Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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219138CHRISTIANI HUGENII ducantur autem ab omnibus datis punctis, ad pun-
11Decentro
OSCILLA-
TIONIS.
ctum aliquod in circuli illius circumferentia lineæ
rectæ erit ſumma quadratorum ab omnibus ſem-
per eidem plano æqualis.
Sint data puncta A B C D: centrumque gravitatis eorum,
22TAB. XX.
Fig. 5.
ſive magnitudinum æqualium ab ipſis ſuſpenſarum, ſit E;
& centro E deſcribatur circulus quilibet F f, in cujus cir-
cumferentia ſumpto puncto aliquo, ut F, ducantur ad id,
à datis punctis, rectæ A F, B F, C F, D F.
Dico earum
omnium quadrata, ſimul ſumpta, æqualia eſſe plano cuidam
dato, ſemperque eidem, ubicunque in circumferentia pun-
ctum F ſumptum fuerit.
Ducantur enim rectæ G H, G K, angulum rectum con-
ſtituentes, &
quarum unicuique omnia data puncta ſint po-
ſita ad eandem partem.
Et à ſingulis in utramque harum
perpendiculares agantur A L, A K;
B M, B O; C N,
C P;
D H, D Q. A centro autem gravitatis E, & à pun-
cto F, in alterutram duarum, G H vel G K, perpendi-
culares E R, F S.
Et item, à datis punctis, in ipſam
F S perpendiculares A V, B X, C Y, D Z.
Et F T per-
pendicularis in ipſam E R.
Porro ſit jam
33
A L = a # A K = e # radius # E F = z
B M = b # B O = f # # G S = x
C N = c # C P = g
D H = d # D Q = h
Quia autem E eſt centrum gravitatis punctorum A, B, C, D;
ſi addantur in unum perpendiculares A L, B M, C N, D H,
compoſitaque ex omnibus dividatur in tot partes, quot ſunt
data puncta;
earum partium uni æqualis erit E R . 44Prop. 2.
huj.
terque, divisâ in totidem partes ſummâ perpendicularium
A K, B O, C P, D Q, earum uni æqualis erit perpendi-
cularis, ducta ex E in rectam G K, ſive ipſa R G .
55Prop. 2.
huj.
que, ſi ſumma omnium A L, B M, C N, D H, ſive
a + b + c + d vocetur l:
ſumma vero omnium, A K, B O,
C P, D Q ſive e + f + g + h, vocetur m:
&

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