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

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

Table of contents

[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.

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.

[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)

144417ET HYPERBOLÆ QUADRATURA.

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.

11TAB. XLIII.
Fig. 1. 2. 3.

In antecedente demonſtratum eſt trapezia A B F P, A B I P
ſimul, eſſe ad duplum trapezii A B I P, ſicut trapezium
A B F P ad polygonum A B D L P: & permutando tra-
pezia A B F P, A B I P ſimul, ſunt ad trapezium A B F P,
ut duplum trapezii A B I P ad polygonum A B D L P. &
quoniam trapezium A B F P, trapezium A B I P & trian-
gulum A B P, ſunt continuè proportionalia; erit trape-
zium A B I P ad trapezium A B F P, ut triangulum A B P
ad trapezium A B I P; & componendo, ut trapezia A B I P,
A B F P ſimul, ad trapezium A B F P, ita triangulum
A B P & trapezium A B I P ſimul, ad trapezium A B I P:
erat autem, ut trapezia A B I P, A B F P, ſimul, ad tra-
pezium A B F P, ita duplum trapezii A B I P ad polygo-
num A B D L P; & igitur ut triangulum A B P & trape-
zium A B I P ſimul, ad trapezium A B I P, ita duplum
trapezii A B I P ad polygonum A B D L P, quod demon-
ſtrare oportuit.

Producantur (ſi opus ſit) rectæ A D, A L, ſegmentum
ſecantes in punctis E & O, & rectas B I, I P, in H & M:
deinde jungantur rectæ B E, E I, I O, O P, ut complea-
tur polygonum A B E I O P.

PROP. IV. THEOREMA.

Dico polygonum A B E I O P eſſe medium pro-
portionale inter polygonum A B D L & trapezium A B I P.

22TAB. XLIII.
Fig. 1. 2. 3.

Ex hujus prima manifeſtum eſt trapezium A I L P, tra-
pezium A I O P & triangulum A I P eſſe

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