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

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15295HOROLOG. OSCILLATOR.

Sunto lineæ A B C, A D E, in partem unam inflexæ,
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE.& quarum uttraque in eaſdem partes cava exiſtat, habeant-
que communem terminum A punctum. Omnes autem rectæ
tangentes lineam A B C, velut B D, C E, occurrant
22TAB. XII.
Fig. 4. lineæ A D E ad angulos rectos. Dico evolutione ipſius
A B C, à termino A incepta, deſcribi A D E.

Si enim fieri poteſt, deſcribatur dicta evolutione alia
quædam curva A F G. Ergo lineæ rectæ quælibet, evolu-
tam A B C tangentes, ut B D, C E, occurrent ipſi A F G
ad angulos rectos, puta in F & G. Sed eædem 33Prop. 1.
huj. etiam ad rectos angulos occurrere ponuntur lineæ A D E.
Sunt igitur lineæ curvæ A D E, A F G, eodem puncto
A terminatæ, inque partem unam flexæ, & ambæ in ean-
dem partem cavæ, quippe utraque in eandem atque ipſa
A B C; nam de linea A D E conſtat ex hypotheſi, de
A F G vero ex propoſitione prima hujus; & omnes quæ
uni earum occurrunt ad angulos rectos, etiam alteri ſimili-
ter occurrunt. quod quidem fieri non poſſe antea oſtenſum
eſt. Quare conſtat ipſam A D E deſcriptum iri 44Prop. 3.
huj. lineæ A B C. quod erat demonſtrandum.

PROPOSITIO V.

SI Cycloidem recta linea in vertice contingat, ſu-
per qua, tanquam baſi, alia cyclois priori ſimi-
lis & æqualis conſtituatur, initium ſumens à pun-
cto dicti verticis; recta quælibet inferiorem cycloi-
dem tangens, occurret ſuperioris portioni, ſibi ſu-
perpoſitæ, ad angulos rectos.

Tangat cycloidem A B C in vertice A recta A G, ſuper
55TAB. XVI.
Fig. 1. qua, tanquam baſi, ſimilis alia cyclois conſtituta ſit A E F,
cujus vertex F. Cycloidem autem A B C tangat recta B K
in B. Dico eam productam occurrere cycloidi A E F ad an-
gulos rectos.

Deſcribatur enim circa A D, axem cycloidis A B C,

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Scan	Original
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
148
149
150	93
151	94
152	95
153	96
154
155
156
157	97
158	98
159	99
160	100