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

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12678CHRISTIANI HUGENII tiones B D & E F, æqualis altitudinis, hoc eſt, ejusmodi
11De motu
IN Cy-
CLOIDE. ut parallelæ horizontales B C, D H, quæ ſuperiorem por-
tionem B D includunt, æque inter ſe diſtent ac E G,
F K, inferiorem partionem E F includentes. Dico tempus
deſcenſus per curvam B D brevius fore tempore per E F.

Sumatur enim in B D punctum quodlibet L, & in E F
punctum M, ita ut eadem ſit altitudo E ſupra M quæ B
ſupra L. Et deſcripto ſuper axe A C ſemicirculo, occurrant
ei rectæ horizontales L N, M O, in N & O, & jungan-
tur N A, O A. Itaque quum punctum N ſit altius puncto
O, manifeſtum eſt rectam N A minus ad horizontem incli-
nari quam O A. Eſt autem ipſi N A parallela tangens curvæ
in L puncto , & ipſi O A parallela tangens curvæ in M. 22Prop. 15.
huj. Ergo curva B D in puncto L minus inclinata eſt quam curva
E F in puncto M. Quod ſi igitur portio E F, invariata in-
clinatione, altius extolli intelligatur velut in e f, ita ut in-
ter eaſdem parallelas cum portione B D comprehendatur,
invenietur punctum M in m, æquali altitudine cum puncto
L. eritque etiam inclinatio curvæ e f in puncto m, quæ ea-
dem eſt inclinationi curvæ E F in M, major inclinatione
curvæ B D in L. Similiter vero, & in quolibet alio puncto
curvæ e f, major oſtendetur inclinatio quam curv æ B D
in puncto æque alto. Itaque tempus deſcenſus per B D bre-
vius erit tempore per e f, ſive, quod idem eſt, per E F. 33Prop.
præced. quod erat demonſtrandum.

LEMMA.

ESto circulus diametro A C, quem ſecet ad an-
44TAB. IX.
Fig. 4. gulos rectos D E, & à termino diametri A e-
ducta recta A B occurrat circumferentiæ in B, ipſi
vero D E in F. Dico tres haſce, A B, A D, A F,
proportionales eſſe.

Sit enim primo interſectio F intra circulum; & arcui B D
recta ſubtenſa ducatur. Quia igitur arcus æquales ſunt A

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95	59
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97	61
98	62
99	63
100	64
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

Scan	Original
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
111	69
112	70
113	71
114	72
115
116
117
118	73
119	74
120	75

Scan	Original
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
111	69
112	70
113	71
114	72
115
116
117
118	73
119	74
120	75