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

Table of contents

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[21.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S. I. EPISTOLA. Cl. Viro D°. XAVERIO AINSCOM CHRISTIANUS HUGENIUS S. D.
[22.] CHRISTIANI HUGENII, Const. F. DE CIRCULI MAGNITUDINE INVENTA. ACCEDUNT EJUSDEM Problematum quorundam illuſtrium Conſtructiones.
[23.] PRÆFATIO.
[24.] CHRISTIANI HUGENII, Const. f. DE CIRCULI MAGNITUDINE INVENTA. Theorema I. Propositio I.
[25.] Theor. II. Prop. II.
[26.] Theor. III. Prop. III.
[27.] Theor. IV. Prop. IV.
[28.] Theor. V. Prop. V.
[29.] Theor. VI. Prop. VI.
[30.] Theor. VII. Prop. VII.
[31.] Theor. VIII. Prop. VIII.
[32.] Theor. IX. Prop. IX.
[33.] Problema I. Prop. X. Peripheriæ ad diametrum rationem invenire quamlibet veræ propinquam.
[34.] Problema II. Prop. XI.
[35.] Aliter.
[36.] Aliter.
[37.] Problbma III. Prop. XII. Dato arcui cuicunque rectam æqualem ſumere.
[38.] Theor. X. Prop. XIII.
[39.] Lemma.
[40.] Theor. XI. Prop. XIV.
[41.] Theor. XII. Prop. XV.
[42.] Theor. XIII. Prop. XVI.
[43.] Theorema XIV. Propos. XVII.
[44.] Theor. XV. Propos. XVIII.
[45.] Theor. XVI. Propos. XIX.
[46.] Problema IV. Propos. XX.
[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.
[48.] LEMMA.
[49.] Probl. II. Cubum invenire dati cubi duplum.
[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.
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          <head xml:id="echoid-head100" xml:space="preserve">PROP. III. THEOREMA.</head>
          <head xml:id="echoid-head101" style="it" xml:space="preserve">Dico triangulum B A P, & trapezium A B I P ſimul,
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          eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.</head>
          <note position="right" xml:space="preserve">TAB. XLIII.
            <lb/>
          Fig. 1. 2. 3.</note>
          <p>
            <s xml:id="echoid-s2831" xml:space="preserve">In antecedente demonſtratum eſt trapezia A B F P, A B I P
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            ſimul, eſſe ad duplum trapezii A B I P, ſicut trapezium
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            A B F P ad polygonum A B D L P: </s>
            <s xml:id="echoid-s2832" xml:space="preserve">& </s>
            <s xml:id="echoid-s2833" xml:space="preserve">permutando tra-
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            pezia A B F P, A B I P ſimul, ſunt ad trapezium A B F P,
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            ut duplum trapezii A B I P ad polygonum A B D L P. </s>
            <s xml:id="echoid-s2834" xml:space="preserve">& </s>
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            quoniam trapezium A B F P, trapezium A B I P & </s>
            <s xml:id="echoid-s2836" xml:space="preserve">trian-
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            gulum A B P, ſunt continuè proportionalia; </s>
            <s xml:id="echoid-s2837" xml:space="preserve">erit trape-
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            zium A B I P ad trapezium A B F P, ut triangulum A B P
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            ad trapezium A B I P; </s>
            <s xml:id="echoid-s2838" xml:space="preserve">& </s>
            <s xml:id="echoid-s2839" xml:space="preserve">componendo, ut trapezia A B I P,
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            A B F P ſimul, ad trapezium A B F P, ita triangulum
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            A B P & </s>
            <s xml:id="echoid-s2840" xml:space="preserve">trapezium A B I P ſimul, ad trapezium A B I P:
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            </s>
            <s xml:id="echoid-s2841" xml:space="preserve">erat autem, ut trapezia A B I P, A B F P, ſimul, ad tra-
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            pezium A B F P, ita duplum trapezii A B I P ad polygo-
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            num A B D L P; </s>
            <s xml:id="echoid-s2842" xml:space="preserve">& </s>
            <s xml:id="echoid-s2843" xml:space="preserve">igitur ut triangulum A B P & </s>
            <s xml:id="echoid-s2844" xml:space="preserve">trape-
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            zium A B I P ſimul, ad trapezium A B I P, ita duplum
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            trapezii A B I P ad polygonum A B D L P, quod demon-
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            ſtrare oportuit.</s>
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            <s xml:id="echoid-s2846" xml:space="preserve">Producantur (ſi opus ſit) rectæ A D, A L, ſegmentum
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            ſecantes in punctis E & </s>
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            <s xml:id="echoid-s2848" xml:space="preserve">rectas B I, I P, in H & </s>
            <s xml:id="echoid-s2849" xml:space="preserve">M:
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            <s xml:id="echoid-s2850" xml:space="preserve">deinde jungantur rectæ B E, E I, I O, O P, ut complea-
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            tur polygonum A B E I O P.</s>
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          <head xml:id="echoid-head102" xml:space="preserve">PROP. IV. THEOREMA.</head>
          <head xml:id="echoid-head103" style="it" xml:space="preserve">Dico polygonum A B E I O P eſſe medium pro-
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          portionale inter polygonum A B D L & trapezium A B I P.</head>
          <note position="right" xml:space="preserve">TAB. XLIII.
            <lb/>
          Fig. 1. 2. 3.</note>
          <p>
            <s xml:id="echoid-s2852" xml:space="preserve">Ex hujus prima manifeſtum eſt trapezium A I L P, tra-
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            pezium A I O P & </s>
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