Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

HYPERB. ELLIPS. ET CIRC. A D ad D F; multoque major quam A D ad D H, vel
quàm L K ad K E. Sit itaque M K ad K E ſicut portio
A B C ad exceſſum quo ipſa ſuperatur à figura ordinatè cir-
cumſcripta. Itaque cum K ſit centrum grav. figuræ portio-
ni circumſcriptæ, & E centrum grav. ipſius portionis; erit
M centrum gravitatis omnium ſpatiorum quæ eundem exceſ-
ſum conſtituunt . Quod eſſe non poteſt; Nam ſi per M linea ducatur diametro B D parallela, erunt ab una parte
omnia quæ diximus ſpatia. Manifeſtum eſt igitur, portio-
nis A B C centrum grav. eſſe in B D portionis diametro.

12.1.

Theor. 1.
8. lib. 1.
Arch. de
Æquipond.

Eſto nunc A B C portio ellipſis vel circuli, dimidiâ fi-
gurá major. Abſolvatur figura, & producatur B D uſque
dum ſectioni occurrat in E; erit igitur portionis A E C dia-
meter E D, & B D E diameter totius figuræ. Et quoniam
in B D E diametro eſt figuræ totius centrum gravitatis, (hoc
enim ex prædemonſtratis conſtabit, ſi in duo æqualia tota
figura dividatur diametro quæ ipſi A C ſit parallela,) & in
eadem centr. gravitatis A E C portionis minoris, ſicut mo-
dò oſtenſum fuit; erit quoque centr. gravitatis portionis re-
liquæ A B C in B D E ; quod erat oſtendendum.

12.1.

TAB. XXXIV.
Fig. 5.
8. lib. 1.
Archim. dc
Æqu@pond.

13. Lemma .

Eſto linea E B, cui ad utrumque terminum adjiciantur æ-
quales duæ E S, B P, & inſuper alia P D. Dico id quo
rectangulum E D B excedit E P B, æquari rectangulo S D P. Eſt enim rectangulum E D B æquale iſtis duobus, rectangulo
E D P & rectangulo ſub E D, P B: quorum ultimum ſuperat
rectangulum E P B rectangulo D P B. Igitur exceſſus rectan-
guli E D B ſupra rectangulum E P B æqualis eſt duobus iſtis,
rectangulo E D P, & D P B. Sed rectangulum E D P addito
rectangulo D P B, id eſt rectangulo ſub E S, D P, æquale
fit rectangulo S D P. Manifeſtum eſt igitur, exceſſum re-
ctanguli E D B ſupra E P B, æquari rectangulo S D P.

13.1.

TAB. XXXIV.
Fig. 6.

Eſto rurſus linea E B, cui ad utrumque terminum aufe-

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