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

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            <s xml:id="echoid-s8720" xml:space="preserve">
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            Et quoniam angulus quoque G B C ponitur æqualis angulo D E F, & </s>
            <s xml:id="echoid-s8721" xml:space="preserve">latus
              <lb/>
            B C lateri E F æquale, erunt in triangulis G C B, D F E reliqua latera G
              <lb/>
            B, D E æqualibus angulis oppoſita, inter ſe æqualia, ſed eſt latus A B ma-
              <lb/>
            ius latere B G, cum recta C G ſecet angulum A C B, ergo latus A B erit
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            quoque maius latere D E. </s>
            <s xml:id="echoid-s8722" xml:space="preserve">Quod erat probandum.</s>
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          <head xml:id="echoid-head374" xml:space="preserve">PROBL. XVI. PROP. XCIII.</head>
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            <s xml:id="echoid-s8724" xml:space="preserve">A data circuli peripheria arcum abſcindere, ita vt rectangulum
              <lb/>
            ſub eius chorda in ſagittam ſit MINIMVM.</s>
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            <s xml:id="echoid-s8726" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">ESto circulus, cuius diameter A B, centrum C, & </s>
            <s xml:id="echoid-s8728" xml:space="preserve">exequi oporteat,
              <lb/>
            quod imperatum eſt.</s>
            <s xml:id="echoid-s8729" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8730" xml:space="preserve">Sumantur in peripheria, hinc inde à puncto A, duo trientes A D, A E,
              <lb/>
            & </s>
            <s xml:id="echoid-s8731" xml:space="preserve">iungatur chorda D E ſecans diametrum A B in F. </s>
            <s xml:id="echoid-s8732" xml:space="preserve">Dico arcum D A E
              <lb/>
            eſſe quæſitum; </s>
            <s xml:id="echoid-s8733" xml:space="preserve">hoc eſt rectangulum ſub eius chorda D E in ſagittam A F
              <lb/>
            eſſe _MAXIMV M_.</s>
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          <figure number="251">
            <image file="0314-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0314-01"/>
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            <s xml:id="echoid-s8735" xml:space="preserve">Secta enim ſemi - peripheria A K B bifariam in K, iunctaque K C, ac
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            ſumpto in arcu D K quolibet puncto G, quod vel in ipſum K, vel inter
              <lb/>
            K, & </s>
            <s xml:id="echoid-s8736" xml:space="preserve">D vbicunque cadat, demiſſaque ex G ſuper diametrum A B per-
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            pendiculari G H, quæ producta occurrat peripheriæ in I, iungatur G D.</s>
            <s xml:id="echoid-s8737" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8738" xml:space="preserve">Et cum arcus A G ſit non minor quadrante A K, erit duplus G A I
              <lb/>
            non minor ſemi - circulo, atque arcus D A I omnino maior ſemi - circu-
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            lo; </s>
            <s xml:id="echoid-s8739" xml:space="preserve">vnde iuncta G D, angulus I G D erit acutus, eſtque G H B rectus,
              <lb/>
            quare duo ſimul D G H, G H B duobus rectis minores erunt, ex quo G
              <lb/>
            D producta conueniet cum diametro ad partes D, vt in L. </s>
            <s xml:id="echoid-s8740" xml:space="preserve">Et cum ar-
              <lb/>
            cus A K D, A I E ſint trientes totius peripheriæ, erit D B E, quod ſupe-
              <lb/>
            reſt de aſſe, eiuſdem peripheriæ triens, ſiue æqualis arcui A I E, itaque
              <lb/>
            arcus D B I erit maior arcu A I E: </s>
            <s xml:id="echoid-s8741" xml:space="preserve">ſi ergo iungatur A D, erit angulus A
              <lb/>
            D E, ſiue A D F minor angulo I G D, ſiue parallelarum externo F D </s>
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