Full text: Volumen primum. Opera mechanica (1)

HOROLOG. OSCILLATOR. nas habeat pendulo ſimplici A N, etiam totum Ellipſeos
planum, ex A ſuſpenſum & in latus agitatum, ipſi A N
pendulo iſochronum fore. Sed & partem Ellipſeos quamli-
bet, quæ lineis una vel duabus, ad A N perpendicularibus,
abſcindetur.

120.1.

De centro
OSCILLA-
TIONIS .

Cæterum adſcribemus & aliud loci plani exemplum, in
quo nonnulla notatu digna occurrunt.

Sit virga A B ponderis expers, ſuſpenſa ex A; oporteat-
que, ad datum in ea punctum B, affigere triangula duo pa-
ria, & paribus angulis ab axe A B recedentia, quorum an-
guli ad B minimi, ſive infinite parvi exiſtimandi, quæque,
ita ſuſpenſa ab A, oſcillationes iſochronas faciant pendulo
ſimplici datæ longitudinis A L.

120.1.

TAB.XXIV.
Fig. 6.

Hic, ducta C G perpendiculari in B G, & ponendo
A B = a; A L = b; B G = x; C G = y: invenitur æqua-
tio y = 2 a b - 2 a a - {8/3} a x + {4/3} b x - x x ex qua patet, baſes
triangulorum C, & D, quæ baſes hic ut puncta conſide-
rantur, eſſe ad circuli circumferentiam; quia nempe habetur
terminus ſimplex - x x.

Licet autem hic animadvertere, quod ſi a ſit nihilo æqua-
lis, hoc eſt, ſi punctum, ubi affiguntur trianguli B C,
B D, ſit idem cum puncto A; tum futura ſit æquatio
y = {4/3} b x - x x . Ac proinde, hoc caſu, ſi ſumatur A O
= {2/3} b, hoc eſt, = {2/3} A L, centroque O per A circulus de-
ſcribatur A D N; erunt baſes triangulorum A C, A D, ad
illius circumferentiam. Cum igitur quælibet duo triangula
acutiſſima, quæ ex A ad circumferentiam A C N D conſti-
tuuntur, magnitudine & ſitu ſibi reſpondentia, centrum
oſcillationis habeant punctum L, poſitâ A L = {3/4} diametri
A N; cumque circulus totus ex ejusmodi triangulorum pa-
ribus componatur; uti & portio ejus quælibet, ut A C N D,
latera A C, A D æqualia habens; manifeſtum eſt, tum cir-
culi totius, tum portionis qualem diximus, centrum oſcilla-
tionis eſſe in L.

120.1.

TAB. XXV.
Fig. 1.

Rurſus, ſi in æquatione inventa ponatur {8/3} a = {4/3} b, ſeu

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