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

Table of contents

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[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.
[271.] THEOR. XXIII. PROP. XXXX.
[272.] COROLL. I.
[273.] COROLL. II.
[274.] COROLL. III.
[275.] PROBL. VI. PROP. XXXXI.
[276.] PROBL. VII. PROP. XXXXII.
[277.] COROLL.
[278.] THEOR. XXIV. PROP. XXXXIII.
[279.] THEOR. XXV. PROP. XXXXIV.
[280.] SCHOLIVM.
[281.] THEOR. XXVI. PROP. XLV.
[282.] COROLL.
[283.] THEOR. XXVII. PROP. XLVI.
[284.] COROLL. I.
[285.] COROLL. II.
[286.] THEOR. XXVIII. PROP. XLVII.
[287.] THEOR. XXIX. PROP. XLVIII.
[288.] THEOR. XXX. PROP. XLIX.
[289.] THEOR. XXXI. PROP. L.
[290.] COROLL.
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            per M applicetur recta N M O, quæ applicatæ E G F æquidiſtabit.</s>
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          <p>
            <s xml:id="echoid-s6641" xml:space="preserve">Iam, in prima figura, cum ſit B D parallela ad I M, & </s>
            <s xml:id="echoid-s6642" xml:space="preserve">B I ad D M, erit
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            diametri ſegmentum B D æquale diametri ſegmento I M; </s>
            <s xml:id="echoid-s6643" xml:space="preserve">ſuntque ex D, M
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            applicatæ diametris rectæ A D C, N M O, vnde portiones A B C, N I O
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            æquales erunt.</s>
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          <note symbol="a" position="right" xml:space="preserve">40. h.</note>
          <figure number="197">
            <image file="0239-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0239-01"/>
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            <s xml:id="echoid-s6645" xml:space="preserve">In reliquis verò, cum in triangulo D H M ſit B I parallela ad D M, erit
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            H B ad B D, vt H I ad I M, ſuntque ex D, M applicatæ diametris rectæ
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            A D C, N M O, quare portiones A B C, N I O æquales erunt. </s>
            <s xml:id="echoid-s6646" xml:space="preserve">Cum
              <note symbol="b" position="right" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">ibidem.</note>
            go in ſingulis figuris portio A B C demonſtrata ſit æqualis portioni N I O,
              <lb/>
            & </s>
            <s xml:id="echoid-s6647" xml:space="preserve">ſit portio N I O minor portione E I F, pars toto, ergo portio A B C erit
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            quoque minor portione E I F, & </s>
            <s xml:id="echoid-s6648" xml:space="preserve">ſic quacunque alia portione, ab applicata
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            per D abſciſſa, minor demonſtrabitur. </s>
            <s xml:id="echoid-s6649" xml:space="preserve">Vnde portio A B C eſt _MINIMA_
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            quæſita. </s>
            <s xml:id="echoid-s6650" xml:space="preserve">Quod faciendum erat.</s>
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          <head xml:id="echoid-head286" xml:space="preserve">COROLL.</head>
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            <s xml:id="echoid-s6652" xml:space="preserve">HInc eſt, quod dum per datum punctum D intra Ellipſim, ducitur appli-
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            cata A D C _MINIMAM_ portionem abſcindes, habetur ſimul _MA_-
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            _XIMA_ portio, quæ eſt reliqua A P C, vt per ſe ſatis conſtat.</s>
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