Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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Table of Notes
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HOROLOG. OSCILLATOR.
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<
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xml:space
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">PROPOSITIO XXV.</
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<
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.</
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<
s
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echoid-s1938
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xml:space
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">IN Cycloide cujus axis ad perpendiculum erectus
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eſt, vertice deorſum ſpectante, tempora deſcen-
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ſus quibus mobile, à quocunque in ea puncto dimis-
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ſum, ad punctum imum verticis pervenit, ſunt in-
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ter ſe æqualia; </
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<
s
xml:id
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echoid-s1939
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xml:space
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preserve
">habentque ad tempus caſus perpen-
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dicularis per totum axem cycloidis eam rationem,
<
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quam ſemicircumferentia circuli ad diametrum.</
s
>
<
s
xml:id
="
echoid-s1940
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</
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<
s
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echoid-s1941
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">Eſto cyclois A B C cujus vertex A deorſum ſpectet, axis
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Fig. 1.</
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vero A D ad perpendiculum erectus ſit, & </
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">à puncto quovis
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in cycloide ſumpto, velut B; </
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<
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">deſcendat mobile impetu na-
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turali per arcum B A, ſive per ſuperficiem ita inflexam. </
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<
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echoid-s1944
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">Di-
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co tempus deſcenſus hujus eſſe ad tempus caſus per axem
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D A, ſicut ſemicircumferentia circuli ad diametrum. </
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>
<
s
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echoid-s1945
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">Quo
<
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demonſtrato, etiam tempora deſcenſus, per quoslibet cy-
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cloidis arcus ad A terminatos, inter ſe æqualia eſſe conſta-
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bit.</
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<
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="
echoid-s1946
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</
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<
s
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">Deſcribatur ſuper axe D A ſemicirculus, cujus circumfe-
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rentiam ſecet recta B F, baſi D C parallela, in E; </
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<
s
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="
echoid-s1948
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">junctâ-
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que E A, ducatur ei parallela B G, quæ quidem cycloidem
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tanget in B. </
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<
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echoid-s1949
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">Eadem vero occurrat rectæ horizontali per A
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ductæ in G: </
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<
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">ſitque etiam ſuper F A deſcriptus ſemicirculus
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F H A.</
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<
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<
s
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="
echoid-s1952
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">Eſt igitur, per præcedentem, tempus deſcenſus per ar-
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cum cycloidis B A, ad tempus motus æquabilis per rectam
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B G cum celeritate dimidia ex B G, ſicut arcus ſemicirculi
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F H A ad rectam F A. </
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<
s
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="
echoid-s1953
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xml:space
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">Tempus vero dicti motus æquabilis
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per B G, æquatur tempori deſcenſus naturaliter accelerati
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per eandem B G, ſive per E A, quæ ipſi parallela eſt & </
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<
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="
echoid-s1954
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æqualis, hoc eſt, tempori deſcenſus accelerati per axem
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D A. </
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<
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="
echoid-s1955
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xml:space
="
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">Itaque tempus per arcum B A, erit quoque ad
<
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="
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xlink:href
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">Prop. 6.
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Galil. de
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motu Accel.</
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pus deſcenſus per axem D A, ut ſemicirculi circumferentia
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F H A ad diametrum F A. </
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<
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echoid-s1956
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">quod erat demonſtrandum.</
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