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

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[111.] III. DOMINI GREGORII RESPONSUM AD ANIMADVERSIONES DOMINI HUGENII, IN EJUS LIBRUM, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
Page: 196 (466)
[112.] PROP. X. PROBLEMA.
Page: 197 (467)
[113.] Tom. II. Nnn
Page: 197 (467)
[114.] CONSECTARIUM.
Page: 198 (468)
[115.] IV. EXCERPTA EX LITERIS Dni. HUGENII DE RESPONSO, QUOD Dnus. GREGORIUS DEDIT AD EXAMEN LIBRI, CUI TITULUS EST, VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
Page: 202 (472)
[116.] V. EXCERPTA EX EPISTOLA D. JACOBI GREGORII, CONTINENTE QUASDAM EJUS CONSIDERATIO-NES, SUPER EPISTOLA D. HUGENII, IMPRESSA IN VINDICATIONEM EXAMINIS SUI LIBRI, DE VERA CIRCULI ET HY-PERBOLÆ QUADRATURA.
Page: 206 (476)
[117.] FINIS.
Page: 212 (482)
[118.] CHRISTIANI HUGENII GEOMETRICA VARIA. Tom. II. Ppp
Page: 213
[119.] I. CONSTRUCTIO LOCI AD HYPERBOLAM PER ASYMPTOTOS.
Page: 215 (485)
[120.] DEMONSTRATIO.
Page: 217 (487)
[121.] II. DEMONSTRATIO REGULÆ DE MAXIMIS ET MINIMIS.
Page: 220 (490)
[122.] Tom. II. Qqq
Page: 224 (491)
[123.] III. REGULA Ad inveniendas Tangentes linearum curvarum.
Page: 231 (498)
[124.] Tom. II. Rrr
Page: 232 (499)
[125.] IV. CHRISTIANI HUGENII EPISTOLA DE CURVIS QUIBUSDAM PECULIARIBUS.
Page: 243 (507)
[126.] V. PROBLEMA AB ERUDITIS SOLVENDUM: A JOHANNE BERNOULLIO IN ACTIS LIPSIENSIBUS ANNI MDCXCIII. PROPOSITUM.
Page: 251 (515)
[127.] Tom. II. Ttt
Page: 251 (515)
[128.] VI. C. H. Z. DE PROBLEMATE BERNOULLIANO IN ACTIS LIPSIENSIBUS PROPOSITO.
Page: 252 (516)
[129.] VII. C. H. Z. CONSTRUCTIO UNIVERSALIS PROBLEMATIS A CLARISSIMO VIRO JOH. BERNOULLIO PROPOSITI.
Page: 254 (518)
[130.] FINIS.
Page: 256 (520)
[131.] CHRISTIANI HUGENII OPERA ASTRONOMICA. Tomus Tertius.
Page: 260
[132.] Tomi tertii contenta.
Page: 261
[133.] CHRISTIANI HUGENII DE SATURNILUNA OBSERVATIO NOVA. Tom. III. Ttt
Page: 262
[134.] CHRISTIANI HUGENII DE SATURNI LUNA OBSERVATIO NOVA.
Page: 264 (523)
[135.] Tom. III. Vvv.
Page: 264 (523)
[136.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. SYSTEMA SATURNIUM, SIVE DE CAUSIS MIRANDORUM SATURNI PHÆNOMENON; ET COMITE EJUS PLANETA NOVO.
Page: 268
[137.] SERENISSIMO PRINCIPI LEOPOLDO AB HETRURIA Chriſtianus Hugenius S.D.
Page: 270 (529)
[138.] Tom. III. Xxx
Page: 272 (531)
[139.] NICOLAUS HEINSIUS, D. F. AD AUCTOREM SYSTEMATIS.
Page: 273 (532)
[140.] CHRISTIANI HUGENII Zulichemii, Cθnst. F. SYSTEMA SATURNIUM.
Page: 276 (535)
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PROP. VI. THEOREMATA.
Dico differentiam inter triangulum A B P & trape-
11TAB. XLIII.
Fig. 1. 2. 3. zium A B F P majorem eſſe duplo differentiæ inter
trapezium A B I P & polygonum A B D L P.
Sit triangulum A B P, A; trapezium A B F P, B; tra-
pezium A B I P, C, & polygonum A B D L P, D: quo-
niam A eſt ad C ut C ad B, igitur ut differentia inter A
& C ad A, ita differentia inter C & B ad C; & permutan-
do, ut differentia inter A & C ad differentiam inter C & B
ita A ad C; & componendo, ut differentia inter A & C &
differentia inter C & B ſimul, hoc eſt differentia inter A &
B, ad differentiam inter C & B, ita A + C ad C; ſed ut
A + C ad C ita 2 C ad D, & ideo differentia inter A &
B eſt ad differentiam inter C & B ut 2 C ad D. quoniam
A + C eſt ad C ut 2 C ad D, erit permutando ut A + C
ad 2 C ita C ad D; & dividendo, ut differentia inter A &
C ad 2 C ita differentia inter C & D ad D; & permutan-
do, differentia inter A & C eſt ad differentiam inter C & D
ut 2 C ad D; ſed demonſtratum eſt differentiam inter A &
B eſſe ad differentiam inter C & B ut 2 C ad D; & proin-
de differentia inter A & B eſt ad differentiam inter C & B,
ut differentia inter A & C ad differentiam inter C & D; ſed
differentia inter A & B eſt major differentia inter C & B,
& ideo differentia inter A & C eſt major differentia inter C
& D: & prædictam analogiam permutando, differentia in-
ter A & B eſt ad differentiam inter A & C, ut differentia
inter C & B ad differentiam inter C & D; at differentia in-
ter A & B eſt major differentia inter A & C, & ideo diffe-
rentia inter C & B eſt major differentia inter C & D; atque
differentia inter A & B æqualis eſt differentiis, inter A & C,
inter C & B; cumque earum utravis ſit major differentia

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