Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s1847" xml:space="preserve">
              <pb o="54" file="0078" n="78" rhead=""/>
            ſita cum dato recto CL. </s>
            <s xml:id="echoid-s1848" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s1849" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1851" xml:space="preserve">Iam ſit data Hyperbolæ portio AMCNE, cuius tranſuerſum CH, rectum
              <lb/>
            CL, regula HLG, baſis AE, diameter CI, & </s>
            <s xml:id="echoid-s1852" xml:space="preserve">oporteat, per verticem C, _MI_-
              <lb/>
            _NIMAM_ Parabolæ portionem circumſcribere.</s>
            <s xml:id="echoid-s1853" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1854" xml:space="preserve">Producatur applicata AI, conueniens cum re-
              <lb/>
              <figure xlink:label="fig-0078-01" xlink:href="fig-0078-01a" number="48">
                <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0078-01"/>
              </figure>
            gula HL in G, & </s>
            <s xml:id="echoid-s1855" xml:space="preserve">per G ducatur GF parallela ad
              <lb/>
            IC contingentem ſecans in F, cumque recto CF
              <lb/>
            adſcribatur per C Parabole ABCDE, quæ
              <note symbol="a" position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">5. huius.</note>
            cabit Hyperbolen in ijſdem punctis A, & </s>
            <s xml:id="echoid-s1856" xml:space="preserve">E, ob
              <lb/>
            rationem ſuperius allatam, & </s>
            <s xml:id="echoid-s1857" xml:space="preserve">datę Parabolæ AB
              <lb/>
            CD erit circumſcripta; </s>
            <s xml:id="echoid-s1858" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s1859" xml:space="preserve">_MINIMA_ portio.</s>
            <s xml:id="echoid-s1860" xml:space="preserve"/>
          </p>
          <note symbol="b" position="left" xml:space="preserve">1. Co-
            <lb/>
          roll. prop.
            <lb/>
          19. huius.</note>
          <p>
            <s xml:id="echoid-s1861" xml:space="preserve">Quoniam, quæ cum recto maiore ipſo CF eſt
              <lb/>
            maior ipſa ABCDE, quæ verò cum recto
              <note symbol="c" position="left" xlink:label="note-0078-03" xlink:href="note-0078-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            re ipſo CF eſt quidem minor ABCDE, ſed
              <note symbol="d" position="left" xlink:label="note-0078-04" xlink:href="note-0078-04a" xml:space="preserve">ibidem.</note>
            tota cadit intra Hyperbolen AMCN ſi
              <note symbol="e" position="left" xlink:label="note-0078-05" xlink:href="note-0078-05a" xml:space="preserve">21. h.</note>
            rectum æquale fuerit ipſo CL, & </s>
            <s xml:id="echoid-s1862" xml:space="preserve">eò magis ſi mi-
              <lb/>
            nus eſſet BL; </s>
            <s xml:id="echoid-s1863" xml:space="preserve">vel ſaltẽ ſecat Hyperbolen AMCN
              <lb/>
            ſupra applicatam AE tum cum rectum ſit medium inter CF, & </s>
            <s xml:id="echoid-s1864" xml:space="preserve">CL,
              <note symbol="f" position="left" xlink:label="note-0078-06" xlink:href="note-0078-06a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            eſt CP: </s>
            <s xml:id="echoid-s1865" xml:space="preserve">nam regula, quæ ex P, ducitur æquidiſtans CI, omninò ſecat regu-
              <lb/>
            lam LG infra contingentem CF, & </s>
            <s xml:id="echoid-s1866" xml:space="preserve">ſupra applicatam AG. </s>
            <s xml:id="echoid-s1867" xml:space="preserve">Quare ipſa Para-
              <lb/>
            bolæ portio ABCDE, eſt _MINIMA_ circumſcripta quæſita. </s>
            <s xml:id="echoid-s1868" xml:space="preserve">Quod tandem
              <lb/>
            faciendum erat.</s>
            <s xml:id="echoid-s1869" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div170" type="section" level="1" n="88">
          <head xml:id="echoid-head93" xml:space="preserve">PROBL. XIII. PROP. XXVIII.</head>
          <p>
            <s xml:id="echoid-s1870" xml:space="preserve">Datæ portioni Hyperbolæ, cum dato tranſuerſo vel recto, quod
              <lb/>
            minus ſit tranſuerſo, vel recto datæ Hyperbolæ, per eius verticem
              <lb/>
            MAXIMAM Hyperbolæ portionem inſcribere: </s>
            <s xml:id="echoid-s1871" xml:space="preserve">& </s>
            <s xml:id="echoid-s1872" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1873" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1874" xml:space="preserve">Datæ portioni Hyperbolæ, cum dato tranſuerſo vel recto, quod
              <lb/>
            excedat tranſuerſum, aut rectum datæ Hyperbolæ, per eius verti-
              <lb/>
            cem MINIMAM Hyperbolæ portionem circumſcribere.</s>
            <s xml:id="echoid-s1875" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1876" xml:space="preserve">SIt data Hyperbolæ portio ABCDE, cuius
              <lb/>
              <figure xlink:label="fig-0078-02" xlink:href="fig-0078-02a" number="49">
                <image file="0078-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0078-02"/>
              </figure>
            tranſuerſum CF, rectum CG, regula FGL,
              <lb/>
            baſis AE, diameter CH. </s>
            <s xml:id="echoid-s1877" xml:space="preserve">Oporter primò cum
              <lb/>
            dato tranſuerſo CI, quod minus ſit ipſo CF
              <lb/>
            _MAXIMAM_ Hyporbolæ portionem inſcribere.</s>
            <s xml:id="echoid-s1878" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1879" xml:space="preserve">Producta enim applicata AH, cõueniat cum
              <lb/>
            regula FG in L, & </s>
            <s xml:id="echoid-s1880" xml:space="preserve">iuncta IL contingentem CG
              <lb/>
            ſecant in M, cum regula IM, per verticem C ad-
              <lb/>
            ſcribatur portioni ABCDE Hyperbole
              <note symbol="a" position="left" xlink:label="note-0078-07" xlink:href="note-0078-07a" xml:space="preserve">6. huius.</note>
            OE, quę datam ABCD ſecabit in A, & </s>
            <s xml:id="echoid-s1881" xml:space="preserve">E, at
              <note symbol="b" position="left" xlink:label="note-0078-08" xlink:href="note-0078-08a" xml:space="preserve">1. Co-
                <lb/>
              roll prop.
                <lb/>
              19. huius.</note>
            ipſi erit inſcripta. </s>
            <s xml:id="echoid-s1882" xml:space="preserve">Dico portionẽ ANCOE eſſe
              <lb/>
            _MAXIMAM_ quæſitam.</s>
            <s xml:id="echoid-s1883" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1884" xml:space="preserve">Quoniam, quę adſcribitur cum eodem tranſ-
              <lb/>
            uerſo CI, ſed cum recto, quod ſit minus CM, eſt minor ipſa ANCO,
              <note symbol="c" position="left" xlink:label="note-0078-09" xlink:href="note-0078-09a" xml:space="preserve">2. corol.
                <lb/>
              prop. 19.
                <lb/>
              huius.</note>
            </s>
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