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

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147420VERA CIRCULI fieri poſſit) generalis methodus inveniendi omnium ſerierum
convergentium terminationes.

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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