Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of contents

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[61.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA AUTHORE JACOBO GREGORIO. LECTORI GEOMETRÆ SALUTEM.
[62.] DEFINITIONES.
[63.] PETITIONES.
[64.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[65.] PROP. I. THEOREMA. Dico trapezium B A P I eſſe medium propor-tionale inter trapezium B A P F, & triangulum B A P.
[66.] PROP. II. THEOREMA. Dico trapezia A B F P, A B I P ſimul, eſſe ad du- plum trapezii A B I P, ſicut trapezium A B F P ad polygonum A B D L P.
[67.] PROP. III. THEOREMA. Dico triangulum B A P, & trapezium A B I P ſimul, eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.
[68.] PROP. IV. THEOREMA. Dico polygonum A B E I O P eſſe medium pro- portionale inter polygonum A B D L P & trapezium A B I P.
[69.] PROP. V. THEOREMA.
[70.] SCHOLIUM.
[71.] PROP. VI. THEOREMATA.
[72.] SCHOLIUM.
[73.] PROP. VII. PROBLEMA. Oportet prædictæ ſeriei terminationem invenire.
[74.] PROP. VIII. PROBLEMA.
[75.] PROP. IX. PROBLEMA.
[76.] PROP. X. PROBLEMA.
[77.] CONSECTARIUM.
[78.] PROP. XI. THEOREMA.
[79.] SCHOLIUM.
[80.] PROP. XII. THEOREMA.
[81.] PROP. XIII. THEOREMA.
[82.] PROP. XIV. THEOREMA.
[83.] PROP. XV. THEOREMA.
[84.] PROP. XVI. THEOREMA.
[85.] PROP. XVII. THEOREMA.
[86.] PROP. XVIII. THEOREMA.
[87.] PROP. XIX. THEOREMA.
[88.] CONSECTARIUM.
[89.] PROP. XX. THEOREMA.
[90.] PROP. XXI. THEOREMA.
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          <head xml:id="echoid-head43" xml:space="preserve">CHRISTIANI HUGENII,
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            <emph style="sc">Const. f</emph>
          .
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            <emph style="sc">DE</emph>
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          <head xml:id="echoid-head44" xml:space="preserve">CIRCULI MAGNITUDINE
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          INVENTA.</head>
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            <emph style="sc">Theorema</emph>
          I.
            <emph style="sc">Propositio</emph>
          I.</head>
          <p style="it">
            <s xml:id="echoid-s1147" xml:space="preserve">SI Circuli portioni, ſemicirculo minori, trian-
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            gulum maximum inſcribatur, & </s>
            <s xml:id="echoid-s1148" xml:space="preserve">portioni-
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            bus reliquis triangula ſimiliter inſcribantur,
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            erit triangulum primo deſcriptum duorum ſimul
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            quæ in portionibus reliquis deſcripta ſunt minus
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            quam quadruplum.</s>
            <s xml:id="echoid-s1149" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1150" xml:space="preserve">Eſto circuli portio A B C, ſemicirculo minor, cujus diameter
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              <note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">TAB. XXXVI@
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              Fig. 1.</note>
            B D; </s>
            <s xml:id="echoid-s1151" xml:space="preserve">maximum autem inſcriptum ſit triangulum A B C,
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            hoc eſt, quod baſin & </s>
            <s xml:id="echoid-s1152" xml:space="preserve">altitudinem habeat cum portione eandem.
              <lb/>
            </s>
            <s xml:id="echoid-s1153" xml:space="preserve">Et reliquis duabus portionibus inſcribantur triangula item ma-
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            xima A E B, B F C. </s>
            <s xml:id="echoid-s1154" xml:space="preserve">Dico triangulum A B C minus eſſe quam
              <lb/>
            quadruplum triangulorum A E B, B F C ſimul ſumpto-
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            rum. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Jungatur enim E F, quæ ſecet diametrum portionis
              <lb/>
            in puncto G. </s>
            <s xml:id="echoid-s1156" xml:space="preserve">Quoniam igitur arcus A B bifariam dividitur
              <lb/>
            in E puncto, erit utraque harum E A, E B, major dimi-
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            diâ A B. </s>
            <s xml:id="echoid-s1157" xml:space="preserve">Quamobrem quadratum A B minus erit quam qua-
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            druplum quadrati E B vel E A. </s>
            <s xml:id="echoid-s1158" xml:space="preserve">Sicut autem quadratum A B
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            ad quadr. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">E B, ita eſt D B ad B G longitudine; </s>
            <s xml:id="echoid-s1160" xml:space="preserve">quia qua-
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            dratum quidem A B æquale eſt rectangulo quod à D B & </s>
            <s xml:id="echoid-s1161" xml:space="preserve">
              <lb/>
            circuli totius diametro continetur, quadratum vero E B æ-
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            quale rectangulo ſub eadem diametro & </s>
            <s xml:id="echoid-s1162" xml:space="preserve">recta B G. </s>
            <s xml:id="echoid-s1163" xml:space="preserve">Minor
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            igitur eſt B D quam quadrupla B G. </s>
            <s xml:id="echoid-s1164" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1165" xml:space="preserve">A C minor
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            eſt quam dupla E F, quoniam hæc ipſi A B æquatur. </s>
            <s xml:id="echoid-s1166" xml:space="preserve">Er-
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            go patet triangulum A B C minus eſſe quam octuplum </s>
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