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

[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)

[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.

161434VERA CIRCULI

PROP. XII. THEOREMA.

Sit trapezium A B I P, A; polygonum
11TAB. XLIII.
Fig. 1. 2. 3.22
A # C # D # B
A B E I O P, C; polygonum A B C G
K N P, D; & polygonum A B D L P, B. di-
co D eſſe medium harmonicum inter C & B. ex hujus 4,
A: C: : C: B, & componendo A + C: C: : C + B: B, ſed ex
hujus 5, A + C: C: : 2 C: D; & ideo C + B: B: : 2 C: D, &
permutando B + C: 2 C: : B: D, & dividendo, differentia in-
ter B & C eſt ad 2 C, ut differentia inter B & D ad D, & per-
mutando differentia inter B & C eſt ad differentiam inter
B & D ut 2 C ad D, hoc eſt, ut C + B ad B, & dividendo,
differentia inter D & C eſt ad differentiam inter B & D ut
C ad B; & proinde D eſt medium harmonicum inter C & B,
quod demonſtrare oportuit.

Hæc propoſitio eodem modo locum habet in omnibus po-
lygonis complicatis, ut patet ex ſcholio 5 hujus.

PROP. XIII. THEOREMA.

Inter duas quantitates A, B, ſit media a-
33
A ## B
C # D # E
rithmetica C, media geometrica D & me-
dia harmonica E. dico C, D, E, eſſe con-
tinuè proportionales. quoniam A, E, B,
ſunt in ratione harmonica; erit differentia inter A & E ad
differentiam inter E & B ut A ad B; & componendo erit
differentia inter A & B ad differentiam inter E & B, ut
A + B ad B; deinde permutando & componendo 2 A: A + B: :
E: B, ſed 2A eſt duplum ipſius A & A + B duplum ipſius C;
& ideo A: C: : E: B; & proinde CE = AB, & AB = DD, ideo-
que CE = DD; & igitur C: D: : D: E, quod demonſtrare o-
portuit.

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