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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115
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118	73
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125	77
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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