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.
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 May 29, 2024.

Pages

Prop. XLIII. Prob. XXX.
Efficiendum est ut corpus in Trajectoria quacun{que} circa centrum viri∣um revolvente perinde moveri possit, at{que} corpus aliud in eadem Trajectoria quiescente.

In Orbe VPK positione dato revolvatur corpus P pergendo a V versus K. A centro C agatur semper Cp, quae sit ipsi CP ae∣qualis, angulum{que} VCp angulo VCP proportionalem constitu∣at; & area quam linea Cp describit erit ad aream VCP quam li∣nea

[illustration]
CP describit, ut ve∣locitas lineae describen∣tis Cp ad velocitatem li∣neae describentis CP; hoc est, ut angulus VCp ad angulum VCP, adeo{que} in data ratione, & propte∣rea tempori proportio∣nalis. Cum area tem∣pori proportionalis sit quam linea Cp in plano immobili describit, ma∣nifestum est quod cor∣pus, cogente justae quan∣titatis vi centripeta, revolvi possit una cum puncto p in curva il∣la linea quam punctum idem p ratione jam exposita describit in plano immobili. Fiat angulus VCv angulo PCp, & linea Cv li∣neae

Page 133

CV, at{que} figura vCp figurae VCP aequalis, & corpus in p semper existens movebitur in perimetro figurae revolventis vCp, eodem{que} tempore describet arcum ejus vp quo corpus aliud P arcum ipsi similem & aequalem VP in figura quiescente VPK de∣scribere potest. Quaeratur igitur, per Corollarium Propositionis VI, vis centripeta qua corpus revolvi possit in curva illa linea quam punctum p describit in plano immobili, & solvetur Proble∣ma. Q.E.F.

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