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

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          <p>
            <s xml:id="echoid-s4082" xml:space="preserve">
              <pb o="121" file="0145" n="145" rhead=""/>
            rectangulum AKF ad rectangulum DKE, vt quadratum AK ad KD (ob la-
              <lb/>
            terum proportionalitatem) vel vt quadratum IO ad OE (ob triangulorum
              <lb/>
            AKD, IOE ſimilitudinem) vel vt rectangulum IOL ad EOM (ob homolo-
              <lb/>
            gorum laterum proportionalitatem) erit, ex æquali, rectangulum GKH,
              <lb/>
            vel quadratum GK ad rectangulum DKE, ſiue vt rectũ latus Ellipſis GEHD
              <lb/>
            ad eiuſdem tranſuerſum, vt rectangulum POQ, ſiue quadratum PO, ad re-
              <lb/>
            ctangulum EOM, vel vt rectum Ellipſis PMQE ad ipſius tranſuerſum: </s>
            <s xml:id="echoid-s4083" xml:space="preserve">cum
              <lb/>
            ergo huiuſmodi Ellipſes habeant latera proportionalia, ſintque æqualiter
              <lb/>
              <note symbol="a" position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">6. ſec.
                <lb/>
              defin. h.</note>
            inclinatæ, erunt inter ſe ſimiles. </s>
            <s xml:id="echoid-s4084" xml:space="preserve">Quod erat primò demonſtrandum.</s>
            <s xml:id="echoid-s4085" xml:space="preserve"/>
          </p>
          <figure number="111">
            <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0145-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s4086" xml:space="preserve">Præterea, cum ſit AD´ ad DK, vt IE ad EO, ſitque AD maior IE,
              <note symbol="b" position="right" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">32. vel
                <lb/>
              63. h.</note>
            DK maior EO. </s>
            <s xml:id="echoid-s4087" xml:space="preserve">Item, cum ſit FE ad EK, vt LM ad MO, ſitque FE maior
              <lb/>
            LM, erit EK maior MO, ergo integra tranſuerſa diameter DE, maior toto
              <lb/>
            tranſuerſo latere EM; </s>
            <s xml:id="echoid-s4088" xml:space="preserve">ſed tranſuerſum DE ad tranſuerſum EM, eſt vt rectum
              <lb/>
            vnius ad rectum alterius, vt ſuperiùs demonſtrauimus, eſtq; </s>
            <s xml:id="echoid-s4089" xml:space="preserve">tranſuerſum DE
              <lb/>
            maios EM, quare rectum recto maios erit, ſiue Ellipſis GEHD maiorum la-
              <lb/>
            terum, maior erit Ellipſi PMQE minorum laterum, quæ tùm in
              <note symbol="c" position="right" xlink:label="note-0145-03" xlink:href="note-0145-03a" xml:space="preserve">5. Co-
                <lb/>
              roll. 19. h.</note>
            tùm in ſectione, aut ſemi-Ellipſi, vel ſemi-circulo vertici B propior eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s4090" xml:space="preserve">Quod vltimò oſtendere propoſitum fuit.</s>
            <s xml:id="echoid-s4091" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div397" type="section" level="1" n="167">
          <head xml:id="echoid-head172" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s4092" xml:space="preserve">SI ergo in figuris 29. </s>
            <s xml:id="echoid-s4093" xml:space="preserve">& </s>
            <s xml:id="echoid-s4094" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4095" xml:space="preserve">Problematis, concipiantur methodo ſuperiùs
              <lb/>
            allata, per datum punctum inſcribi Ellipſes ad partes verticis, vel angu-
              <lb/>
            li, vel ſectionis, quæ ſimiles ſint alijs ad oppoſitas partes per idem punctum
              <lb/>
            inſcriptis (ſi tamen ſectionis, vel circuli portio, quæ ab applicata per datum
              <lb/>
            punctum terminatur, huius Ellipſis ſit capax, quod accidet, quando in ſe-
              <lb/>
            cunda præcedentium figurarum, diagonalis IL, quæ ex I ducitur diagonali
              <lb/>
            AF æquidiſtans, & </s>
            <s xml:id="echoid-s4096" xml:space="preserve">occurrens ſectioni in L, punctum L pertingat ad B, </s>
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