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

Scan	Original
131
132
133
134	83
135	84
136	85
137	86
138
139
140
141	87
142	88
143
144	90
145	91
146	92
147
148
149
150	93
151	94
152	95
153	96
154
155
156
157	97
158	98
159	99
160	100

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.

Page concordance

Text layer

Text normalization

Search

Scan	Original
131
132
133
134	83
135	84
136	85
137	86
138
139
140
141	87
142	88
143
144	90
145	91
146	92
147
148
149
150	93
151	94
152	95
153	96
154
155
156
157	97
158	98
159	99
160	100

Scan	Original
131
132
133
134	83
135	84
136	85
137	86
138
139
140
141	87
142	88
143
144	90
145	91
146	92
147
148
149
150	93
151	94
152	95
153	96
154
155
156
157	97
158	98
159	99
160	100

Scan	Original
131
132
133
134	83
135	84
136	85
137	86
138
139
140
141	87
142	88
143
144	90
145	91
146	92
147
148
149
150	93
151	94
152	95
153	96
154
155
156
157	97
158	98
159	99
160	100