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

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            <s xml:id="echoid-s4536" xml:space="preserve">
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            & </s>
            <s xml:id="echoid-s4537" xml:space="preserve">ex puncto A in ſectione extra verticem ſumpto ipſam contingat
              <note symbol="a" position="right" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve">2.4. h.</note>
            AE, quæ cum axe SB, conueniet, & </s>
            <s xml:id="echoid-s4538" xml:space="preserve">in Ellipſi cum vtraque axe SB, TH;</s>
            <s xml:id="echoid-s4539" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-0159-02" xlink:href="note-0159-02a" xml:space="preserve">24. 25.
                <lb/>
              pr. conic.</note>
            ſintque occurſus E, L, & </s>
            <s xml:id="echoid-s4540" xml:space="preserve">à contactu A erigatur ipſi perpendicularis AD.
              <lb/>
            </s>
            <s xml:id="echoid-s4541" xml:space="preserve">Dico primùm hanc cum axe conuenire, & </s>
            <s xml:id="echoid-s4542" xml:space="preserve">in Ellipſi cum vtraque axe, ſed
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            priùs cum maiori.</s>
            <s xml:id="echoid-s4543" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4544" xml:space="preserve">Ducatur ex A recta
              <lb/>
              <figure xlink:label="fig-0159-01" xlink:href="fig-0159-01a" number="125">
                <image file="0159-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0159-01"/>
              </figure>
            AF axi ordinatim appli-
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            cata, quæ cum axe re-
              <lb/>
            ctum angulum AFE cõ-
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            ſtituet, ac ideo angulus
              <lb/>
            AEF acutus erit, ſed eſt
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            rectus EAD, quare AD
              <lb/>
            conuenit cum EBD, vt-
              <lb/>
            puta in D. </s>
            <s xml:id="echoid-s4545" xml:space="preserve">Eadem ra-
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            tione in Ellipſi demon-
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            ſtrabitur ipſam AD con-
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            uenire quoque cum mi-
              <lb/>
            nori axe HT, ſi ex A or-
              <lb/>
            dinatè ei applicetur AR: </s>
            <s xml:id="echoid-s4546" xml:space="preserve">nam cum angulus ARL ſit rectus, angulus ALR
              <lb/>
            acutus erit, ſed LAD rectus ponitur, quare AD conuenit quoque cum axe
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            minori HT, vt in I. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">Quod autem priùs cum maiori axe conueniat, ita oſten-
              <lb/>
            detur. </s>
            <s xml:id="echoid-s4548" xml:space="preserve">Etenim cum recta AF ſit ad axim applicata, & </s>
            <s xml:id="echoid-s4549" xml:space="preserve">contingens AE cum
              <lb/>
            axe in E conueniat, N verò ſit centrum Ellipſis, erit rectangulum EFN ad
              <lb/>
            quadratum AF, vt tranſuerſum latus ad rectum, ſed quadratum AF
              <note symbol="c" position="right" xlink:label="note-0159-03" xlink:href="note-0159-03a" xml:space="preserve">37. pri-
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              mi conic.</note>
            tur rectangulo EFD, ergo rectangulum EFN ad rectangulum EFD, ſiue li-
              <lb/>
            nea FN ad FD, erit vt tranſuerſum latus ad rectum, hoc eſt vt quadratum
              <lb/>
            BS ad quadratum HT (nam ſecunda diameter HT media proportionalis eſt
              <lb/>
            inter tranſuerſum BS, & </s>
            <s xml:id="echoid-s4550" xml:space="preserve">latus rectum) ſed quadratum BS maius eſt quadra-
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            to HT, cum ſit BS axis maior, ergo & </s>
            <s xml:id="echoid-s4551" xml:space="preserve">linea NF maior erit ipſa FD. </s>
            <s xml:id="echoid-s4552" xml:space="preserve">Perpen-
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            dicularis ergo AD ſecat priùs maiorem axem, quàm minorem.</s>
            <s xml:id="echoid-s4553" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4554" xml:space="preserve">Dico inſuper in vtraque ſigura interceptam DA minorem eſſe intercepto
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            axis ſegmento DB.</s>
            <s xml:id="echoid-s4555" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4556" xml:space="preserve">_Ducta enim ex B recta BG_ ordinatim ductæ FA æquidiſtant, ipſa quidem
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            ſectionem continget, & </s>
            <s xml:id="echoid-s4557" xml:space="preserve">alteri contingenti AE occurret, vt in G. </s>
            <s xml:id="echoid-s4558" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-0159-04" xlink:href="note-0159-04a" xml:space="preserve">32. pri-
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              mi conic.</note>
            GD: </s>
            <s xml:id="echoid-s4559" xml:space="preserve">cumque anguli GAD, GBD ſint recti, erunt duo quadrata DA, AG
              <lb/>
              <note symbol="e" position="right" xlink:label="note-0159-05" xlink:href="note-0159-05a" xml:space="preserve">58. h.</note>
            quadrato DG itemque duo quadrata DB, BG eidem quodrato DG æqua-
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            lia, ergo duo ſimul DA, AG duobus ſimul DB, BG æqualia erunt, ſed AG
              <lb/>
            quadratum maius eſt quadrato BG cum ipſa tangens AG, ſit maior
              <note symbol="f" position="right" xlink:label="note-0159-06" xlink:href="note-0159-06a" xml:space="preserve">87. h.</note>
            te BG, ergo quadtatum DA minus erit quadrato DB, ſiue perpendicularis
              <lb/>
            DA minor maioris axis ſegmento DB. </s>
            <s xml:id="echoid-s4560" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s4561" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4562" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4563" xml:space="preserve">Cum verò in Ellipſi tangens AL occurret minori axi TH, vt in L. </s>
            <s xml:id="echoid-s4564" xml:space="preserve">Dico in-
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            terceptam perpendicularem AI maiorem eſſe axis ſegmento IH.</s>
            <s xml:id="echoid-s4565" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4566" xml:space="preserve">Si enim ex H ducatur HM ordinatim applicatæ NB æquidiſtans hæc Elli-
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            pſim continget, & </s>
            <s xml:id="echoid-s4567" xml:space="preserve">alteritangenti AL occurret vt in M; </s>
            <s xml:id="echoid-s4568" xml:space="preserve">iuncta ergo M
              <note symbol="g" position="right" xlink:label="note-0159-07" xlink:href="note-0159-07a" xml:space="preserve">32. pri-
                <lb/>
              mi conic.</note>
            erunt duo triangula rectangula MAI, MHI, quorum anguli ad A, & </s>
            <s xml:id="echoid-s4569" xml:space="preserve">H recti
              <lb/>
              <note symbol="h" position="right" xlink:label="note-0159-08" xlink:href="note-0159-08a" xml:space="preserve">58. h.</note>
            ſunt; </s>
            <s xml:id="echoid-s4570" xml:space="preserve">quare duo quadrata MA, AI vnico MI, & </s>
            <s xml:id="echoid-s4571" xml:space="preserve">duo MH, HI eidem MI æ-
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            qualia erunt, ergo duo ſimul MA, AI duobus ſimul MH, HI ſunt </s>
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