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

Table of contents

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[51.] ALITER.
Page: 115 (394)
[52.] ALITER.
Page: 116 (395)
[53.] Probl. IV.
Page: 117 (396)
[54.] Probl. V.
Page: 118 (397)
[55.] Probl. VI.
Page: 118 (397)
[56.] Probl. VII.
Page: 123 (399)
[57.] Utrumque præcedentium Aliter.
Page: 125 (401)
[58.] Probl. VIII. In Conchoide linea invenire confinia flexus contrarii.
Page: 127 (403)
[59.] FINIS.
Page: 128 (404)
[60.] DE CIRCULI ET HYPERBOLÆ QUADRATURA CONTROVERSIA.
Page: 132
[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)
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142415
VERA
CIRCULI ET HYPERBOLÆ
QUADRATURA.
Sit circuli, ellipſeos vel hyperbolæ ſegmentum B I P
11TAB. XLIII.
Fig. 1. 2. 3. cujus centrum A: compleatur triangulum A B P, &
ſegmentum in punctis, B, P, tangentes ducantur re-
ctæ B F, P F, ſe invicem ſecantes in puncto F; pro-
ducatur (ſi opus ſit) recta A F ſegmentum interſecans in
puncto I & rectam B P in puncto Q; deinde jungantur re-
ctæ B I, P I.
PROP. I. THEOREMA.
Dico trapezium B A P I eſſe medium propor-
tionale inter trapezium B A P F, &
triangulum B A P.
Quoniam recta A Q ducitur per F concurſum duarum re-
ctarum F B, F P, ſegmentum in punctis B, P, tan-
gentium; igitur recta A Q rectam B P contactuum
puncta jungentem bifariam ſecabit in puncto Q; & proinde
triangulum A B Q eſt æquale triangulo A Q P, & trian-
gnlum F B Q triangulo F Q P; & igitur triangulum A B F
æquale eſt triangulo A P F; eſt ergo triangulum A B F di-
midium trapezii A B F P: eodem modo probatur triangu-
lum A B I eſſe dimidium trapezii A B I P; & triangulum
A B Q eſt dimidium trianguli A B P: cumque triangula
A B F, A B I, A B Q, eandem habeant altitudinem, in-
ter ſe ſunt ut baſes, ſed eorum baſes nempe A F, A I, A Q,
ſunt continuè proportionales; & igitur ipſa quoque triangu-
la ſunt continuè proportionalia; & proinde eorum dupla ni-
mirum trapezia A B F P, A B I P, & triangulum A B P
ſunt continuè proportionalia in ratione A F ad A I, quod
demonſtrare oportuit.

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