Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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131 - 140
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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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<
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">CLOIDE</
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>
.</
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<
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="
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">
<
s
xml:id
="
echoid-s1938
"
xml:space
="
preserve
">IN Cycloide cujus axis ad perpendiculum erectus
<
lb
/>
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; </
s
>
<
s
xml:id
="
echoid-s1939
"
xml:space
="
preserve
">habentque ad tempus caſus perpen-
<
lb
/>
dicularis per totum axem cycloidis eam rationem,
<
lb
/>
quam ſemicircumferentia circuli ad diametrum.</
s
>
<
s
xml:id
="
echoid-s1940
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1941
"
xml:space
="
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">Eſto cyclois A B C cujus vertex A deorſum ſpectet, axis
<
lb
/>
<
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xlink:label
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note-0131-02
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xlink:href
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xml:space
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">TAB. XI.
<
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Fig. 1.</
note
>
vero A D ad perpendiculum erectus ſit, & </
s
>
<
s
xml:id
="
echoid-s1942
"
xml:space
="
preserve
">à puncto quovis
<
lb
/>
in cycloide ſumpto, velut B; </
s
>
<
s
xml:id
="
echoid-s1943
"
xml:space
="
preserve
">deſcendat mobile impetu na-
<
lb
/>
turali per arcum B A, ſive per ſuperficiem ita inflexam. </
s
>
<
s
xml:id
="
echoid-s1944
"
xml:space
="
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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. </
s
>
<
s
xml:id
="
echoid-s1945
"
xml:space
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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-
<
lb
/>
bit.</
s
>
<
s
xml:id
="
echoid-s1946
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1947
"
xml:space
="
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">Deſcribatur ſuper axe D A ſemicirculus, cujus circumfe-
<
lb
/>
rentiam ſecet recta B F, baſi D C parallela, in E; </
s
>
<
s
xml:id
="
echoid-s1948
"
xml:space
="
preserve
">junctâ-
<
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/>
que E A, ducatur ei parallela B G, quæ quidem cycloidem
<
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/>
tanget in B. </
s
>
<
s
xml:id
="
echoid-s1949
"
xml:space
="
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">Eadem vero occurrat rectæ horizontali per A
<
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ductæ in G: </
s
>
<
s
xml:id
="
echoid-s1950
"
xml:space
="
preserve
">ſitque etiam ſuper F A deſcriptus ſemicirculus
<
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/>
F H A.</
s
>
<
s
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="
echoid-s1951
"
xml:space
="
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"/>
</
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<
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>
<
s
xml:id
="
echoid-s1952
"
xml:space
="
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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
<
lb
/>
F H A ad rectam F A. </
s
>
<
s
xml:id
="
echoid-s1953
"
xml:space
="
preserve
">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 & </
s
>
<
s
xml:id
="
echoid-s1954
"
xml:space
="
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">
<
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/>
æqualis, hoc eſt, tempori deſcenſus accelerati per axem
<
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/>
D A. </
s
>
<
s
xml:id
="
echoid-s1955
"
xml:space
="
preserve
">Itaque tempus per arcum B A, erit quoque ad
<
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="
*
"
position
="
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"
xlink:label
="
note-0131-03
"
xlink:href
="
note-0131-03a
"
xml:space
="
preserve
">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. </
s
>
<
s
xml:id
="
echoid-s1956
"
xml:space
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">quod erat demonſtrandum.</
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>
<
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="
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