Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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10768CHRISTIANI HUGENII nis intercepto, & in eandem partem cavo. Ergo & F D
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.

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.

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.

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.

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Scan	Original
101
102
103
104	65
105	66
106	67
107	68
108
109
110
111	69
112	70
113	71
114	72
115
116
117
118	73
119	74
120	75
121	76
122
123
124
125	77
126	78
127	79
128	80
129	81
130	82

Scan	Original
101
102
103
104	65
105	66
106	67
107	68
108
109
110
111	69
112	70
113	71
114	72
115
116
117
118	73
119	74
120	75
121	76
122
123
124
125	77
126	78
127	79
128	80
129	81
130	82

Scan	Original
101
102
103
104	65
105	66
106	67
107	68
108
109
110
111	69
112	70
113	71
114	72
115
116
117
118	73
119	74
120	75
121	76
122
123
124
125	77
126	78
127	79
128	80
129	81
130	82