o.q.</var>
                  ſecundum
                    <lb/>
                  quod ſe habet
                    <var>.t.r.</var>
                  ad
                    <var>.r.e</var>
                  . </s>
                  <s xml:id="echoid-s3782" xml:space="preserve">Atque ita ſolu-
                    <lb/>
                  tum erit problema, vt exte ipſo ratiotina-
                    <lb/>
                  ri facile potes.</s>
                </p>
              </div>
              <div xml:id="echoid-div599" type="letter" level="4" n="4">
                <head xml:id="echoid-head463" style="it" xml:space="preserve">Fdem de quadrilatero in genere.</head>
                <head xml:id="echoid-head464" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3783" xml:space="preserve">SEd ſi nullum latus parallelum reliquo erit, ita faciendum erit. </s>
                  <s xml:id="echoid-s3784" xml:space="preserve">ſi ſit tale quadrila
                    <lb/>
                  terum
                    <var>.b.d.u.p.</var>
                  oportet vt ipſum conuertamus in triangulum, producendo duo
                    <lb/>
                  quęuis eius latera oppoſita uſque ad interſectionem ut pote
                    <var>.u.p.</var>
                  et
                    <var>.d.b.</var>
                  in puncto
                    <var>.x.</var>
                    <lb/>
                  quo facto, ſupponemus
                    <var>.o.</var>
                  eſſe punctum datum, proportio verò data ſit
                    <var>.t.r.</var>
                  ad
                    <var>.r.i.</var>
                  ad
                    <lb/>
                  iungatur deinde
                    <var>.i.e.</var>
                  ad
                    <var>.t.i.</var>
                  ad quam
                    <var>.e.i.</var>
                  ipſa
                    <var>.t.i.</var>
                  ſe habeat vt quadrilaterum
                    <var>.b.d.u.p.</var>
                  </s>
                </p>
              </div>
            </div>
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