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

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14591HOROLOG. OSCILLATOR. C D & ipſa D G. Sed propter evolutionem, apparet utris-
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. que ſimul, rectæ C D, & lineæ D G, æquari rectam H G.
Ergo duæ ſimul C F, F G majores quoque erunt recta H G.
& ablata communi F G, erit C F major quam H F. Sed
F E major eſt quam F C, quia angulus C trianguli F C E
eſt rectus. Ergo F E omnino major quam F H. Unde ap-
paret, ab hac quidem parte puncti C, fili extremitatem non
pertingere ad rectam C E.

Sit jam punctum H propinquius principio evolutionis A
22TAB. XII.
Fig. 1. quam punctum C, ſitque fili poſitio H G, tunc cum ejus
extremitas eſſet in H, & ducantur rectæ D G, D H, qua-
rum hæc occurrat rectæ C E in E: apparet autem D G re-
ctam non poſſe eſſe in directum ipſi H G, adeoque H G D
fore triangulum. Jam quia recta D G vel minor eſt quam
D K G, vel eadem, ſi nempe evolutæ pars D G recta ſit;
additâ utrique G H, erunt rectæ D G, G H ſimul mino-
res vel æquales duabus iſtis, ſcilicet D K G & G H, ſive
his æquali rectæ D C. Duabus autem rectis D G, G H mi-
nor eſt recta D H. Ergo hæc minor utique erit rectâ D C.
Sed D E major eſt quam D C, quia in triangulo D C E
angulus C eſt rectus. Ergo D H multo minor quam D E.
Situm eſt ergo punctum H, hoc eſt extremitas fili G H, in-
tra angulum D C E. Unde apparet neque inter A & C us-
quam illam pertingere ad rectam C E. Ergo C E tangit
curvam A C in C; ac proinde D C, cui C E ducta eſt
perpendicularis, occurrit curvæ ad angulos rectos. quod
erat demonſtrandum.

Hinc etiam manifeſtum eſt curvam A H C in partem u-
nam inflexam eſſe, & in eandem partem cavam ac ipſa A G B,
cujus evolutione deſcripta eſt. Omnes enim tangentes lineæ
A H C, cadunt extra ſpatium D G A H C: omnes vero
tangentes lineæ A G D, intra dictum ſpatium. unde liquet
cavitatem A H C reſpicere convexitatem A G D.

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Scan	Original
121	76
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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
147
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150	93