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 4, 2025.
Pages
Prop. XVI. Theor. XII.
Si Medii densitas in locis singulis sit reciproce ut dignitas aliqua di∣stantiae locorum a centro, sitque vis centripeta reciproce ut distantia in dignitatem illam ducta: dico quod corpus gyrari potest in Spirali, quae radios omnes a centro illo ductos intersecat in angulo dato.
Demonstratur eadem methodo cum Propositione superiore. Nam si vis centripeta in P sit reciproce ut distantiae SP dignitas quaelibet SPn+1 cujus index est n+1; colligetur ut supra, quod tempus quo corpus describit arcum quemvis PQ erit ut PQ×SP½n
descriptionPage 289
& resistentia in P ut Rr / PQq.×SPn sive ut ½nVQ / PQ×SPn×SQ, ade∣que ut ½nOS / OP×SPn+1. Et propterea densitas in P est reciproce ut SPn.
Scholium.
Caeterum haec Propositio & superiores, quae ad Media inaequali∣ter densa spectant, intelligendae sunt de motu corporum adeo parvorum, ut Medii ex uno corporis latere major densitas quam ex altero non consideranda veniat. Resistentiam quoque caeteris paribus densitati proportionalem esse suppono. Unde in Mediis quorum vis resistendi non est ut densitas, debet densitas eo usque augeri vel diminui, ut resistentiae vel tollatur excessus vel defectus suppleatur.
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