Philosophiæ naturalis principia mathematica autore Js. Newton ...
About this Item
Title
Philosophiæ naturalis principia mathematica autore Js. Newton ...
Author
Newton, Isaac, Sir, 1642-1727.
Publication
Londini :: Jussu Societatis Regiae ac Typis Josephi Streater ...,
1687.
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Subject terms
Mechanics -- Early works to 1800.
Celestial mechanics -- Early works to 1800.
Link to this Item
http://name.umdl.umich.edu/A52251.0001.001
Cite this Item
"Philosophiæ naturalis principia mathematica autore Js. Newton ..." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52251.0001.001. University of Michigan Library Digital Collections. Accessed June 10, 2024.
Pages
Pro. VI. Theor. V.
Si corpus P revolvendo circa centrum S, describat lineam quamvis curvam APQ, tangat vero recta ZPR curvam illam in puncto quovis P, & ad tangentem ab alio quovis curvae puncto Q agatur QR distantiae SP parallela, ac demittatur QT perpendicularis ad distantiam SP: Dico quod vis centripeta sit reciproce ut so∣lidum SP quad.×QT quad./QR, si modo solidi illius ea semper su∣matur quantilas quae ultimo fit
[illustration]
ubi coeunt puncta P & Q.
Nam{que} in figura indefinite parva QRPT lineola nascens QR, data tempore, est ut vis centripeta (per Leg. II.) &
descriptionPage 45
data vi, ut quadratum temporis (per Lem. X.) at{que} adeo, neu∣tro dato, ut vis centripeta & quadratum temporis conjunctim, ade∣o{que} vis centripeta ut lineola QR directe & quadratum temporis inverse. Est autem tempus ut area SPQ, ejusve dupla SP×QT, id est ut SP & QT conjunctim, adeo{que} vis centripeta ut QR di∣recte at{que} SP quad. in QT quad. inverse, id est ut SP quad.×QT quad./QR inverse. Q.E.D.
Corol. Hinc si detur figura quaevis, & in ea punctum ad quod vis centripeta dirigitur; inveniri potest lex vis centripetae quae corpus in figurae illius perimetro gyrari faciet. Nimirum compu∣tandum est solidum SP quad.×QT quad./QR huic vi reciproce pro∣portionale. Ejus rei dabimus exempla in problematis sequenti∣bus.
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