Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1
DE MOTU
CORPORUM
PROPOSITIO XXXIV. THEOREMA X.
Si FiguraBED Parabola eſt, dico
83[Figure 83]
quod corporis cadentis Veloci­
tas in loco quovisC æqualis eſt
velocitati qua corpus centroB
dimidio intervalli ſuiBC Cir­
culum uniformiter deſcribere
potest.
Nam corporis Parabolam
RPBcirca centrum Sdeſcri­
bentis velocitas in loco quovis
P(per Corol. 7. Prop. XVI) æ­
qualis eſt velocitati corporis di­
midio intervalli SPCirculum cir­
ca idem centrum Suniformiter
deſcribentis. Minuatur Parabolæ
latitudo CPin infinitum eo, ut
arcus Parabolicus PfBcum rec­
ta CB,centrum Scum vertice B,
& intervallum SPcum intervallo BCcoincidat, & conſtabit Pro­
poſitio. que E. D.
PROPOSITIO XXXV. THEOREMA XI.
Iiſdem poſitis, dico quod area FiguræDES, radio indefinitoSD de­
ſcripta, æqualis ſit areæ quam corpus, radio dimidium lateris recti
FiguræDES æquante, circa centrumS uniformiter gyrando, eo­
dem tempore deſcribere potest.
Nam concipe corpus Cquam minima temporis particula lineo­
lam Cccadendo deſcribere, & interea corpus aliud K,uniformi­
ter in Circulo OKkcirca centrum Sgyrando, arcum Kkdeſcri­
bere. Erigantur perpendicula CD, cdoccurrentia Figuræ DES
in D, d.Jungantur SD, Sd, SK, Sk& ducatur Ddaxi ASoc­
rens in T,& ad eam demittatur perpendiculum SY.

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