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

Table of contents

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[41.] Theor. XII. Prop. XV.
Page: 91 (376)
[42.] Theor. XIII. Prop. XVI.
Page: 95 (377)
[43.] Theorema XIV. Propos. XVII.
Page: 96 (378)
[44.] Theor. XV. Propos. XVIII.
Page: 98 (380)
[45.] Theor. XVI. Propos. XIX.
Page: 100 (382)
[46.] Problema IV. Propos. XX.
Page: 102 (384)
[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.
Page: 109
[48.] LEMMA.
Page: 111 (390)
[49.] Probl. II. Cubum invenire dati cubi duplum.
Page: 112 (391)
[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.
Page: 114 (393)
[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)
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20320THEOR. DE QUADRAT. rantur duæ æquales E S, B P, & inſuper alia P D. Dico
iterum, id quo rectangulum E D B excedit E P B, æquari
rectangulo S D P. Rectangulum enim E D B æquale eſt iſtis
duobus, rectangulo E D P, & rectangulo ſub E D, P B;
horum autem E D P rurſus æquale eſt duobus, rectangulo ni-
mirum S D P, & ei quod continetur ſub E S, D P, ſive
rectangulo D P B. Igitur rectangulum E D B iſtis tribus æ-
quale eſt rectangulis, S D P, D P B, & rectangulo ſub
E D, P B; horum vero duo poſtrema æquantur rectangu-
lo E P B; ergo rectangulum E D B æquale eſt duobus, re-
ctangulo nimirum S D P & E P B, unde apparet exceſ-
ſum rectanguli E D B ſupra rectangulum E P B æquari re-
ctangulo S D P.

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