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

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12779HOROLOG. OSCILLATOR. A D, erunt anguli ad circumferentiam ipſis inſiſtentes,
11De motu
IN Cy-
CLOIDE. E D A, A B D æquales. Itaque in triangulis A B D,
A D F, æquales anguli A B D, A D F. Communis au-
tem utrique eſt angulus ad A. Ergo dicti trianguli ſimiles
erunt, ideoque B A ad A D ut A D ad A F.

Sit jam punctum interſectionis f extra circulum, & du-
catur b H parallela D E, quæ occurrat rectæ A D in H.
Itaque ſecundum jam demonſtrata erit ut D A ad A b, ita
A b ad A H, hoc eſt, ita A f ad A D: Ideoque rurſus
proportionales erunt A f, A D, A b. Quare conſtat propo-
ſitum.

PROPOSITIO XXIII.

SIt Cyclois A B C, cujus vertex A deorſum con-
22TAB. IX.
Fig. 5. verſus ſit, axe A D ad perpendiculum erecto;
ſumptoque in ea quolibet puncto B, ducatur inde
deorſum recta B I quæ Cycloidem tangat, terminetur-
que recta horizontali A I. recta vero B F ad axem
perpendicularis agatur, & diviſa bifariam F A in
X, ſuper ea deſcribatur ſemicirculus F H A. Du-
ctâ deinde per punctum quodlibet G in curva B A
ſumptum, rectâ Σ G parallelâ B F, quæ circum-
ferentiæ F H A occurrat in H, axi A D in Σ, in-
telligantur per puncta G & H rectæ tangentes u-
triusque curvæ, earumque tangentium partes iis-
dem duabus horizontalibus M S, N T interceptæ
ſint M N, S T. Iisdemque rectis M S, N T in-
cludantur tangentis B I pars O P, & axis D A
pars Q R.

Quibus ita ſe habentibus, dico tempus quo gra-
ve percurret rectam M N, celeritate

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106	67
107	68
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114	72
115
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Scan	Original
101
102
103
104	65
105	66
106	67
107	68
108
109
110
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

Scan	Original
101
102
103
104	65
105	66
106	67
107	68
108
109
110
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