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

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            quo angulus N I L eſt acutus, atque I M O rectus eſt, ideoque duo ſimul
              <lb/>
            N I L, I M B duobus rectis minores.) </s>
            <s xml:id="echoid-s8787" xml:space="preserve">Et cum arcus A E æqualis ſit arcui
              <lb/>
            D E, erit arcus A P minor arcu D E, & </s>
            <s xml:id="echoid-s8788" xml:space="preserve">multò minor arcu L B N: </s>
            <s xml:id="echoid-s8789" xml:space="preserve">vnde
              <lb/>
            iuncta A L, erit angulus A L P, ſiue A L O minor angulo L I N, ſiue L I
              <lb/>
            M, ſiue angulo Q L O parallelarum externo, eſtque in triangulis A L O,
              <lb/>
            Q L O latus O L commune, & </s>
            <s xml:id="echoid-s8790" xml:space="preserve">anguli ad O ſunt æquales, cum ſint recti,
              <lb/>
            ergo latus A O erit minus latere O Q, & </s>
            <s xml:id="echoid-s8791" xml:space="preserve">A M eò minus O Q; </s>
            <s xml:id="echoid-s8792" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">92. h.</note>
            igitur O M ad M A maiorem rationem, quàm M O ad O Q, & </s>
            <s xml:id="echoid-s8793" xml:space="preserve">compo-
              <lb/>
            nendo O A ad A M maiorem quàm M Q ad Q O, vel quàm I M ad L O,
              <lb/>
            vnde rectangulum A O L ſub extremis, quod propinquius eſt puncto D,
              <lb/>
            maius erit rectangulo A M I ſub medijs, quod à puncto D magis diſtat.</s>
            <s xml:id="echoid-s8794" xml:space="preserve"/>
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          <note symbol="b" position="left" xml:space="preserve">16. ſept.
            <lb/>
          Pappi.</note>
          <figure number="252">
            <image file="0316-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0316-01"/>
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          <p>
            <s xml:id="echoid-s8795" xml:space="preserve">De rectangulis denique pertingentibus ad puncta in ſextante D B, nimi-
              <lb/>
            rum ad S, T, idem ſic demonſtrabitur. </s>
            <s xml:id="echoid-s8796" xml:space="preserve">Ductis enim S V Y, T X diametro
              <lb/>
            perpendicularibus, & </s>
            <s xml:id="echoid-s8797" xml:space="preserve">iunctis A S, & </s>
            <s xml:id="echoid-s8798" xml:space="preserve">S T, hæc producta conueniet cum
              <lb/>
            A B in Z, quoniam angulus T S Y eſt in portione T A Y ſemi- circulo ma-
              <lb/>
            iori, nempe acutus, & </s>
            <s xml:id="echoid-s8799" xml:space="preserve">angulus S V B rectus eſt, &</s>
            <s xml:id="echoid-s8800" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8801" xml:space="preserve">Et cum arcus A E Y
              <lb/>
            ſit triente maior, & </s>
            <s xml:id="echoid-s8802" xml:space="preserve">arcus Y B T minor E B D, ſiue minor triente, erit an-
              <lb/>
            gulus A S Y, ſiue A S V maior angulo Y S T, ſiue V S Z, & </s>
            <s xml:id="echoid-s8803" xml:space="preserve">in triangulis
              <lb/>
            A S V, Z S V ſunt anguli ad V æquales, cum ſint recti, & </s>
            <s xml:id="echoid-s8804" xml:space="preserve">latus S V com-
              <lb/>
            mune, ergo latus A V erit maius latere V Z, & </s>
            <s xml:id="echoid-s8805" xml:space="preserve">eò maius latere X Z: </s>
            <s xml:id="echoid-s8806" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-0316-03" xlink:href="note-0316-03a" xml:space="preserve">92. h.</note>
            bebit ergo V X ad X Z maiorem rationem quàm ad V A, & </s>
            <s xml:id="echoid-s8807" xml:space="preserve">componen-
              <lb/>
            do, V Z ad Z X, ſiue S V ad T X maiorem rationem quàm X A ad A
              <lb/>
            V: </s>
            <s xml:id="echoid-s8808" xml:space="preserve">quapropter rectangulum S V A ſub extremis, quod propius eſt puncto
              <lb/>
            D maius erit rectangulo T X A ſub medijs, quod à puncto D magis
              <note symbol="d" position="left" xlink:label="note-0316-04" xlink:href="note-0316-04a" xml:space="preserve">16. ſept.
                <lb/>
              Pappi.</note>
            ſtat. </s>
            <s xml:id="echoid-s8809" xml:space="preserve">Qnod ex abundanti oſtendere propoſitum fuit.</s>
            <s xml:id="echoid-s8810" xml:space="preserve"/>
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        <div xml:id="echoid-div916" type="section" level="1" n="366">
          <head xml:id="echoid-head375" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s8811" xml:space="preserve">EX eo, quod ad num. </s>
            <s xml:id="echoid-s8812" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8813" xml:space="preserve">ſuperiùs oſtenſum fuit; </s>
            <s xml:id="echoid-s8814" xml:space="preserve">facilè conſtat, in prima
              <lb/>
            figura, quæſitam chordam D E ſecare circuli diametrum A B in F,
              <lb/>
            in 3. </s>
            <s xml:id="echoid-s8815" xml:space="preserve">ratione ad 1.</s>
            <s xml:id="echoid-s8816" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8817" xml:space="preserve">Nam iunctis C B, B D. </s>
            <s xml:id="echoid-s8818" xml:space="preserve">Cum ſit arcus B D circuli ſextans, ipſius </s>
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