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

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          <p>
            <s xml:id="echoid-s6302" xml:space="preserve">Sit verò A B C D in ſecunda figura Ellipſis, cuius axis maior B D, mi-
              <lb/>
            nor A C, centrum E, & </s>
            <s xml:id="echoid-s6303" xml:space="preserve">punctum intra datum ſit F. </s>
            <s xml:id="echoid-s6304" xml:space="preserve">Oportet per F re-
              <lb/>
            ctas in ſectione applicare quales inuenire propoſuimus.</s>
            <s xml:id="echoid-s6305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6306" xml:space="preserve">Sit per F maiori axi B D ordinatim ducta G F H, minori verò ſit I F L.
              <lb/>
            </s>
            <s xml:id="echoid-s6307" xml:space="preserve">Dico rectangulum G F H eſſe _MINIMVM, MAXIMVM_ verò I F L.</s>
            <s xml:id="echoid-s6308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6309" xml:space="preserve">Sit quælibet alia per F ap-
              <lb/>
              <figure xlink:label="fig-0225-01" xlink:href="fig-0225-01a" number="187">
                <image file="0225-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0225-01"/>
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            plicata M F N, & </s>
            <s xml:id="echoid-s6310" xml:space="preserve">portionis
              <lb/>
            M O N ſit vertex O, atque ex
              <lb/>
            axium verticibus A, B, vti e-
              <lb/>
            tiam ex O agantur contingen-
              <lb/>
            tes A P, B Q, P O Q, quæ ſi-
              <lb/>
            mul occurrent in R, P, Q.</s>
            <s xml:id="echoid-s6311" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-0225-01" xlink:href="note-0225-01a" xml:space="preserve">58. pri-
                <lb/>
              mih.</note>
            Erit ergo rectangulum G F H
              <lb/>
            ad I F L, vt quadratum B
              <note symbol="b" position="right" xlink:label="note-0225-02" xlink:href="note-0225-02a" xml:space="preserve">16. tertij
                <lb/>
              conic.</note>
            ad quadratum A R, ſed eſt
              <lb/>
            contingens B R, minor A
              <note symbol="c" position="right" xlink:label="note-0225-03" xlink:href="note-0225-03a" xml:space="preserve">87 primi
                <lb/>
              huius.</note>
            ſiue quadratum B R minus quadrato A R, ergo, & </s>
            <s xml:id="echoid-s6312" xml:space="preserve">rectangulum G F H
              <lb/>
            minus erit rectangulo I F L.</s>
            <s xml:id="echoid-s6313" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6314" xml:space="preserve">Præterea rectangulum G F H ad M F N eſt vt quadratum B Q ad qua-
              <lb/>
            dratum O Q, ſed eſt contingens B Q minor contingente O Q, ſiue
              <note symbol="d" position="right" xlink:label="note-0225-04" xlink:href="note-0225-04a" xml:space="preserve">ibidem.</note>
            dratum B Q minus quadrato O Q, ergo rectangulum G F H minus eſt re-
              <lb/>
            ctangulo M F N, & </s>
            <s xml:id="echoid-s6315" xml:space="preserve">hoc ſemper vbicunque cadat applicata M F N: </s>
            <s xml:id="echoid-s6316" xml:space="preserve">qua-
              <lb/>
            re rectangulum G F H eſt _MINIMVM_ quæſitum.</s>
            <s xml:id="echoid-s6317" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6318" xml:space="preserve">Demùm cum rectangulum I F L ad N F M, ſit vt quadratum A P
              <note symbol="e" position="right" xlink:label="note-0225-05" xlink:href="note-0225-05a" xml:space="preserve">16. tertij
                <lb/>
              huius.</note>
            quadratum QP, ſitque contingens A P maior contingente Q P erit
              <note symbol="f" position="right" xlink:label="note-0225-06" xlink:href="note-0225-06a" xml:space="preserve">87. primi
                <lb/>
              huius.</note>
            dratum A P maius quadrato Q P, ergo rectangulum quoque I F L maius
              <lb/>
            erit rectangulo N F M, & </s>
            <s xml:id="echoid-s6319" xml:space="preserve">hoc ſemper vbicunque ſit ducta N F M inter
              <lb/>
            applicatas I F L, G F H quare rectangulum I F L eſt _MAXIMVM_ quæſi-
              <lb/>
            tum. </s>
            <s xml:id="echoid-s6320" xml:space="preserve">Quod vltimò inuenire propoſitum fuit.</s>
            <s xml:id="echoid-s6321" xml:space="preserve"/>
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        <div xml:id="echoid-div661" type="section" level="1" n="263">
          <head xml:id="echoid-head271" xml:space="preserve">DEFINITIONES.</head>
          <head xml:id="echoid-head272" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s6322" xml:space="preserve">PLANVM ACVMINATVM REGVLARE, vel ACVMINATVM
              <lb/>
            tantùm voco omnem figuram planam, circa diametrum, in alteram par-
              <lb/>
            tem deficientem, & </s>
            <s xml:id="echoid-s6323" xml:space="preserve">cuius perimeter ſit in eaſdem partes cauus.</s>
            <s xml:id="echoid-s6324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6325" xml:space="preserve">Hoc eſt figura plana A B C,
              <lb/>
              <figure xlink:label="fig-0225-02" xlink:href="fig-0225-02a" number="188">
                <image file="0225-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0225-02"/>
              </figure>
            in qua omnes rectæ lineæ A
              <lb/>
            C, E F, G H, &</s>
            <s xml:id="echoid-s6326" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6327" xml:space="preserve">à figurę pe-
              <lb/>
            rimetro terminatæ, ac inter ſe
              <lb/>
            æquidiſtantes, à quadam re-
              <lb/>
            cta B D bifariam ſecentur, & </s>
            <s xml:id="echoid-s6328" xml:space="preserve">
              <lb/>
            in alteram partem, vt puta ad
              <lb/>
            B, continuò decreſcant, do-
              <lb/>
            nec abeant in punctum B, ſit-
              <lb/>
            que earum perimeter A G B H C ad eaſdem partes cauus vocetur </s>
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