Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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trahitur verſus centrum
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S,
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eſt ut planum illud ductum in diſtantiam </
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ſuam
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Pg,
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ſive ut huic æquale planum
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EF
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ductum in diſtantiam
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illam
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Pg
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; & ſumma virium plani utriuſque ut planum
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EF
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duc
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tum in ſummam diſtantiarum
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PG+Pg,
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id eſt, ut planum illud
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ductum in duplam centri & corpuſculi diſtantiam
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PS,
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hoc eſt, ut
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duplum planum
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EF
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ductum in diſtantiam
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PS,
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vel ut ſumma æ
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qualium planorum
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EF+ef
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ducta in diſtantiam eandem. </
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mili argumento, vires omnium planorum in Sphæra tota, hinc in
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de æqualiter a centro Sphæræ diſtantium, ſunt ut ſumma planorum
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ducta in diſtantiam
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PS,
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hoc eſt, ut Sphæra tota ducta in diſtan
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tiam centri ſui
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S
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a corpuſculo
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P.
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E. D.
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LIBER
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PRIMUS.</
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Cas.
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2. Trahat jam corpuſculum
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Sphæram
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AEBF.
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Et eo
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dem argumento probabitur quod vis, qua Sphæra illa trahitur, erit:
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ut diſtantia
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PS.
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E. D.
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Cas.
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3. Componatur jam Sphæra altera ex corpuſculis innume
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ris
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P
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; & quoniam vis; qua corpuſculum unumquodque trahitur,
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eſt ut diſtantia corpuſculi a centro Sphæræ primæ ducta in Sphæ
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ram eandem, atque adeo eadem eſt ac ſi prodiret tota de corpuſ
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culo unico in centro Sphæræ; vis tota qua corpuſcula omnia in
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Sphæra ſecunda trahuntur, hoc eſt, qua Sphæra illa tota trahitur,
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eadem erit ac ſi Sphæra illa traheretur vi prodeunte de corpuſculo
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unico in centro Sphæræ primæ, & propterea proportionalis eſt di
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ſtantiæ inter centra Sphærarum.
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E. D.
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Cas.
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4. Trahant Sphæræ ſe mutuo, & vis geminata proportio
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nem priorem ſervabit.
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E. D.
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Cas.
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5. Locetur jam corpuſculum
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p
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intra Sphæram
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AEBF
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; &
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quoniam vis plani
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ef
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in corpuſculum eſt ut contentum ſub plano
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illo & diſtantia
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pg
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; & vis contraria plani
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EF
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ut contentum ſub
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plano illo & diſtantia
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pG
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; erit vis ex utraque compoſita ut diffe
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rentia contentorum, hoc eſt, ut ſumma æqualium planorum ducta
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in ſemiſſem differentiæ diſtantiarum, id eſt, ut ſumma illa ducta in
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pS
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diſtantiam corpuſculi a centro Sphæræ. </
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<
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attractio planorum omnium
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EF, ef
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in Sphæra tota, hoc eſt, at
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tractio Sphæræ totius, eſt ut ſumma planorum omnium, ſeu Sphæra
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tota, ducta in
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pS
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diſtantiam corpuſculi a centro Sphæræ.
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E. D.
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Cas.
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6. Et ſi ex corpuſculis innumeris
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p
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componatur Sphæra
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nova, intra Sphæram priorem
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AEBF
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ſita; probabitur ut prius
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quod attractio, ſive ſimplex Sphæræ unius in alteram, ſive mutua
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utriuſQ.E.I. ſe invicem, erit ut diſtantia centrorum
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pS. Q.E.D.
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