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

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15093HOROLOG. OSCILLATOR. major erit ratio K B ad B N quam E F ad F G. Sed A B
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. major eſt quam K B, quoniam angulus K in triangulo A K B
eſt obtuſus, eſt enim major angulo H E F qui eſt obtuſus
ex conſtructione. Ergo ratio A B ad B N major erit ratio-
ne K B ad B N, ac proinde omnino major ratione E F ad
F G. Eodem modo & ratio B C ad C O, & C D ad D P,
major oſtendetur ratione E F ad F G. Itaque conſtat pro-
poſitum.

PROPOSITIO III.

DUæ curvæ in unam partem inflexæ & in eas-
dem partes cavæ ex eodem puncto egredi ne-
queunt, ita ad ſe invicem comparatæ, ut recta
omnis quæ alteri earum ad angulos rectos occurrit,
ſimiliter occurrat & reliquæ.

Sint enim, ſi fieri poteſt, hujuſmodi lineæ curvæ A C E,
22TAB. XII.
Fig. 3. A G K, communem terminum habentes A, & ſumpto in ex-
teriore illarum puncto quolibet K, ſit inde educta K E recta,
curvæ A G K occurrens ad angulos rectos, ac proinde
etiam curvæ A C E.

Poteſt jam recta quædam ſumi major curva K G A, quæ
ſit Q. Diviſa autem intelligatur ipſa K G A, ut in propo-
ſitione antecedenti dictum fuit, in tot partes punctis H G F,
ut ſubtenſæ ſingulæ K H, H G, G F, F A, ad perpen-
diculares curvæ ſibi contiguas H M, G N, F O, A P
majorem rationem habeant quam linea Q ad rectam K E.
Itaque & omnes ſimul dictæ ſubtenſæ ad omnes dictas per-
pendiculares majorem habebunt rationem quam Q ad K E.
Producantur autem perpendiculares eædem & occurrant cur-
væ A C E in D, C, B, nimirum ad angulos rectos ex
hypotheſi. Erit jam K E minor quam M D. Etenim, ducta
E L ipſi K E perpendiculari, quoniam K E occurrit lineæ
curvæ E C A ad angulos rectos, tanget E L curvam A C E,
occurretque neceſſario rectæ M D inter D & M.

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Scan	Original
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145	91
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Scan	Original
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
141	87
142	88
143
144	90
145	91
146	92
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150	93