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

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11472CHRISTIANI HUGENII

Item rurſus oſtenditur angulus L V C major L C V. Qua-
11De de-
SCENSU
GRAVIUM. re C V P, qui cum L V C duos rectos æquat, minor erit
quam V C D. Atqui addendo ad V C D angulum D C N,
fit V C N; & auferendo ab C V P angulum P V N, fit
C V N. Ergo angulus V C N omnino major quam C V N.
In triangulo itaque C V N, latus V N majus erit quam
C N. Eſt autem ipſi V N æqualis C A ſive C M. Ergo &
C M major quam C N, ideoque punctum circumferentiæ
M erit ultra curvam N A B à centro C remotum. Itaque
conſtat circumferentiam M A F tangere curvam in puncto A.
quod erat demonſtrandum.

Quod ſi punctum curvæ per quod tangens ducenda eſt,
ſit illud ipſum ubi regula curvam ſecat, erit tangens quæſi-
ta ſemper regulæ perpendicularis; ut facile eſſet oſtendere.

PROPOSITIO XVI.

SI circuli circumferentiam, cujus centrum E, ſe-
22De motu
IN Cy-
CLOIDE. cent rectæ duæ parallelæ A F, B G, quarum
33TAB. VIII.
Fig. 2. utraque ad eandem partem centri transeat, vel
altera A F per centrum ipſum: & à puncto A,
quo centro propior circumferentiam ſecat, ducatur
recta ipſam contingens: dico partem hujus A B, à
parallela utraque interceptam, minorem eſſe arcu
A C, ab utraque eadem parallela intercepto.

Ducatur enim arcui A C ſubtenſa recta A C. Quia ergo
angulus B A F eſt æqualis ei quem capit portio circuli A H F,
quæ vel major eſt ſemicirculo vel ſemicirculus, erit proinde
angulus B A F, vel minor recto vel rectus; ideoque angu-
lus A B C vel major recto vel rectus. Quare in triangulo
A B C latus A C, angulo B ſubtenſum, majus erit latere
A B. ſed idem latus A C minus eſt arcu A C. Ergo omni-
no & A B arcu A C minor erit.

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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
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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