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.
Page: 134
[62.] DEFINITIONES.
Page: 139
[63.] PETITIONES.
Page: 141 (414)
[64.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
Page: 142 (415)
[65.] PROP. I. THEOREMA. Dico trapezium B A P I eſſe medium propor-tionale inter trapezium B A P F, & triangulum B A P.
Page: 142 (415)
[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.
Page: 143 (416)
[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.
Page: 144 (417)
[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.
Page: 144 (417)
[69.] PROP. V. THEOREMA.
Page: 145 (418)
[70.] SCHOLIUM.
Page: 146 (419)
[71.] PROP. VI. THEOREMATA.
Page: 147 (420)
[72.] SCHOLIUM.
Page: 148 (421)
[73.] PROP. VII. PROBLEMA. Oportet prædictæ ſeriei terminationem invenire.
Page: 150 (423)
[74.] PROP. VIII. PROBLEMA.
Page: 152 (425)
[75.] PROP. IX. PROBLEMA.
Page: 153 (426)
[76.] PROP. X. PROBLEMA.
Page: 154 (427)
[77.] CONSECTARIUM.
Page: 155 (428)
[78.] PROP. XI. THEOREMA.
Page: 156 (429)
[79.] SCHOLIUM.
Page: 159 (432)
[80.] PROP. XII. THEOREMA.
Page: 161 (434)
[81.] PROP. XIII. THEOREMA.
Page: 161 (434)
[82.] PROP. XIV. THEOREMA.
Page: 162 (435)
[83.] PROP. XV. THEOREMA.
Page: 162 (435)
[84.] PROP. XVI. THEOREMA.
Page: 163 (436)
[85.] PROP. XVII. THEOREMA.
Page: 164 (437)
[86.] PROP. XVIII. THEOREMA.
Page: 164 (437)
[87.] PROP. XIX. THEOREMA.
Page: 165 (438)
[88.] CONSECTARIUM.
Page: 165 (438)
[89.] PROP. XX. THEOREMA.
Page: 165 (438)
[90.] PROP. XXI. THEOREMA.
Page: 166 (439)
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            proportionalia, & </s>
            <s xml:id="echoid-s2854" xml:space="preserve">ex prædictis ſatis facile colligi poteſt
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            trapezium A I L P eſſe dimidium polygoni A B D L P & </s>
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            trapezium A I O P eſſe dimidium polygoni A B E I O P
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            & </s>
            <s xml:id="echoid-s2856" xml:space="preserve">triangulum A I P eſſe dimidium trapezii A B I P: </s>
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            proinde terminos duplicando, polygonum A B D L P, po-
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            lygonum A B E I O P & </s>
            <s xml:id="echoid-s2859" xml:space="preserve">trapezium A B I P ſunt continuè
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            proportionalia, quod demonſtrare oportuit.</s>
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            <s xml:id="echoid-s2861" xml:space="preserve">Ducantur rectæ C G, K N, ſegmentum tangentes in
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            punctis E, O, & </s>
            <s xml:id="echoid-s2862" xml:space="preserve">rectis D L, D B, L P, occurrentes in
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            punctis C, G, K, N, ut compleatur polygonum
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            A B C G K N P.</s>
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          <head xml:id="echoid-head104" xml:space="preserve">PROP. V. THEOREMA.</head>
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            <s xml:id="echoid-s2864" xml:space="preserve">Dico trapezium A B I P & </s>
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              <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">TAB. XLIII.
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              Fig. 1. 2. 3.</note>
            ſimul, eße ad polygonum A B E I O P, ut
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            duplum polygoni A B E I O P ad poly-
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            gonum A B C G K N P.</s>
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            <s xml:id="echoid-s2867" xml:space="preserve">Ex hujus tertia manifeſtum eſt triangulum A B I & </s>
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            pezium A B E I ſimul, eſſe ad trapezium A B E I,
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            ut duplum trapezii A B E Iad polygonum A B C G I: </s>
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            ex prædictis facile concludi poteſt triangulum A B I eſſe di-
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            midium trapezii A B I P, & </s>
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            dium polygoni A B E I O P, & </s>
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            eſſe dimidium polygoni A B C G K N P; </s>
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            <s xml:id="echoid-s2874" xml:space="preserve">proinde termi-
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            nos duplicando, trapezium A B I P & </s>
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            ſimul, erunt ad polygonum A B E I O P ut duplum polygo-
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            ni A B E I O P ad polygonum A B C G K N P, quod
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            demonſtrandum erat.</s>
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            <s xml:id="echoid-s2877" xml:space="preserve">Hinc facile colligi poteſt polygonum A B C G K N P
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            eſſe medium harmonicum inter polygona A B E I O P,
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            A B D L P, quod hic admonuiſſe ſufficiat, in ſequentibus
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            enim demonſtrabitur.</s>
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