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

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16316THEOR. DE QUADRAT. minor erit dato ſpatio; ſit ea parallelogrammum B F, & di-
vidatur baſis A C in partes æquales ipſi D F, punctis
G, H, K & c. atque inde ducantur ad ſectionem rectæ
G L, H M, K N & c. diametro B D parallelæ, & perfi-
ciantur parallelogramma D O, G P, H Q, K R & c. Di-
co figuram ex omnibus iſtis parallelogrammis compoſitam
(quæ impoſterum ordinatè circumſcripta vocabitur) ſupera-
re portionem A B C minori quàm datum ſit ſpatio.

Jungantur enim A N, N M, M L, L B, B S, & c.
eritque hac ratione inſcripta quoque portioni figura quædam
rectilinea; majorque erit exceſſus figuræ circumſcriptæ quæ
ex parallelogrammis compoſita eſt, ſuper inſcriptam, quàm
ſupra portionem A B C. Exceſſus autem circumſcriptæ ſuper
inſcriptam ex triangulis conſtat, quorum quæ ſunt ab una
diametri parte, ut A R N, N Q M, M P L, L O B,
æquantur dimidio parallelogrammi O D vel B F, quia ſin-
gulorum baſes baſi D F æquales ſunt, & omnium ſimul al-
titudo, parallelogrammi B F altitudini. Eâdem ratione trian-
gula qu& ſunt ab altera diametri parte, æquantur dimidio
parallelogrammi B F: Ergo omnia ſimul triangula ſive di-
ctus exceſſus æqualis eſt parallelogrammo B F, eóque mi-
nor ſpatio dato. Sed eodem exceſſu adhuc minor erat ex-
ceſſus figuræ circumſcriptæ ſupra portionem A B C: igitur
hic exceſſus dato ſpatio multo minor eſt. Et apparet fieri
poſſe quod proponebatur.

Theorema II.

DAtâ portione hyperboles, vel ellipſis vel circuli
portione, dimidiâ ellipſi dimidiove circulo non
majore, & dato triangulo qui baſin habeat baſi por-
tionis æqualem; poteſt utrique figura circumſcribi ex
parallelogrammis quorum ſit omnium eadem latitu-
do, ita ut uterque ſimulexceſſus quo figuræ circum-
ſcriptæ portionem & triangulum ſuperant, ſit minor
ſpatio quovis dato.

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