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

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1
culis
, ſed pluribus ſatis equinis à quibus eius gra­
uitas
in aqua non alteratur ſaltem differentia ſenſibi­
li
; poterit ergò ſumi additamentum ponderis F ac ſi
augeret
craſſitiem pilæ plumbeæ BC; ſit ergo GE pon­
dus
totius pilæ BACL vnà cum pondere adiuncto F
in
aere trutinato; GH verò ſit pondus eiuſdem ag­
gregati
BALCF intra aquam examinatum.
quia verò,

ex
Archimede, pondus corporis intra aquam demerſi
imminuitur
pro quantitate ponderis molis aquæ quæ
æqualis
ſit integro corpori demerſo, igitur differen­
tia
HE erit pondus molis aquæ PQ, quæ æqualis ſit
corpori
demerſo BALCF. poſtea pilam plumbeam
BC
eodem modo clauſam violentèr malleo contudi,
vt
ad minus ſpatium BLC redigeretur; manifeſtum
eſt
conſtipatum reſtrictumque ſuiſſe aerem incluſum
vt
nimirùm portio aeris A incluſa ſit in eodem ſpa­
tio
, quod occupabat reliqua aeris portio L. denuò
igitur
pilam plumbeam contuſam BLCF ponderaui
in
aere, & in aqua, atque in aere pondus eius fuit
GN
maius, quàm GE, eius verò pondus in aqua fuit
GM
, quaproptèr ponderum differentia MN erit gra­
uitas
molis aquæ RS quæ æqualis ſit corpori demer­
ſo
BLCF, & ſecetur EO æqualis MN.
Quia verò aer
AL
in ipſomet aere eiuſdem grauitatis nil grauitat ob
æquilibrium
, igitur pondus GE tribui debet plum­
bo
BCF, cùm verò pila contuſa in aere magis graui­
tet
pro menſura nimirùm GN, tunc quoque tota gra­
uitas
GE plumbo eidem tribui debet, at exceſſus
grauitatis
EN nullo pacto tribui poteſt portioni ae-

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