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 May 11, 2025.

Pages

Scholium

Casus Corollarii sexti obtinet in corporibus caelestibus (ut se∣orsum colligerunt etiam nostrates Wrennus, Hockius & Halleus) & propterea quae spectant ad vim centripetam decrescentem in duplicata ratione distantiarum a centris decrevi susius in sequenti∣bus exponere.

Porro praecedentis demonstrationis beneficio colligitur etiam proportio vis centripetae ad vim quamlibet notam, qualis est ea gravitatis. Nam cum vis illa, quo tempore corpus percurrit arcum BC, impellat ipsum per spatium CD, quod ipso motus initio aequale est quadrato arcus illius BD ad circuli diametrum applicato; & corpus omne vi eadem in eandem semper plagam

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continuata, describat spatia in duplicata ratione temporum: Vis illa, quo tempore corpus revolvens arcum quemvis datum de∣scribit, efficiet ut corpus idem recta progrediens describat spati∣um quadrato arcus illius ad circuli diametrum applicato aequale; adeo{que} est ad vim gravitatis ut spatium illud ad spatium quod grave cadendo eodem tempore describit. Et hujusmodi Proposi∣tionibus Hugenius, in eximio suo Tractatu de Horologio oscillato∣rio, vim gravitatis cum revolventium viribus centrifugis contulit.

Demonstrari etiam possunt praecedentia in hunc modum. In circulo quovis describi intelligatur Polygonum laterum quotcun{que} Et si corpus in Polygoni lateribus data cum velocitate movendo, ad ejus angulos singulos a circulo reflectatur; vis qua singulis re∣flexionibus impingit in circulum erit ut ejus velocitas, adeo{que} summa virium in dato tempore erit ut velocitas illa & numerus re∣flexionum conjunctim, hoc est (si Polygonum detur specie) ut longitudo dato illo tempore descripta & longitudo eadem appli∣cata ad Radium circuli, id est ut quadratum longitudinis illius ap∣plicatum ad Radium; adeo{que} si Polygonum lateribus infinite dimi∣nutis coincidat cum circulo, ut quadratum arcus dato tempore descripti applicatum ad radium. Haec est vis qua corpus urget circlum, & huic aequalis est vis contraria qua circulus continuo repellit corpus centrum versus.

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