Stevin, Simon - Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis

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5757DE INVENIENDO GRAVITATIS CENTRO.

DEMONSTRATIO.

Quadrangulo delineâ HI ſuſpenſo, ſe-

91[Figure 91] gmentum H I D A ſegmĕto H I C B æqui-
libre pendebit, quia æqualia ſunt, ſimilia, &
ſimiliter ſita. H I igitur in parallelogrammo
A B C D gravitatis diameter eſt, eandemq́;
ob cauſam & F G. Atqui iſtæ in E mutuo
ſe interſecantes gravitatis centrum in ſeſe
habent. Quapropter E illud eſſe conclu-
ditur.

3 Exemplum.

D*ATVM*. A B C D E ordinatum ſive circulo inſcriptũ quinquangulum
eſto, & figuræ centrum F. Q*VAESITVM*. F gravitatis centrum quoq; eſſe
demonſtrandum eſt. P*RAEPARATIO*. Ab A in medium latus D C recta
A G; conſimiliter à B in medium latus E D recta B H ducatur.

DEMONSTRATIO.

Quinquangulo de A G ſuſpenſo, ſegmentũ A G D E ſegmento A G C B
æquilibre erit. ſunt enim æqualia, ſimilia, & ſimiliter ſi-

92[Figure 92] ta. A G igitur nec non B H in codem quinquangulo
gravitatis diametereſt. Atqui mutuò ſe in F figuræ cen-
tro interſecant, & illarum quæq́ue gravitatis centrum in
ſe habet. F igitur illud ipſum eſt. Eadem demonſtratio
aliarum omnium fuerit, quæcunque figuræ, centrum
habebunt, cujuſmodi ſunt ſexangulum, Circulus, & c.

C*ONCLVSIO*. In omni igitur plano figuræ cen-
trum, gravitatis quoque centrum eſt, quod nobis de-
monſtrandum fuit.

2 THEOREMA. 2 PROPOSITIO.

Trianguli cujusq́ue gravitatis centrum eſt in rectâ ab
angulo in oppoſitum latus medium ductâ.

D*ATVM*. A B C contingentis figuræ triangulum eſto, ab ejusq́ue angu-
lo, A in D medium oppoſiti lateris B C punctum, recta A D ducta.

Q*VAESITVM*. Gravitatis centrum dati trianguli in rectâ A D eſſe, de-
monſtrandum eſt. PRAEPARATIO. Rectæ E F, G H, I K ad B C paral-
lelæ ducuntor, ſecantes A D in L, M, N. ducuntor conſimiliter E O, G P,
I Q, K R, H S, F T ad A D parallelæ.

DEMONSTRATIO.

Quandoquidem E F ad B C parallela eſt, idemq́ue E O & F T ad L D,
quadrang ulum E F T O parallelogrammum erit, in quo E L, L F, O D &
D T æqualia ſunt, ideoq́ue gravitatis centrum in D L per 1 hujus propoſit.
eandemq́ue ob cauſam parallelogrammi G H S P gravitatis centrum in L M.

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