10768CHRISTIANI HUGENII
nis intercepto, &
in eandem partem cavo.
Ergo &
F D
11De de-
SCENSU
GRAVIUM. eodem arcu B D major erit: quare conſtat propoſitum.
11De de-
SCENSU
GRAVIUM. eodem arcu B D major erit: quare conſtat propoſitum.
PROPOSITIO XIII.
IIsdem poſitis, ſi recta A B occurrat ipſi D G in-
22TAB. VI.
Fig. 6. tra circulum; Dico arcum B D, rectis G D,
A B interceptum, majorem eſſe recta D F.
22TAB. VI.
Fig. 6. tra circulum; Dico arcum B D, rectis G D,
A B interceptum, majorem eſſe recta D F.
Jungatur enim D C &
ducatur arcui D B ſubtenſa D B.
Quoniam ergo angulus A B D æqualis A C D, hoc eſt,
angulo A D G; angulus autem D F B major angulo A D F,
ſive A D G; erit idem D F B etiam major D B F. Ergo
in triangulo D F B latus D B majus latere D F; unde mul-
to magis arcus D B ſuperabit eandem D F. Quare conſtat
propoſitum.
Quoniam ergo angulus A B D æqualis A C D, hoc eſt,
angulo A D G; angulus autem D F B major angulo A D F,
ſive A D G; erit idem D F B etiam major D B F. Ergo
in triangulo D F B latus D B majus latere D F; unde mul-
to magis arcus D B ſuperabit eandem D F. Quare conſtat
propoſitum.
PROPOSITIO XIV.
SIt cyclois A B C cujus baſis A C axis B D.
Quomodo autem generetur ex definitione &
deſcriptione mechanica ſuperius traditis ſatis ma-
nifeſtum arbitror. Et circa axem B D, circulus
deſcriptus ſit B G D, & à quolibet puncto E in cy-
cloide ſumpto agatur E F baſi A C parallela, quæ
occurrat axi B D in F, ſecetque circumferentiam
B G D in G, Dico rectam G E arcui G B æqua-
lem eſſe.
Quomodo autem generetur ex definitione &
deſcriptione mechanica ſuperius traditis ſatis ma-
nifeſtum arbitror. Et circa axem B D, circulus
deſcriptus ſit B G D, & à quolibet puncto E in cy-
cloide ſumpto agatur E F baſi A C parallela, quæ
occurrat axi B D in F, ſecetque circumferentiam
B G D in G, Dico rectam G E arcui G B æqua-
lem eſſe.
Deſcribatur enim per E punctum circulus L E K ipſi
B G D æqualis, quique tangat baſin cycloidis in K, & du-
catur diameter K L. Eſt igitur recta A K arcui E K æqua-
lis; ſed tota A D æqualis ſemicircumferentiæ K E L; ergo
K D æqualis arcui E L ſive G B. Eſt autem K D ſive N F
æqualis E G, quoniam E N æqualis G F, & communis
utrique N G. Ergo conſtat & G E æqualem eſſe arcui G B.
B G D æqualis, quique tangat baſin cycloidis in K, & du-
catur diameter K L. Eſt igitur recta A K arcui E K æqua-
lis; ſed tota A D æqualis ſemicircumferentiæ K E L; ergo
K D æqualis arcui E L ſive G B. Eſt autem K D ſive N F
æqualis E G, quoniam E N æqualis G F, & communis
utrique N G. Ergo conſtat & G E æqualem eſſe arcui G B.