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
81
82	49
83	50
84	51
85	52
86
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89	53
90	54
91	55
92	56
93	57
94	58
95	59
96	60
97	61
98	62
99	63
100	64
101
102
103
104	65
105	66
106	67
107	68
108
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110

Scan	Original
81
82	49
83	50
84	51
85	52
86
87
88
89	53
90	54
91	55
92	56
93	57
94	58
95	59
96	60
97	61
98	62
99	63
100	64
101
102
103
104	65
105	66
106	67
107	68
108
109
110