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

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          <p>
            <s xml:id="echoid-s6375" xml:space="preserve">
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            fas portiones eſſe Acuminata Proportionalia.</s>
            <s xml:id="echoid-s6376" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6377" xml:space="preserve">Repertis enim earum diametris B G, E H, diuidantur ipſæ proportio-
              <lb/>
            naliter in I, L, applicenturque M I N, O L P. </s>
            <s xml:id="echoid-s6378" xml:space="preserve">Cum ſit ergo G I ad I B,
              <lb/>
            vt H L ad L E, erit componendo G B ad B I, hoc eſt quadratum A
              <note symbol="a" position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve">20. pri-
                <lb/>
              mi conic.</note>
            ad M N, vt H E ad E L, ſiue vt quadratum D F ad O P, ideoque & </s>
            <s xml:id="echoid-s6379" xml:space="preserve">ap-
              <lb/>
            plicata A C ad M N, vt applicata D F ad O P. </s>
            <s xml:id="echoid-s6380" xml:space="preserve">Quare, ex ſecunda præ-
              <lb/>
            cedentium definitionum, ipſæ portiones A B C, D E F erunt Acuminata
              <lb/>
            Proportionalia. </s>
            <s xml:id="echoid-s6381" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s6382" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6383" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6384" xml:space="preserve">Præterea ſint A B C, D E
              <lb/>
              <figure xlink:label="fig-0228-01" xlink:href="fig-0228-01a" number="191">
                <image file="0228-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0228-01"/>
              </figure>
            F duæ portiones eiuſdem, vel
              <lb/>
            diuerſarum Hyperbolarum, vt
              <lb/>
            in ſecunda figura, vel Elli-
              <lb/>
            pſium, aut circulorum, vt in
              <lb/>
            tertia, quarum baſes A C, D
              <lb/>
            F, & </s>
            <s xml:id="echoid-s6385" xml:space="preserve">diametrorum ſegmenta
              <lb/>
            in ipſis intercepta ſint B G, E
              <lb/>
            H, quæ vſque ad ſectionum
              <lb/>
            centra Q, R producantur, & </s>
            <s xml:id="echoid-s6386" xml:space="preserve">
              <lb/>
            ſit vt G B ad BQ, ita H E ad
              <lb/>
            E R. </s>
            <s xml:id="echoid-s6387" xml:space="preserve">Dico item has portio-
              <lb/>
            nes A B C, D E F eſſe inter ſe
              <lb/>
            Acuminata Proportionalia.</s>
            <s xml:id="echoid-s6388" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6389" xml:space="preserve">Nam diuiſis diametris B G,
              <lb/>
            E H proportionaliter in I, L,
              <lb/>
            per I, L applicentur M I N,
              <lb/>
            O L P, & </s>
            <s xml:id="echoid-s6390" xml:space="preserve">productis ſemi-dia-
              <lb/>
            metris B Q, E R ſumantur eis
              <lb/>
            æquales Q S, R T, ita vt S B,
              <lb/>
            T E ſint ſectionum diametri.</s>
            <s xml:id="echoid-s6391" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6392" xml:space="preserve">Iam cum ſit G B ad B Q vt
              <lb/>
            H E ad E R, erit conuerten-
              <lb/>
            do, & </s>
            <s xml:id="echoid-s6393" xml:space="preserve">ſumptis antecedentium duplis S B ad B G, vt T E ad E H, ſuntq;
              <lb/>
            </s>
            <s xml:id="echoid-s6394" xml:space="preserve">S B, T E bifariam ſectæ in Q, R, & </s>
            <s xml:id="echoid-s6395" xml:space="preserve">partes adiectæ, in ſecunda figura,
              <lb/>
            vel demptæ in tertia B G, E H proportionaliter diuiſæ ſunt in I, L, ergo
              <lb/>
            rectangulum S G B ad S I B, ſiue quadratum A C, ad M N, erit vt
              <note symbol="b" position="left" xlink:label="note-0228-02" xlink:href="note-0228-02a" xml:space="preserve">21. primi
                <lb/>
              conic.</note>
              <note symbol="c" position="left" xlink:label="note-0228-03" xlink:href="note-0228-03a" xml:space="preserve">35. h.</note>
            ctangulum T H E, ad T L E, vel vt quadratum D F ad O P, nempe
              <note symbol="d" position="left" xlink:label="note-0228-04" xlink:href="note-0228-04a" xml:space="preserve">21. primi
                <lb/>
              conic.</note>
            plicata A C ad M N erit vt applicata D F ad O P, & </s>
            <s xml:id="echoid-s6396" xml:space="preserve">permutando A C
              <lb/>
            ad D F, vt M N ad O P, & </s>
            <s xml:id="echoid-s6397" xml:space="preserve">hoc ſemper de quibuslibet applicatis per
              <lb/>
            pnncta diametrorum B G, E H ipſas proportionaliter ſecantia, quare, ex
              <lb/>
            definitione ſecunda, ipſæ portiones A B C, D E F erunt Acuminata pro-
              <lb/>
            portionalia. </s>
            <s xml:id="echoid-s6398" xml:space="preserve">Quod vltimò demonſtrandum erat.</s>
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