Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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id eſt, ut
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SPXRPq
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ad (
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SP cub.XPV cub/PT cub.
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) ſive (ob ſimilia
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triangula
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PSG, TPV
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) ad
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SG cub.
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DE MOTU
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CORPORUM</
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Corol.
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3. Vis, qua corpus
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P
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in Orbe quocunque circum virium
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centrum
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S
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revolvitur, eſt ad vim qua corpus idem
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P
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in eodem
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orbe eodemque tempore periodico circum aliud quodvis virium
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centrum
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R
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revolvi poteſt, ut
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SPXRPq
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contentum utique ſub di
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ſtantia corporis a primo virium centro
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S
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& quadrato diſtantiæ ejus
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a ſecundo virium centro
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R
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ad cubum rectæ
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SG
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quæ a primo vi
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rium centro
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S
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ad orbis tangentem
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PG
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ducitur, & corporis a ſe
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cundo virium centro diſtantiæ
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RP
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parallela eſt. </
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<
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>Nam vires in
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hoc Orbe, ad ejus punctum quodvis
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P,
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eædem ſunt ac in Circulo
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ejuſdem curvaturæ. </
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PROPOSITIO. VIII. PROBLEMA. III.
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Moveatur corpus in Circulo
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PQA:
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ad hunc effectum requiritur Lex
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vis centripetæ tendentis ad punctum adeo longinquum
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S,
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ut lineæ
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omnes
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PS, RS
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ad id ductæ, pro parallelis haberi poſſint.
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>A Circuli centro
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C
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agatur ſemidiameter
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CA
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parallelas iſtas
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perpendiculariter ſecans in
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M
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&
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N,
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& jungatur
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CP.
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Ob ſimilia
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triangula
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CPM, PZT
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&
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RZQ
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eſt
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CPq
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ad
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PMq
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ut
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PRq
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ad
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QTq
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& ex natura Circuli
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PRq
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æquale eſt rectangulo
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QRX√RN+QN
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&c.
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<
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>ſive coeuntibus punctis
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P, Q
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rect
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angulo
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QRX2PM.
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Ergo eſt
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CPq
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ad
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PM quad.
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ut
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QRX2PM
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ad
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QT quad.
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adeoque (
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QT quad./QR
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)
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æquale (2
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PM cub./CP quad.
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), & (
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QT quad.XSP quad./QR
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) æquale (2
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PM cub.XSP qu./CP quad.
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)
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Eſt ergo (per Corol. </
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>1 & 5 Prop. </
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>VI.) vis centripeta reciproce ut
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(2
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PMcub.XSP quad./CP quad.
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) hoc eſt (neglecta ratione determinata (2
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SP quad./CP quad.
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))
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reciproce ut
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PM cub. </
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<
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E. I.
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<
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>Idem facile colligitur etiam ex Propoſitione præcedente. </
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