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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150423ET HYPERBOLÆ QUADRATURA. quos terminos æquales appellamus ſeriei terminatio-
nem.
PROP. VII. PROBLEMA.
Ut huic problemati ſatisfiat, oportet primò invenire
quantitatem quæ eodem modo componitur ex termi-
nis convergentibus a, b, quo ex terminis convergentibus
{ca + bd - ad/c}, {bc - bc + ae/c}, hoc autem facile fit hoc modo: inveniatur
quantitas quæ multiplicata in a & addita b multiplicata in
quantitatem data m, eandem quantitatem facit ac ſi multi-
plicaretur in {ca + bd - ad/c} & adderetur {bc - be + ae/c} multiplicata etiam
in eandem quantitatem data\m m. ſit quantitas illa z, & pro-
inde za + bm æquatur {zca + zbd - zad + mbe - mbe + mae/c}, & æquatione
reducta invenitur {z = mac - mbe/ad - bd}; quæ quantitas ſive multiplica-
ta in a & addita m, ſive multiplicata in {ca + bd - ad/c} & addita
{mbe - mbe + mae/c} efficit eandem in utroque caſu quantitatem nempe
{maae - mbae + mbad - mbbd/cd - bd}: & proinde prædicta quantitas eodem mo-
do componitur ex terminis convergentibus a, b, quo compo-
nitur ex terminis convergentibus {ca + bd - ad/c}, {bc - be + ae/c}. atque a
& b quoniam ſunt quantitates indefinitæ poſſunt eſſe quili-
bet totius ſeriei termini convergentes, modò termini con-
vergentes immediatè ſequentes ſint {ca + bd - ad/c} & {bc - be + ae/c}, &
proinde quantitas {maae - mbae + mbad - mbbd/cd - bd} eodem modo componi-
tur ex quibuslibet totius ſeriei terminis convergentibus quo
componitur ex terminis convergentibus a, b; & igitur

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