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

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12577HOROLOG. OSCILLATOR. A B, brevius eſſe tempore per G H poſt N G ſive poſt F G.

11De motu
IN Cy-
CLOIDE.

Similiter oſtendetur, productis D C, K H ſurſum, do-
nec occurrant horizontali A F in O & P, tempus per
C D poſt A B C, ſive poſt O C, brevius eſſe tempore per
H K poſt F G H ſive poſt P H. Ac denique tempus per
D E poſt A B C D, brevius eſſe tempore per K L poſt
F G H K. Quare totum tempus deſcenſus per A B C D E,
brevius erit tempore per F G H K L. quod erat demon-
ſtrandum.

Hinc vero manifeſtum eſt, conſiderando curvas lineas
tanquam ex innumeris rectis compoſitas, ſi fuerint duæ ſu-
perficies, ſecundum lineas curvas ejusdem altitudinis incli-
natæ, quarum in punctis quibuslibet æque altis major ſem-
per ſit inclinatio unius quam reliquæ, etiam tempore bre-
viori per minus inclinatam grave deſcenſurum quam per ma-
gis inclinatam.

Velut ſi ſint duæ ſuperficies inclinatæ ſecundum curvas
22TAB. IX.
Fig. 2. A B, C D, æqualis altitudinis, quarumque in punctis æ-
que altis quibuslibet E, F, major ſit inclinatio ipſius C D
quam A B, hoc eſt, ut recta tangens curvam C D in F,
magis inclinata ſit ad horizontem, quam quæ curvam A B
tangit in puncto E. erit tempus deſcenſus per A B brevius
quam per C D.

Idemque continget ſi altera linearum recta fuerit: dum-
modo inclinatio rectæ, quæ ubique eſt eadem, major mi-
norve fuerit inclinatione curvæ in quolibet ſui puncto.

PROPOSITIO XXII.

SI in Cycloide cujus axis ad perpendiculum erectus
ſtat, vertice deorſum ſpectante, duæ portiones
curvæ æqualis altitudinis accipiantur, ſed quarum
altera propior ſit vertici; erit tempus deſcenſus
per ſuperiorem, brevius tempore per inferiorem.

Sit Cyclois A B, cujus axis A C ad perpendiculum ere-
33TAB. IX.
Fig. 3. ctus, vertex A deorſum ſpectet; & accipiantur in ea

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