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

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18318THEOR. DE QUADRAT.
Quoniam igitur F H, L K ſunt diametro B D parallelæ,
ſuntque D F, D L æquales, oportet lineam H K, quæ duas
F H, L K conjungit, à diametro B D bifariam ſecari;
qua-
re eadem H K parallela erit baſi A C , &
E H K G 115. lib. 2.
con.
linea.
Itaque E C parallelogrammum eſt; cujus oppoſita la-
tera quum bifariam dividat diameter B D, erit in ea paral-
lelogrammi centrum gravitatis .
Eâdem ratione 229. lib. 1.
Arch. de
Æquipond.
gramma erunt H M, N O, P Q, &
ſingulorum centra gra-
vitatis in linea B D.
Ergo & figuræ ex omnibus dictis pa-
rallelogrammis compoſitæ centrum gravitatis in eadem B D
reperiri neceſſe eſt.
Iſta autem figura eadem eſt quæ portio-
ni ordinatè fuerat circumſcripta.
Ergo figuræ portioni ordi-
natè circumſcriptæ centrum gravitatis conſtat eſſe in B D por-
tionis diametro.
Quod erat oſtendendum.
Theorema IV.
POrtionis hyperboles, ellipſis & circuli, centrum
gravitatis eſt in portionis diametro.
Eſto portio hyperboles, vel ellipſis vel circuli dimidiâ pri-
33TAB. XXXIV.
Fig. 4.
mum figurâ non major, A B C;
diameter ejus B D. O-
ſtendendum eſt, in B D reperiri portionis A B C gravitatis
centrum.
Si enim fieri poteſt, ſit extra diametrum in E, & ducatur
E H diametro B D parallela.
Dividendo itaque D C conti-
nuè bifariam, relinquetur tandem linea minor quam D H;
ſit ea D F, & circumſcribatur portioni figura ordinatè ex
parallelogrammis quorum baſes æquales ſint lineæ D F, &

jungantur B A, B C.
Figuræ itaque portioni circumſcri-
ptæ centrum gravitatis eſt in B D portionis diametro.
Sit hoc
K, &
jungatur E K, producaturque, & occurrat ei A L
parallela B D.
Quia autem portio major eſt triangulo A B C,
&
exceſſus quo figura circumſcripta portionem ſuperat, mi-
nor parallelogrammo B F, uti ſupra demonſtratum fuit ;
44Theor. 1. erit major ratio portionis A B C ad dictum exceſſum, quàm
trianguli A B C ad B F parallelogrammum, id eſt

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