Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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A B, brevius eſſe tempore per G H poſt N G ſive poſt F G.</
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<
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.</
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">Similiter oſtendetur, productis D C, K H ſurſum, do-
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nec occurrant horizontali A F in O & </
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<
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xml:space
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">P, tempus per
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C D poſt A B C, ſive poſt O C, brevius eſſe tempore per
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H K poſt F G H ſive poſt P H. </
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<
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">Ac denique tempus per
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D E poſt A B C D, brevius eſſe tempore per K L poſt
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F G H K. </
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<
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">Quare totum tempus deſcenſus per A B C D E,
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brevius erit tempore per F G H K L. </
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<
s
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">quod erat demon-
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ſtrandum.</
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<
s
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">Hinc vero manifeſtum eſt, conſiderando curvas lineas
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tanquam ex innumeris rectis compoſitas, ſi fuerint duæ ſu-
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perficies, ſecundum lineas curvas ejusdem altitudinis incli-
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natæ, quarum in punctis quibuslibet æque altis major ſem-
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per ſit inclinatio unius quam reliquæ, etiam tempore bre-
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viori per minus inclinatam grave deſcenſurum quam per ma-
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gis inclinatam.</
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<
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">Velut ſi ſint duæ ſuperficies inclinatæ ſecundum curvas
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">TAB. IX.
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Fig. 2.</
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A B, C D, æqualis altitudinis, quarumque in punctis æ-
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que altis quibuslibet E, F, major ſit inclinatio ipſius C D
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quam A B, hoc eſt, ut recta tangens curvam C D in F,
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magis inclinata ſit ad horizontem, quam quæ curvam A B
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tangit in puncto E. </
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<
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">erit tempus deſcenſus per A B brevius
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quam per C D.</
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</
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modo inclinatio rectæ, quæ ubique eſt eadem, major mi-
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norve fuerit inclinatione curvæ in quolibet ſui puncto.</
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<
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<
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">SI in Cycloide cujus axis ad perpendiculum erectus
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ſtat, vertice deorſum ſpectante, duæ portiones
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curvæ æqualis altitudinis accipiantur, ſed quarum
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altera propior ſit vertici; </
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<
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">erit tempus deſcenſus
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per ſuperiorem, brevius tempore per inferiorem.</
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<
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">Sit Cyclois A B, cujus axis A C ad perpendiculum ere-
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<
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">TAB. IX.
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Fig. 3.</
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ctus, vertex A deorſum ſpectet; </
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