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

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14490CHRISTIANI HUGENII

IV.

11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE.

Illa vero cui filum circumplicatum erat, dicatur
Evoluta. In figura ſuperiori, A B C eſt evoluta,
22TAB. XI.
Fig. 2. A D E deſcripta ex evolutione A B C, ut nempe
cum extremitas fili ex A venit in D, pars fili ex-
tenſa ſit D B recta, reliqua parte B C adhuc ap-
plicata curvæ A B C. Manifeſtum eſt autem D B
tangere evolutam in B.

PROPOSITIOI.

R Ecta omnis, quæ evolutam tangit, occurret li-
@eæ ex evolutione deſcriptæ ad angulos rectos.

Sit A B evoluta, A H vero quæ ex evolutione illius de-
33TAB. XI.
Fig. 3. ſcripta eſt. Recta autem F D C, tangens curvam A D in D,
occurrat in C curvæ A C H. Dico ei occurrere ad angulos
rectos: hoc eſt, ſi ducatur C E recta perpendicularis C D,
dico eam in C tangere curvam A C H. Quia enim D C
tangit evolutam in D, apparet ipſam referre poſitionem fili
tunc cum ejus extremitas pervenit in C. Quod ſi igitur o-
ſtenderimus filum, in tota reliqua deſcriptione curvæ A C H,
nusquam pertingere ad rectam C E præterquam in C pun-
cto, manifeſtum erit rectam C E ibidem curvam A C H
contingere.

Sumatur punctum aliquod in A C præter C, quod ſit H,
ſitque primo remotius à principio evolutionis A quam pun-
ctum C, & intelligatur pars libera eſſe H G, cum extremi-
tate ſua ad H pervenit. Tangit ergo H G lineam A B in G.
Cumque interea dum deſcribitur pars curvæ C H, evolu-
tus ſit arcus D G, occurret C D à parte D producta ipſi
H G, ut in F. Ponatur autem G H occurrere rectæ C E
in E. Quia igitur duæ ſimul D F, F G, majores ſunt quam
D G, ſive curva ea fuerit ſive recta: fiet addendo utrinque
rectam D C, ut rectæ C F, F G ſimul majores ſint

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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
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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