Newton, Isaac - Philosophia naturalis principia mathematica

Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1

LIBER
PRIMUS.

PROPOSITIO LIII. PROBLEMA XXXV.

Conceſſis Figurarum curvilinearum quadraturis, invenire Vires qui
bus corpora in datis curvis lineis Oſcillationes ſemper Iſochro
nas peragent.

Oſcilletur corpus Tin curva quavis linea STRQ,cujus axis ſit
ORtranſiens per virium centrum C.Agatur TXquæ curvam il
lam in corporis loco quovis Tcontingat, inque hac tangente TX

101[Figure 101]
capiatur TYæqualis arcui TR.Nam longitudo arcus illius ex Fi
gurarum quadraturis (per Methodos vulgares) innoteſcit. De pun
cto Yeducatur recta YZtangenti perpendicularis. Agatur CTper
pendiculari illi occurrens in Z,& erit Vis centripeta proportiona
lis rectæ TZ. que E. I.

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