Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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Corol.
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5. Eadem valent ubi attractio oritur a Sphæræ utriuſque
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virtute attractiva, mutuo exercita in Sphæram alteram. </
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bus ambabus geminatur attractio, proportione ſervata. </
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Corol.
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6. Si hujuſmodi Sphæræ aliquæ circa alias quieſcentes re
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volvantur, ſingulæ circa ſingulas, ſintQ.E.D.ſtantiæ inter centra re
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volventium & quieſcentium proportionales quieſcentium diame
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tris; æqualia erunt Tempora periodica. </
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Corol.
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7. Et viciſſim, ſi Tempora periodica ſunt æqualia; diſtan
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tiæ erunt proportionales diametris. </
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Corol.
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8. Eadem omnia, quæ ſuperius de motu corporum circa
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umbilicos Conicarum Sectionum demonſtrata ſunt, obtinent ubi
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Sphæra attrahens, formæ & conditionis cujuſvis jam deſcriptæ, lo
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catur in umbilico. </
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Corol.
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9. Ut & ubi gyrantia ſunt etiam Sphæræ attrahentes, con
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ditionis cujuſvis jam deſcriptæ. </
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PROPOSITIO LXXVII. THEOREMA XXXVII.
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Si ad ſingula Sphærarum puncta tendant vires centripetæ, proper
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tionales diſtantiis punctorum a corporibus attractis: dico quod
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vis compoſita, qua Sphæræ duæ ſe mutuo trahent, est ut di
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ſtantia inter centra Sphærarum.
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Cas.
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1. Sit
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AEBF
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Sphæra,
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S
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centrum ejus,
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P
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corpuſculum at
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tractum,
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PASB
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axis Sphæræ per
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centrum corpuſculi tranſiens,
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EF,
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ef
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plana duo quibus Sphæra ſe
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catur, huic axi perpendicularia &
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hinc inde æqualiter diſtantia a
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centro Sphæræ;
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G, g
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interſectio
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nes planorum & axis, &
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H
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pun
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ctum quodvis in plano
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EF.
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Pun
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cti
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H
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vis centripeta in corpuſculum
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P,
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ſecundum lineam
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PH
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exer
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cita, eſt ut diſtantia
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PH
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; & (per Legum Corol. </
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neam
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PG,
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ſeu verſus centrum
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S,
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ut longitudo
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PG.
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Igitur pun
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ctorum omnium in plano
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EF,
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hoc eſt plani totius vis, qua corpuſ
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culum
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P
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trahitur verſus centrum
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S,
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eſt ut numerus punctorum
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ductus in diſtantiam
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PG:
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id eſt, ut contentum ſub plano ipſo
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EF
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& diſtantia illa
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PG.
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Et ſimiliter vis plani
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ef,
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qua corpuſculum
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P
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