Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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PRIMUS.</
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PROPOSITIO LIII. PROBLEMA XXXV.
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Conceſſis Figurarum curvilinearum quadraturis, invenire Vires qui
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bus corpora in datis curvis lineis Oſcillationes ſemper Iſochro
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nas peragent.
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>Oſcilletur corpus
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T
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in curva quavis linea
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STRQ,
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cujus axis ſit
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OR
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tranſiens per virium centrum
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C.
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Agatur
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TX
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quæ curvam il
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lam in corporis loco quovis
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T
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contingat, inque hac tangente
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TX
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capiatur
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TY
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æqualis arcui
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TR.
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Nam longitudo arcus illius ex Fi
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gurarum quadraturis (per Methodos vulgares) innoteſcit. </
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cto
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Y
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educatur recta
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YZ
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tangenti perpendicularis. </
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CT
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per
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pendiculari illi occurrens in
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Z,
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& erit Vis centripeta proportiona
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lis rectæ
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TZ.
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E. I.
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