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

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11371HOROLOG. OSCILLATOR. fublatum in V: & jungantur C N, N V, V C, V L. E-
11De de-
SCENSU
GRAVIUM. rit ergo V N æqualis C A; imo erit ipſa C A translata in
V N. Jam quia recta L C æquatur curvæ L V, ac proin-
de major eſt recta L V, erit in triangulo C L V angulus
L V C major quam L C V. Quare addito inſuper angulo
L V N ad L V C, fiet totus N V C major utique quam
L C V, ac proinde omnino major angulo N C V, qui pars
eſt L C V. Ergo in triangulo C V N latus C N majus erit
latere V N, cui æquatur C A, ideoque C N major quo-
que quam C A, hoc eſt quam C M. Unde apparet pun-
ctum N cadere extra circulum M A F, qui proinde tanget
curvam in puncto A. quod erat demonſtrandum.

Eſt autem eadem quoque tum conſtructio tum demonſtra-
tio, ſi curva genita ſit à puncto deſcribente, vel intra vel
extra ambitum figuræ circumvolutæ ſumpto. Niſi quod,
hoc poſteriori caſu, pars quædam curvæ infra regulam de-
ſcendit, unde nonnulla in demonſtratione oritur diverſitas.

Sit enim punctum A, per quod tangens ducenda eſt, da-
22TAB. VIII.
Fig. 1. tum in parte curvæ N A B, quæ infra regulam C L de-
ſcendit, deſcripta nimirum à puncto N extra figuram revo-
lutam ſumpto, ſed certam poſitionem in eodem ipſius pla-
no habente. Invento igitur puncto C, ubi figura revoluta
tangit regulam C D quum punctum deſcribens eſſet in A,
ducatur recta C A. Dico hanc curvæ N A B occurrere ad
rectos angulos, ſive circumferentiam radio C A centro C
deſcriptam tangere curvam N A B in puncto A. Oſtendetur
autem exterius ipſam contingere, cum in curvæ parte ſupra
regulam C D poſita interius contingat.

Poſitis enim & deſcriptis iisdem omnibus quæ prius, os-
tenditur rurſus angulus E C H major quam C E H. atqui
ad E C H addito H C B fit angulus E C B; & à C E H
auferendo H E B, qui æqualis eſt D C A, fit angulus
C E B. Ergo E C B major omnino quam C E B. unde in
triangulo E C B latus E B majus quam C B. ſed ipſi E B
æqualis eſt C A, ſive C F. Ergo & C F major quam C B:
ideoque punctum circumferentiæ F eſt ultra curvam N A B
à centro remotum.

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Scan	Original
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
131
132
133
134	83
135	84
136	85
137	86
138
139
140

Scan	Original
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
131
132
133
134	83
135	84
136	85
137	86
138
139
140