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

Table of handwritten notes

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          <p>
            <s xml:id="echoid-s8887" xml:space="preserve">
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            minus eſt, prout in præcedenti demonſtratum fuit: </s>
            <s xml:id="echoid-s8888" xml:space="preserve">idemque ſequetur,
              <note symbol="*" position="right" xlink:label="note-0319-01" xlink:href="note-0319-01a" xml:space="preserve">94. h.</note>
            dicatur Hyperbolen alibi quàm in G arcui D B occurrere. </s>
            <s xml:id="echoid-s8889" xml:space="preserve">Itaque inuenta
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            ſunt in ſemi - circulo, vel ſemi - Ellipſi vltrò citròque à _MAXIMO_ rectangu-
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            lo, duo rectangula inter ſe æqualia. </s>
            <s xml:id="echoid-s8890" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s8891" xml:space="preserve"/>
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        <div xml:id="echoid-div924" type="section" level="1" n="369">
          <head xml:id="echoid-head378" xml:space="preserve">PROBL. XIX. PROP. XCVI.</head>
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            <s xml:id="echoid-s8892" xml:space="preserve">In quocunque Cono terminato, ex infinitis Parabolæ portioni-
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            bus, quæ à planis inter ſe æquidiſtantibus, iuxta quodlibet Coni
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            latus, tanquam regulam ductis, in ipſo Cono procreantur, MA-
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            XIMAM aſſignare.</s>
            <s xml:id="echoid-s8893" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8894" xml:space="preserve">ESto Conus quicunque terminatus A B C, cuius vertex B, baſis circu-
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            lus A C, & </s>
            <s xml:id="echoid-s8895" xml:space="preserve">quodcunque triangulum per axem ductum ſit A B C.
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            </s>
            <s xml:id="echoid-s8896" xml:space="preserve">Patet, ſi huinſmodi Conus, & </s>
            <s xml:id="echoid-s8897" xml:space="preserve">triangulum per axem alio plano ſecetur, quo-
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            rum communis ſectio D E æquidiſtet alterutri laterum trianguli per axem,
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            nempe B C, & </s>
            <s xml:id="echoid-s8898" xml:space="preserve">communis ſectio plani ſecantis per D E cum baſi A C, quę
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            ſit F G, ſit ad baſim A C trianguli per axem perpendicularis, patet inquam
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            ſectionem in Cono genitam G E F (quam vocò factam iuxta latus B C,
              <lb/>
            quod communi ſectioni E D æquidiſtat) ſemper eſſe quandam
              <note symbol="a" position="right" xlink:label="note-0319-02" xlink:href="note-0319-02a" xml:space="preserve">1. primi
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              huius.</note>
            portionem: </s>
            <s xml:id="echoid-s8899" xml:space="preserve">quæritur modò, quæ ſit _MAXIMA_ harum æquidiſtantium infi-
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            nitarum Parabolæ portionum in Cono, iuxta latus B C, tanquam regulam,
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            progenitarum.</s>
            <s xml:id="echoid-s8900" xml:space="preserve"/>
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            <s xml:id="echoid-s8901" xml:space="preserve">Secetur diameter A C in D, ita vt A
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              <figure xlink:label="fig-0319-01" xlink:href="fig-0319-01a" number="255">
                <image file="0319-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0319-01"/>
              </figure>
            D ſit tripla ad D C, & </s>
            <s xml:id="echoid-s8902" xml:space="preserve">per D agatur pla-
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            num iuxta regulam B C, vti dictum eſt,
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            ſectionem faciens Parabolen G E F. </s>
            <s xml:id="echoid-s8903" xml:space="preserve">Di-
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            co hanc eſſe _MAXIMAM_ quæſitam.</s>
            <s xml:id="echoid-s8904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8905" xml:space="preserve">Secto enim Cono, quocunque alio
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            plano iuxta eandem regulam B C, quod
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            ſectionem faciat Parabolen H I K, cuius
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            communis ſectio cum triangulo per axem
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            ſit I L, cum circulo verò ſit K L H, erit
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            D E ipſi L I, & </s>
            <s xml:id="echoid-s8906" xml:space="preserve">F D ipſi K L
              <note symbol="b" position="right" xlink:label="note-0319-03" xlink:href="note-0319-03a" xml:space="preserve">16. vnd.
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              Elem.</note>
            quare angulus F D E angulo K L I æqua-
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            lis erit, vnde, ſi concipiantur iungi
              <note symbol="c" position="right" xlink:label="note-0319-04" xlink:href="note-0319-04a" xml:space="preserve">10. ibid.</note>
            ctæ F E, K I, triangula F D E, K L I cum
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            ſint æquiangula ad D, L, habebunt rationem compoſitam ex latere E D
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            ad I L, ſiue ex D A ad A L, & </s>
            <s xml:id="echoid-s8907" xml:space="preserve">ex D F ad L K, ſed rectangulum quoque
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            A D F, ad rectangulum A L K habet rationem ex ijſdem rationibus com-
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            poſitam, ergo triangulum E D F ad I L H erit vt rectangulum A D F ad A
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            L K, ſed rectangulum A D F maius eſt ipſo A L K, cum ſit
              <note symbol="d" position="right" xlink:label="note-0319-05" xlink:href="note-0319-05a" xml:space="preserve">93 h.</note>
            ergo & </s>
            <s xml:id="echoid-s8908" xml:space="preserve">triangulum E D F ipſo I L K maius erit, & </s>
            <s xml:id="echoid-s8909" xml:space="preserve">ſumptis duplis
              <note symbol="e" position="right" xlink:label="note-0319-06" xlink:href="note-0319-06a" xml:space="preserve">17. pri-
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              mi h.</note>
            partibus tertijs, erit Parabolæ portio G E F maior Parabolæ portione H I
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            K, & </s>
            <s xml:id="echoid-s8910" xml:space="preserve">hoc ſemper, vbicunque æquidiſtans planum ducatur extra G E </s>
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