Prop. XXVIII. Theor. XXII.
Si corpus Funependulum in Cycloide oscillans resistitur in ratione momentorum temporis, erit ejus resistentia ad vim gravitatis ut ex∣cessus
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
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http://name.umdl.umich.edu/A52251.0001.001
- Cite this Item
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"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 4, 2024.
Pages
Page 309
arcus descensu toto descripti supra arcum ascensu subsequente descriptum, ad penduli longitudinem duplicatam.
Designet BC arcum descensu descriptum, Ca arcum ascensu descriptum, & Aa differentiam arcuum: & stantibus quae in Propositione XXV. constructa & demonstrata sunt, erit vis qua corpus oscillans urgetur in loco quovis D, ad uim resistentia ut arcus CD ad arcum CO, qui semissis est differentiae illius Aa. Ide∣oque vis qua corpus oscillans urgetur in Cycloidis principio seu puncto altissimo, id est vis gravitatis, erit ad resistentiam ut ar∣cus Cycloidis inter punctum illud supremum & punctum insi∣mum C ad arcum CO; id est (si arcus duplicentur) ut Cycloidis totius arcus, seu dupla penduli longitudo, ad arcum Aa. Q.E.D.