Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1SPXQTut area dato tempore deſcripta, id eſt, per Prop. XIV.
in ſubduplicata ratione lateris recti. Q.E.D.
LIBER
PRIMUS.
25[Figure 25]
Corol.1. Latera recta principalia ſunt in ratione compoſita ex
duplicata ratione perpendiculorum & duplicata ratione veloci­
tatum.
Corol.2. Velocitates corporum in maximis & minimis ab umbi­
lico communi diſtantiis, ſunt in ratione compoſita ex ratione di­
ſtantiarum inverſe & ſubduplicata ratione laterum rectorum princi­
palium directe. Nam perpendicula jam ſunt ipſæ diſtantiæ.
Corol.3. Ideoque velocitas in Conica ſectione, in maxima vel
minima ab umbilico diſtantia, eſt ad velocitatem in Circulo in ea­
dem à centro diſtantia, in ſubduplicata ratione lateris recti princi­
palis ad duplam illam diſtantiam.
Corol.4. Corporum in Ellipſibus gyrantium velocitates in medi­
ocribus diſtantiis ab umbilico communi ſunt eædem quæ corporum
gyrantium in Circulis ad eaſdem diſtantias; hoc eſt (per Corol 6.
Prop. IV.) reciproce in ſubduplicata ratione diſtantiarum. Nam
perpendicula jam ſunt ſemi-axes minores; & hi ſunt ut mediæ
proportionales inter diſtantias & latera recta. Componatur hæc
ratio inverſe cum ſubduplicata ratione laterum rectorum directe, &
fiet ratio ſubduplicata diſtantiarum inverſe.
Corol.5. In eadem figura, vel etiam in figuris diverſis, quarum

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