118106
cycloidem primariam A B C, reuoluto vel cir-
ca F C, vel circa dictam parallelam: Item in
quo puncto ipſius R G, vel ipſi parallelæ ſit cen-
trum grauitatis duplicatæ ſemicycloidis B D C R G,
ad partes F C: ſed admonebimus, centrum graui-
tatis ſolidi orti ex reuolutione figuræ B D C R G, ſic
ſecare dictam R G, vt pars terminata ad R, ſit ad
partem terminatam ad G, vt 7. ad 5. Ratio eſt,
quia ita diuidit B D, centrum grauitatis cycloidis
A B C, ſicuti diuidit FC, centrum figuræ B D C R G.
Item admonebimus, centrum grauitatis ſolidi orti
ex gyratione figuræ A E B F C, circa F C, ſic ſeca-
re F C, vt pars terminata ad F, ſit ad partem ter-
minatam ad C, vt 1. ad 3. Ratio eſt quia ſic di-
uidit B D, centrum grauitatis prædictæ figuræ re-
uolutæ. Nam cum ex Torricellio de dimenſione cy-
cloidis, & ex Tacquet in diſlertatione de circulorum
volutationibus propoſit. 20. demonſtratione nun-
quam ſatis laudata, conſtet, A E B F C, eſſe tertiam
partem cycloidis A B C; & cum ex eodem Torri-
cellio ſupra citato, ſupponamus centrum grauitatis
cycloidis ſic ſecare B D, vt pars terminata ad B, ſit
ad partem terminatam ad D, vt 7. ad 5; & pariter
cum medium punctum B D, ſit centrum grauitatis
torius parallelogrammi E C, nempe centrum gra-
uitatis parallelogramn irelinquat hinc inde 6, par-
tes, quarum B D, ſupponitur 12; lector in doctri-
nis A chimed s exercitatus facile agnoſcet, centrum
grauitatis prædicti exceſſus ſic ſecare B D, vt
ca F C, vel circa dictam parallelam: Item in
quo puncto ipſius R G, vel ipſi parallelæ ſit cen-
trum grauitatis duplicatæ ſemicycloidis B D C R G,
ad partes F C: ſed admonebimus, centrum graui-
tatis ſolidi orti ex reuolutione figuræ B D C R G, ſic
ſecare dictam R G, vt pars terminata ad R, ſit ad
partem terminatam ad G, vt 7. ad 5. Ratio eſt,
quia ita diuidit B D, centrum grauitatis cycloidis
A B C, ſicuti diuidit FC, centrum figuræ B D C R G.
Item admonebimus, centrum grauitatis ſolidi orti
ex gyratione figuræ A E B F C, circa F C, ſic ſeca-
re F C, vt pars terminata ad F, ſit ad partem ter-
minatam ad C, vt 1. ad 3. Ratio eſt quia ſic di-
uidit B D, centrum grauitatis prædictæ figuræ re-
uolutæ. Nam cum ex Torricellio de dimenſione cy-
cloidis, & ex Tacquet in diſlertatione de circulorum
volutationibus propoſit. 20. demonſtratione nun-
quam ſatis laudata, conſtet, A E B F C, eſſe tertiam
partem cycloidis A B C; & cum ex eodem Torri-
cellio ſupra citato, ſupponamus centrum grauitatis
cycloidis ſic ſecare B D, vt pars terminata ad B, ſit
ad partem terminatam ad D, vt 7. ad 5; & pariter
cum medium punctum B D, ſit centrum grauitatis
torius parallelogrammi E C, nempe centrum gra-
uitatis parallelogramn irelinquat hinc inde 6, par-
tes, quarum B D, ſupponitur 12; lector in doctri-
nis A chimed s exercitatus facile agnoſcet, centrum
grauitatis prædicti exceſſus ſic ſecare B D, vt