Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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in caſu hujus Corollarii, ſit
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DS+DH
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ut 4
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L,
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&
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diviſim
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DE MOTU
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CORPORUM</
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Corol.
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2. Unde ſi datur corporis velocitas in vertice principali
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D,
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invenietur Orbita expedite, capiendo ſcilicet latus rectum ejus, ad
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duplam diſtantiam
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DS,
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in duplicata ratione velocitatis hujus datæ
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ad velocitatem corporis in Circulo, ad diſtantiam
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DS,
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gyrantis (per
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Corol. </
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>3. Prop. </
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>XVI.) dein
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ad
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ut latus rectum ad differen
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tiam inter latus rectum & 4
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DS.
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Corol.
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3. Hinc etiam ſi corpus moveatur in Sectione quacunque
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Conica, & ex Orbe ſuo impulſu quocunque exturbetur; cognoſci
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poteſt Orbis in quo poſtea curſum ſuum peraget. </
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>Nam componen
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do proprium corporis motum cum motu illo quem impulſus ſolus
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generaret, habebitur motus quocum corpus de dato impulſus loco,
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ſecundum rectam poſitione datam, exibit. </
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Corol.
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4. Et ſi corpus illud vi aliqua extrinſecus impreſſa conti
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nuo perturbetur, innoteſcet curſus quam proxime, colligendo mu
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tationes quas vis illa in punctis quibuſdam inducit, & ex ſeriei ana
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logia mutationes continuas in locis intermediis æſtimando. </
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Scholium.
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<
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>Si corpus
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P
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vi centripeta ad
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punctum quodcunQ.E.D.tum
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R
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tendente moveatur in perimetro
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datæ cujuſcunque Sectionis co
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nicæ cujus centrum ſit
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C,
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& re
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quiratur Lex vis centripetæ: du
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catur
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CG
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radio
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RP
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paralle
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la, & Orbis tangenti
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PG
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oc
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currens in
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G
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; & vis illa (per
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Corol. </
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>VII.) erit ut
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CG cub./RP quad.
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