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

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        <div xml:id="echoid-div330" type="section" level="1" n="143">
          <head xml:id="echoid-head148" xml:space="preserve">THEOR. XXX. PROP. LIX.</head>
          <p>
            <s xml:id="echoid-s3446" xml:space="preserve">Si coni-ſectionem, vel circuli circumferentiam recta linea con-
              <lb/>
            tingat conueniens cum diametro, cui à tactu ſit ordinatim applica-
              <lb/>
            ta vſque ad ſectionem, recta linea iungens alterum terminum ap-
              <lb/>
            plicatæ, & </s>
            <s xml:id="echoid-s3447" xml:space="preserve">occurſum tangentis cum diametro, erit eidem ſectioni
              <lb/>
            ad alteram diametri partem contingens.</s>
            <s xml:id="echoid-s3448" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3449" xml:space="preserve">SIt coni-ſectio quæcunque, vel circuli circumferentia ABC, cuius diame-
              <lb/>
            ter ſit DE, & </s>
            <s xml:id="echoid-s3450" xml:space="preserve">ſit quæpiam AD ſectionem contingens in A, diametro oc-
              <lb/>
            currens in D, & </s>
            <s xml:id="echoid-s3451" xml:space="preserve">ex contactu A ducta ſit in ſectione diametro DE ordinatim
              <lb/>
            applicata AC, dico iunctam DC ſectionem quoque contingere.</s>
            <s xml:id="echoid-s3452" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3453" xml:space="preserve">Si enim poſſibile eſt, quæ ex C ducitur
              <lb/>
              <figure xlink:label="fig-0127-01" xlink:href="fig-0127-01a" number="92">
                <image file="0127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0127-01"/>
              </figure>
            contingens, non ſit CD, ſed alia CF, quæ
              <lb/>
              <note symbol="a" position="right" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">58. h.</note>
            cum tangente AD conueniet, ſed in alio puncto quàm D, vt in F.</s>
            <s xml:id="echoid-s3454" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3455" xml:space="preserve">Iam cum FA, FC ſectionem contingant,
              <lb/>
            & </s>
            <s xml:id="echoid-s3456" xml:space="preserve">per contactus ducta ſit AC, quæ bifariam
              <lb/>
            ſecta eſt à diametro D E in E, ſi iungatur
              <lb/>
              <note symbol="b" position="right" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">29. ſe-
                <lb/>
              cundi co-
                <lb/>
              nic.</note>
            FEG ipſa erit ſectionis diameter, hoc eſt bifariam ſecabit quamlibet aliã HI ipſi AC
              <lb/>
            æquidiſtanter ductam, vt in G, ſed D E L
              <lb/>
            quoque bifariam ſecat eandem HI in L, cum
              <lb/>
            DEL ſit diameter, per hypoteſim; </s>
            <s xml:id="echoid-s3457" xml:space="preserve">ergo ea-
              <lb/>
            dem recta HI in duobus diuerſis punctis G,
              <lb/>
            & </s>
            <s xml:id="echoid-s3458" xml:space="preserve">L bifariam diuiditur: </s>
            <s xml:id="echoid-s3459" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s3460" xml:space="preserve">Non eſt ergo ex C alia contin-
              <lb/>
            gens linea quàm CD. </s>
            <s xml:id="echoid-s3461" xml:space="preserve">Quod erat,</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s3462" xml:space="preserve">Cum Propoſitionum 13. </s>
            <s xml:id="echoid-s3463" xml:space="preserve">ac 14. </s>
            <s xml:id="echoid-s3464" xml:space="preserve">ſept. </s>
            <s xml:id="echoid-s3465" xml:space="preserve">Pappi, in hac noſtra tractatione fre-
              <lb/>
            quens ſit vſus, liceat hac eas transferre, vtranque ſimul ſequenti Theo-
              <lb/>
            remate demonſtrare.</s>
            <s xml:id="echoid-s3466" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div333" type="section" level="1" n="144">
          <head xml:id="echoid-head149" xml:space="preserve">THEOR. XXXI. PROP. LX.</head>
          <p>
            <s xml:id="echoid-s3467" xml:space="preserve">Rectangulorum ſub partibus datæ rectę terminatæ MAXIMVM
              <lb/>
            eſt id, quod ab æqualibus ſegmentis producitur; </s>
            <s xml:id="echoid-s3468" xml:space="preserve">reliquorum verò
              <lb/>
            id, quod fit à partibus minus inæqualibus, maius eſt eo, quod ab
              <lb/>
            inæqualioribus continetur.</s>
            <s xml:id="echoid-s3469" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3470" xml:space="preserve">SIt data recta linea AB terminata bifariam ſecta in C, & </s>
            <s xml:id="echoid-s3471" xml:space="preserve">non bifariam
              <lb/>
            vtcunque in D, E, &</s>
            <s xml:id="echoid-s3472" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">Dico, &</s>
            <s xml:id="echoid-s3474" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3475" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3476" xml:space="preserve">Cum enim recta AB ſecta ſit bifariam in C, & </s>
            <s xml:id="echoid-s3477" xml:space="preserve">non bifariam in D, erit
              <lb/>
            quadratum AC, ſiue rectangulum ACB, æquale rectangulo ADB, </s>
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