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

Table of contents

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[241.] MONITVM.
[242.] THEOR. XV. PROP. XXI.
[243.] PROBL. II. PROP. XXII.
[244.] PROBL. III. PROP. XXIII.
[245.] MONITVM.
[246.] THEOR. XVI. PROP. XXIV.
[247.] THEOR. XVII. PROP. XXV.
[248.] COROLL.
[249.] THEOR. XIIX. PROP. XXVI.
[250.] COROLL. I.
[251.] COROLL. II.
[252.] SCHOLIVM.
[253.] LEMMA VI. PROP. XXVII.
[254.] LEMMA VII. PROP. XXVIII.
[255.] LEMMA VIII. PROP. XXIX.
[256.] THEOR. XIX. PROP. XXX.
[257.] SCHOLIVM.
[258.] COROLL.
[259.] LEMMA IX. PROP. XXXI.
[260.] THEOR. XX. PROP. XXXII
[261.] PROBL. IV. PROP. XXXIII.
[262.] PROBL. V. PROP. XXXIV.
[263.] DEFINITIONES. I.
[264.] II.
[265.] LEMMA X. PROP. XXXV.
[266.] THEOR. XXI. PROP. XXXVI.
[267.] THEOR. XXII. PROP. XXXVII.
[268.] SCHOLIVM.
[269.] LEMMA XI. PROP. XXXVIII.
[270.] LEMMA XII. PROP. XXXIX.
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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
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            B C lateri E F æquale, erunt in triangulis G C B, D F E reliqua latera G
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            B, D E æqualibus angulis oppoſita, inter ſe æqualia, ſed eſt latus A B ma-
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            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
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            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,
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            quod imperatum eſt.</s>
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            <s xml:id="echoid-s8730" xml:space="preserve">Sumantur in peripheria, hinc inde à puncto A, duo trientes A D, A E,
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            & </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
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            eſſe quæſitum; </s>
            <s xml:id="echoid-s8733" xml:space="preserve">hoc eſt rectangulum ſub eius chorda D E in ſagittam A F
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            eſſe _MAXIMV M_.</s>
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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>
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            <s xml:id="echoid-s8738" xml:space="preserve">Et cum arcus A G ſit non minor quadrante A K, erit duplus G A I
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            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,
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            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-
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            cus A K D, A I E ſint trientes totius peripheriæ, erit D B E, quod ſupe-
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            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
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            D E, ſiue A D F minor angulo I G D, ſiue parallelarum externo F D </s>
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