Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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velocitas, altera ut quadratum velocitatis: & ipſius (1/
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GD
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) decremen
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tum eſt ut ſumma quantitatum (1/
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GD
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) & (
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CG/GDq
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), quarum prior eſt
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ipſa (1/
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GD
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), & poſterior (
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CG/GDq
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) eſt ut (1/
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GDq
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). Proinde (1/
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GD
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), ob an
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alogum decrementum, eſt ut velocitas. </
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>Et ſi quantitas
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GD,
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ipſi (1/
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)
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reciproce proportionalis, quantitate data
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CG
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augeatur; ſumma
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CD,
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tempore
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ABED
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uniformiter creſcente, creſcet in progreſſione
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Geometrica.
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Q.E.D.
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DE MOTU
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CORPORUM</
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Corol.
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1. Igitur. </
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>ſi, datis punctis
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A, G,
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exponatur tempus per
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aream Hyperbolicam
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ABED,
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exponi poteſt velocitas per ipſius
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GD
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reciprocam (1/
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GD
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). </
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Corol.
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2. Sumendo autem
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GA
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ad
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GD
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ut velocitatis reciproca ſub
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initio, ad velocitatis reciprocam in fine temporis cujuſvis
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ABED,
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invenietur punctum
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G.
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Eo autem invento, velocitas ex dato quo
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vis alio tempore inveniri poteſt. </
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PROPOSITIO XII. THEOREMA IX.
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Iiſdem poſitis, dico quod ſi ſpatia deſcripta ſumantur in progreſſio
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ne Arithmetica, velocitates data quadam quantitate auctæ e
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runt in progreſſione Geometrica.
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<
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>In Aſymptoto
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CD
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detur pun
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ctum
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R,
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& erecto perpendiculo
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RS,
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quod occurrat Hyperbolæ in
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S,
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ex
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ponatur deſcriptum ſpatium per a
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ream Hyperbolicam
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RSED
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; &
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velocitas erit ut longitudo
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GD,
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quæ cum data
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CG
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componit longi
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tudinem
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CD,
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in progreſſione Geo
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metrica decreſcentem, interea dum
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ſpatium
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RSED
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augetur in Arith
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metica. </
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<
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EDde,
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lineola
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Dd,
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quæ </
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