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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EPISTOL AE.
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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div680" type="section" level="3" n="31">
              <div xml:id="echoid-div686" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s4283" xml:space="preserve">
                    <pb o="357" rhead="EPISTOL AE." n="369" file="0369" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0369"/>
                  gulus
                    <var>.p.n.q.</var>
                  vnde ex methodo .56.
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0369-01a" xlink:href="fig-0369-01"/>
                  primi triangulorum Monteregij,
                    <lb/>
                  cognoſcemus reliqua trianguli
                    <var>.
                      <lb/>
                    q.p.n</var>
                  . </s>
                  <s xml:id="echoid-s4284" xml:space="preserve">Conſtituendo poſtea angu-
                    <lb/>
                  lum
                    <var>.q.n.u.</var>
                  æqualem angulo
                    <var>.n.q.p.</var>
                    <lb/>
                  propoſitum habebimus.</s>
                </p>
                <div xml:id="echoid-div687" type="float" level="5" n="2">
                  <figure xlink:label="fig-0369-01" xlink:href="fig-0369-01a">
                    <image file="0369-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0369-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4285" xml:space="preserve">Si etiam puncta
                    <var>.q.p.</var>
                  lineæ
                    <var>.q.p.</var>
                    <lb/>
                  orizontali in eodem plano non exi
                    <lb/>
                  ſterent cum puncto
                    <var>.n.</var>
                  nihil refer-
                    <lb/>
                  ret, dummodo in pauimento
                    <reg norm="notem" type="context">notẽ</reg>
                    <lb/>
                  tur
                    <reg norm="puncta" type="context">pũcta</reg>
                    <var>.c.e.</var>
                  proxima
                    <var>.n.</var>
                  in ijſdem
                    <lb/>
                  ſuperficiebus triangulorum
                    <var>.n.o.p.</var>
                    <lb/>
                  et
                    <var>.n.o.q.</var>
                  vnde
                    <var>.n.c.</var>
                  et
                    <var>.n.e.</var>
                  erunt
                    <reg norm="com- munes" type="context">cõ-
                      <lb/>
                    munes</reg>
                  ſectiones dictarum ſuperficierum cum ſuperficie pauimenti ſupra quam fit
                    <lb/>
                  ſtatio.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div690" type="section" level="3" n="32">
              <div xml:id="echoid-div690" type="letter" level="4" n="1">
                <head xml:id="echoid-head524" xml:space="preserve">CONI RECTI DIVISIO A PLANO
                  <lb/>
                parallelo baſi ſecundum datam proportionem.</head>
                <head xml:id="echoid-head525" style="it" xml:space="preserve">Rapbaeli de Auria.</head>
                <p>
                  <s xml:id="echoid-s4286" xml:space="preserve">
                    <emph style="sc">QVotiescvnqve</emph>
                  volueris conum rectum diuidere à plano parallelo ba-
                    <lb/>
                  ſi ſecundum vnam datam proportionem, nullius tibi erit difficultatis, con
                    <lb/>
                  ceſſa
                    <reg norm="tamen" type="wordlist">tamẽ</reg>
                  pro inuenta diuiſione cuiuſuis propoſitę proportionis per tres
                    <lb/>
                  æquales partes.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4287" xml:space="preserve">Sit exempli gratia conus rectus
                    <var>.a.b.c.</var>
                  ſecandus vt dictum eſt, accipiatur latus
                    <lb/>
                  ipſius, quod ſit
                    <var>.a.c.</var>
                    <reg norm="ipſumque" type="simple">ipſumq́;</reg>
                  diuidatur in puncto
                    <var>.d.</var>
                  ſecundum illam proportionem
                    <lb/>
                  quam deſideras, hoc eſt ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.d.</var>
                  quo facto, inter totum
                    <var>.a.c.</var>
                  et
                    <var>.a.d.</var>
                  inuenian
                    <lb/>
                  tur duæ lineæ proportionales, quarum maior ſit
                    <var>.a.i.</var>
                  </s>
                  <s xml:id="echoid-s4288" xml:space="preserve">tunc ſi conus
                    <var>.a.b.c.</var>
                  ſectus fue-
                    <lb/>
                  rit à plano per punctum
                    <var>.i.</var>
                  parallelo baſi, habebimus quod quærebamus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4289" xml:space="preserve">Cuius rei ratio, primò eſt, quia quotieſcunque conus aliquis ſectus fuerit ab ali-
                    <lb/>
                  quo plano parallelo baſi ipſius, pars ſuperior ſimilis ſemper erit totali cono, quod
                    <lb/>
                  ita probo, cogitemus conum ſectum eſſe
                    <lb/>
                  à plano per axem
                    <var>.a.l.</var>
                  vnde ex .3. primi
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0369-02a" xlink:href="fig-0369-02"/>
                  Pergei, talis ſectio triangularis erit, quæ
                    <lb/>
                  ſit
                    <var>.a.b.c.</var>
                  et
                    <var>.b.c.</var>
                  diameter erit baſis.</s>
                </p>
                <div xml:id="echoid-div690" type="float" level="5" n="1">
                  <figure xlink:label="fig-0369-02" xlink:href="fig-0369-02a">
                    <image file="0369-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0369-02"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4290" xml:space="preserve">Imaginemur deinde
                    <var>.K.i.</var>
                  communem
                    <lb/>
                  eſſe ſectionem huiuſmodi trianguli cum
                    <lb/>
                  plano parallelo ipſi baſi, </s>
                  <s xml:id="echoid-s4291" xml:space="preserve">tunc tale
                    <reg norm="planum" type="context">planũ</reg>
                  ,
                    <lb/>
                  circulare erit ex .4. primi ipſius Pergei
                    <var>.K.
                      <lb/>
                    i.</var>
                  verò, eius diameter erit, et
                    <var>.a.m.</var>
                    <reg norm="ſuus" type="simple">ſuꝰ</reg>
                  axis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4292" xml:space="preserve">Cum verò
                    <var>.a.l.</var>
                  ſit perpendicularis ipſi
                    <lb/>
                  baſi conitotalis, eo quod rectus ſupponi-
                    <lb/>
                  tur, ideo eadem
                    <var>.a.m.l.</var>
                  erit perpendicula
                    <lb/>
                  ris eriam ipſi ſecundo plano circulari, ex
                    <lb/>
                  conuerſa .14. vndecimi Euclid. </s>
                  <s xml:id="echoid-s4293" xml:space="preserve">vnde ex </s>
                </p>
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