Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1de datur punctum Bper quod Hyperbola, Aſymptoris CH, CD,
deſcribi debet; ut & ſpatium ABGD,quod corpus incipiendo
motum ſuum cum velocitate illa AB,tempore quovis AD,in Me­
dio ſimilari reſiſtente deſcribere poteſt.
DE MOTU
CORPORUM
PROPOSITIO VI. THEOREMA IV.
Corpora Spherica homogemea & æqualia, reſiſtentiis in duplicata
ratione velocitatum impedita, & ſolis viribus inſitis incitata,
temporibus quæ ſunt reciproce ut velocitates ſub initio, deſcri­
bunt ſemper æqualia ſpatia, & amittunt partes velocitatum pro­
portionales totis.
Aſymptotis rectangulis CD,
150[Figure 150]
CHdeſcripta Hyperbola qua­
vis BbEeſecante perpendicula
AB, ab, DE, de,in B, b, E, e,
exponantur velocitates initi­
ales per perpendicula AB,
DE,& tempora per lineas
Aa, Dd.Eſt ergo ut Aaad
Ddita (per Hypotheſin) DE
ad AB,& ita (ex natura Hy­
perbolæ) CAad CD; & com­
ponendo, ita Caad Cd.Ergo
areæ ABba, DEed,hoc eſt, ſpatia deſcripta æquamtur inter ſe,
& velocitates primæ AB, DEſunt ultimis ab, de,& propterea
(dividendo) partibus etiam ſuis amiſſis AB-ab, DE-depro­
portionales. Q.E.D.
PROPOSITIO VII. THEOREMA V.
Corpora Sphærica quibus reſiſtitur in duplicata ratione velocitatum,
temporibus quæ ſunt ut motus primi directe & reſiſtentiæ pri­
mæ inverſe, amittent partes motuum proportionales totis, &
ſpatia deſcribent temporibus iſtis in velocitates primas ductis
proportionalia.
Namque motuum partes amiſſæ ſunt ut reſiſtentiæ & tempora

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