Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

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1
Cap. 10. de
æquitempo­
ranea natu­
rali veloci­
tate grauium.
PROP. CCVII.
Corpora homogenea commenſurabilem proportionem haben­
tia æquè velocitèr deſcendent ablatis omnibus impe­
dimentis.
SInt quęlibet duo corpora homogenea A, & B, quę
habeant quamcumque commenſurabilem pro­
portionem. Dico, quod ex ſui na­
150[Figure 150]
tura ablatis omnibus impedimen­
tis, hæc duo corpora æquali velo­
citate deſcendent, nempè eodem
tempore T percurrent duo ſpatia
D, & E inter ſe æqualia. Reperia­
tur corpus C homogeneum ipſis
A, & B, quod communis menſura
ſit eorum; hoc verò tempore T deſcendat ſpatium F; &
quia duorum corporum ſimiliarium A multiplex eſt

ipſius C, ergo æquè velocia erunt, nempè ſpatia D, &
F eodem tempore T exacta æqualia ſunt inter ſe. ea­
dem ratione duo ſpatia E, & F tranſacta eodem tem­
pore T ab homogeneis corporibus B, & C multiplicem
proportionem habentibus æqualia erunt inter ſę;
vnde ſequitur quod duo ſpatia D, & E. excurſa eodem
tempore T ab homogeneis corporibus A, & B æqua­
lia ſint inter ſe, cùm æquentur vni tertio F. Quare pa­
tet propoſitum.
151[Figure 151]

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