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

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            ſitque ipſum AB, quod ſecetur quacunque recta linea FN intra angulum.
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            <s xml:id="echoid-s470" xml:space="preserve">BAC, efficient angulum AFN æquale angulo ACB. </s>
            <s xml:id="echoid-s471" xml:space="preserve">Iam dico rectam FN
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            productam cum reliquo latere AC conuenire, cumque baſi BC ad partem
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            minoris lateris AC.</s>
            <s xml:id="echoid-s472" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s473" xml:space="preserve">Quoniam cum in triangulo BAC ſint anguli A, C, minores duobus rectis,
              <lb/>
            permutato C in F, erunt anguli FAC, AFN duobus rectis minores, ex quo
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            rectæ AC, FN conuenient ſimul in H, & </s>
            <s xml:id="echoid-s474" xml:space="preserve">reliquus angulus ABC in triangu-
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            lo BAC æquabitur reliquo angulo AHF in triangulo HAF, hoc eſt triangu-
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            la BAC, HAF erunt ſub contrariè poſita. </s>
            <s xml:id="echoid-s475" xml:space="preserve">Amplius cum ſit BA maior AC,
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            erit HA maior AF, propter ſimilitudinem triangulorum BAC, HAF, vnde
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            angulus AFH erit maior angulo AHF, ſiue angulo ABC, ſed anguli BFH,
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            AFH ſunt duobus rectis æquales, quare anguli BFH, ABC minores erunt
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            duobus rectis, ideoqne FH, BC ſimul conuenient, vt in G. </s>
            <s xml:id="echoid-s476" xml:space="preserve">Nunc verò con-
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              <figure xlink:label="fig-0028-01" xlink:href="fig-0028-01a" number="5">
                <image file="0028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0028-01"/>
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            cipiatur per rectam FHG duci planum ſecans triangulum per axem ABC,
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            communiſque ſectio huius ſecantis plani cum plano baſis coni ſit recta DGE
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            perpendicularis baſi BC trianguli per axem, & </s>
            <s xml:id="echoid-s477" xml:space="preserve">cum conica ſuperficie ſectio-
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            nem efficiens MFTH, cuius diameter ſit FH. </s>
            <s xml:id="echoid-s478" xml:space="preserve">Itaque iam ſuperiùs oſtenſum
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            eſt, ſi fiat vt rectangulum FGH ad rectangulum BGC, ita diameter FH ad
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            aliam lineam FL, quæ ex F ordinatim in ſectione ductis æquidiſtet, iunga-
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            turque HL, quadratum cuiuſcunque applicatæ MN parallelæ communi ſe-
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            ctioni DE, æquari rectangulo NP, applicato rectę FL deficientique rectan-
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            gulo LX ſimili rectangulo ſub HF, FL. </s>
            <s xml:id="echoid-s479" xml:space="preserve">Quod verò talia latera HF, FL inter
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            ſe ſint æqualia ita oſtenditur.</s>
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            <s xml:id="echoid-s481" xml:space="preserve">Cum ſit enim angulus AFH æqualis angulo ACB, erit conſequens BFG
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            conſequenti HCG æqualis, eſtque angulus BGF æqualis angulo HGC, cum
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            in tertia figura idem ſint, in quarta verò ſint ad verticem, quare in triangu-
              <lb/>
            lis BGF; </s>
            <s xml:id="echoid-s482" xml:space="preserve">HGC circa æquales angulos ad G erunt latera proportionalia, ſiue
              <lb/>
            vt FG ad GB ita CG ad GH, ideoque rectangulum FGH æquale erit rectan-
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            gulo BGC, ſed vt rectangulum FGH ad BGC, ita tranſuerſum HF ad </s>
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