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 April 27, 2025.

Pages

Prop. XCV. Theor. XLIX.
Iisdem positis; dico quod velocitas corporis ante incidentiam est ad ejus velocitatem post emergentiam, ut sinus emergentiae ad sinum incidentiae.

Capiantur AH, Id aequales, & erigantur perpendicula AG, dK occurrentia lineis incidentiae & emergentiae GH, IK, in G & K. In GH capiatur TH aequalis IK, & ad planum Aa de∣mittatur normaliter Tv. Et per Legum Corol. 2. distinguatur motus corporis in duos, unum planis Aa, Bb, Cc &c. perpen∣dicularem, alterum iisdem parallelum. Vis attractionis vel im∣pulsus agendo secundum lineas perpendiculares nil mutat motum secundum parallelas, & propterea corpus hoc motu conficiet ae∣qualibus temporibus aequalia illa secundum parallelas intervalla, quae sunt inter lineam AG & punctum H, inter{que} punctum I & lineam dK; hoc est, aequalibus temporibus describet lineas GH,

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IK. Proinde velocitas ante incidentiam est ad velocitatem post emergentiam, ut GH ad IK vel TH, id est, ut AH vel Id ad vH, hoc est (respectu radii TH vel IK) ut sinus emergentiae ad sinum incidentiae. Q.E.D.

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