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-div591" type="section" level="3" n="22">
              <div xml:id="echoid-div599" type="letter" level="4" n="4">
                <p>
                  <s xml:id="echoid-s3784" xml:space="preserve">
                    <pb o="307" rhead="EPISTOLAE." n="319" file="0319" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0319"/>
                  ſe habet ad triangulum
                    <var>b.p.x.</var>
                  ducatur poſtea
                    <var>.o.q.</var>
                  quæ diuidat totale triangulum
                    <var>.d.
                      <lb/>
                    u.x.</var>
                  in duas partes inuicem ita proportionatas, ut ſe habent
                    <var>t.r.</var>
                  et
                    <var>.r.e.</var>
                  quæ quidem
                    <lb/>
                  partes ſint
                    <var>.c.d.u.q.</var>
                  et
                    <var>.c.q.x.</var>
                  ut in primo problemate tibi monſtraui, & habebis pro-
                    <lb/>
                  poſitum, dato quod punctum
                    <var>.c.</var>
                  ſit inter
                    <lb/>
                  b. et
                    <var>.d</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3785" xml:space="preserve">Sed ſi forte linea
                    <var>.o.q.</var>
                  ſecabit
                    <var>.b.x.</var>
                  hoc
                    <lb/>
                    <figure xlink:label="fig-0319-01" xlink:href="fig-0319-01a" number="342">
                      <image file="0319-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0319-01"/>
                    </figure>
                  eſt ſi punctum
                    <var>.c.</var>
                  eſſet inter
                    <var>.b.</var>
                  et
                    <var>.x.</var>
                  mani-
                    <lb/>
                  feſtum eſt, quod
                    <var>.c.q.</var>
                  ſecaret
                    <var>.b.p.</var>
                  in pun-
                    <lb/>
                  cto
                    <var>.y.</var>
                  vnde in tali caſu, alio modo ope-
                    <lb/>
                  randum eſſet, hoc eſt ducendo
                    <var>.b.u.</var>
                  quæ
                    <lb/>
                  diuideret quadrilaterum in duo triangu-
                    <lb/>
                  la, & ut ſe haberet triangulum
                    <var>.b.d.u.</var>
                  ad
                    <lb/>
                  triangulum
                    <var>.b.p.u.</var>
                  vellem vt ita ſecaretur
                    <lb/>
                    <var>t.i.</var>
                  in puncto
                    <var>.n.</var>
                  vt ita ſe haberet
                    <var>.t.n.</var>
                  ad
                    <var>.n.
                      <lb/>
                    i.</var>
                  ut dictum eſt de iſtis duobus triangulis,
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3786" xml:space="preserve">deinde prout ſe habet
                    <var>.n.r.</var>
                  ad
                    <var>.r.i.</var>
                  ita ſeca-
                    <lb/>
                  res triangulum
                    <var>.b.p.u.</var>
                  mediante linea
                    <var>.o.
                      <lb/>
                    K.</var>
                  ex doctrina primi problematis, & ita haberes propoſitum.</s>
                </p>
              </div>
              <div xml:id="echoid-div601" type="letter" level="4" n="5">
                <head xml:id="echoid-head465" style="it" xml:space="preserve">Idem de Pentagono, Exagono, & de reliquis.</head>
                <head xml:id="echoid-head466" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3787" xml:space="preserve">PEntagonum, ſeu hexagonum, vel alias quaſuis multilateras figuras propoſitas its
                    <lb/>
                  diuidere, vt dictum eſt de trilateris, & quadrilateris.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3788" xml:space="preserve">Sit exempli gratia pentagonus
                    <var>.a.d.u.p.b.</var>
                  quem ſecare volumus
                    <reg norm="mediante" type="context">mediãte</reg>
                  linea
                    <var>.o.
                      <lb/>
                    q.</var>
                  in duas partes inuicem ſe habentes, vt ſe habent
                    <var>.t.r.</var>
                  et
                    <var>.r.i.</var>
                  oportet igitur ut ipſum
                    <lb/>
                  pentagonum reducas ad quadrilaterum
                    <var>.x.a.d.u.</var>
                  quod diuidatur ſecundum præce-
                    <lb/>
                  dentem doctrinam, vt ſe habet
                    <var>.t.r.</var>
                  ad
                    <var>.r.e.</var>
                    <lb/>
                  vnde ſi punctum
                    <var>.q.</var>
                  incidit inter
                    <var>.p.</var>
                  et
                    <var>.u</var>
                  . </s>
                  <s xml:id="echoid-s3789" xml:space="preserve">tunc
                    <lb/>
                  habebis propoſitum, ſi verò incidet inter
                    <var>.
                      <lb/>
                      <figure xlink:label="fig-0319-02" xlink:href="fig-0319-02a" number="343">
                        <image file="0319-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0319-02"/>
                      </figure>
                    p.</var>
                  et
                    <var>.x.</var>
                  clarum erit quod linea
                    <var>.o.q.</var>
                  ſecabit
                    <lb/>
                  latus
                    <var>.p.b.</var>
                  trianguli
                    <var>.b.x.p.</var>
                  in puncto
                    <var>.y.</var>
                  qua-
                    <lb/>
                  propter duces lineam
                    <var>.a.p.</var>
                  vt claudat trian-
                    <lb/>
                  gulum
                    <var>.a.b.p.</var>
                    <reg norm="diuidaturque" type="simple">diuidaturq́;</reg>
                    <var>.t.i.</var>
                  in puncto
                    <var>.n.</var>
                  ita
                    <lb/>
                  vt
                    <var>.t.n.</var>
                  ad
                    <var>.n.i.</var>
                  ſe habeat, vt quadrilaterum. a
                    <unsure/>
                    <var>.
                      <lb/>
                    d.u.p.</var>
                  ad
                    <reg norm="triangulum" type="context">triãgulum</reg>
                    <var>.a.b.p</var>
                  . </s>
                  <s xml:id="echoid-s3790" xml:space="preserve">deinde
                    <reg norm="hunc" type="context">hũc</reg>
                  trian
                    <lb/>
                  gulum
                    <var>.a.b.p.</var>
                  diuidas mediante linea
                    <var>.o.K.</var>
                    <lb/>
                  vt
                    <var>.n.r.</var>
                  ad
                    <var>.r.i.</var>
                  ex doctrina primi problematis
                    <lb/>
                  & habebis propoſitum. </s>
                  <s xml:id="echoid-s3791" xml:space="preserve">Idem dico de hexa
                    <lb/>
                  gono, reducendo ipſum ad pentagonum, &
                    <lb/>
                  item de eptagono, ipſum reducendo ad exa
                    <lb/>
                  gonum, & idem infero de infinito ipſarum
                    <lb/>
                  ſuperficialium figurarum rectilinearum.</s>
                </p>
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            </div>
          </div>
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