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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152425ET HYPERBOLÆ QUADRATURA.
PROP. VIII. PROBLEMA.
Sint duæ quantitates datæ A, B, & ratio quæli-
libet data C ad D: oportet invenire aliam
quantitatem, ut ratio ejus ad A ſit multipli-
cata rationis B ad A in ratione C ad D.
Sit primò ratio C ad D commen-
11
EDC # AFBG
ſurabilis, ſitque inter C & D com-
munis menſura E; & quoties E continetur in D toties ſit
ratio F ad A ſubmultiplicata rationis B ad A; & quoties E
continetur in C toties ſit ratio G ad A multiplicata rationis
F ad A: dico G eſſe quantitatem illam quæſitam. ratio G ad
A eſt multiplicata rationis F ad A in ratione C ad E, & ra-
tio F ad A eſt multiplicata rationis B ad A in ratione E ad D; &
igitur ex æqualitate, ratio G ad A eſt multiplicata rationis
B ad A in ratione C ad D, quod demonſtrare oportuit.
Quod ſi ratio C ad D ſit incommenſurabilis, geometricam
hujus problematis praxim eſſe impoſſibilem mihi perſuadeo;
approximatione tamen fieri poteſt, aſſumendo rationem com-
menſurabilem ejus loco, quæ quàm proximè ad illam acce-
dat.
Sit ſeries convergens, cujus primi
22
## G # H # A # B
# N # I # K # C # D
M ## R # S # E # F
# O # T # V # X # Y
### L ## Z
termini convergentes ſint A, B, ſe-
cundi C, D, tertii E, F; ſintque
ſecundi termini ita facti à primis, ut
ratio B majoris ad A minorem ſit
multiplicata rationis C ad A in ra-
tione data mojoris inæqualitatis M ad N, & ut ratio B ad
A ſit multiplicata rationis D ad A in ratione data majoris
inæqualitatis M ad O: ſintque tertii termini eodem modo
facti ex ſecundis quo ſecundi facti ſunt ex primis; atque ita
continuetur ſeries.

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