Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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<
s
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xml:space
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">Itaque tempus aliquod brevius tempore per B E (ſit hoc
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<
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tempus Z) erit ad dictum tempus per B I ut arcus F H ad
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rectam F G. </
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<
s
xml:id
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echoid-s1813
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xml:space
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">Quod ſi jam in Cycloide ſupra punctum B ſu-
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matur punctum aliud N, erit tempus per B E poſt N B,
<
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brevius tempore per B E. </
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>
<
s
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echoid-s1814
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xml:space
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">Manifeſtum eſt autem punctum N
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tam propinquum ſumi poſſe ipſi B, ut differentia eorum
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temporum ſit quamlibet exigua, ac proinde ut minor ſit
<
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ea qua tempus Z ſuperatur à tempore per B E. </
s
>
<
s
xml:id
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echoid-s1815
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xml:space
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">Sit ita-
<
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que punctum N ita ſumptum. </
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<
s
xml:id
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echoid-s1816
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xml:space
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">unde quidem tempus per
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B E poſt N B majus erit tempore Z, majoremque pro-
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inde rationem habebit ad tempus dictum per B I cum di-
<
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midia celeritate ex B Θ, quam arcus F H ad rectam
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F G. </
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>
<
s
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"
xml:space
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">Habeat itaque eam quam arcus F H O ad rectam
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F G.</
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>
<
s
xml:id
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xml:space
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"/>
</
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>
<
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<
s
xml:id
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echoid-s1819
"
xml:space
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">Dividatur F G in partes æquales F P, P Q, &</
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<
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echoid-s1820
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">c. </
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<
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xml:space
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">qua-
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rum unaquæque minor ſit altitudine lineæ N B, atque item
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altitudine arcus H O; </
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>
<
s
xml:id
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echoid-s1822
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xml:space
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">hoc enim fieri poſſe manifeſtum eſt;
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</
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<
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xml:space
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">& </
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>
<
s
xml:id
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xml:space
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">à punctis diviſionum agantur rectæ, baſi D C parallelæ,
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& </
s
>
<
s
xml:id
="
echoid-s1825
"
xml:space
="
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">ad tangentem B Θ terminatæ P Λ, Q Ξ, &</
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>
<
s
xml:id
="
echoid-s1826
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xml:space
="
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">c. </
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<
s
xml:id
="
echoid-s1827
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xml:space
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">Quibus-
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que in punctis hæ ſecant circumferentiam F H, ab iis,
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itemque à puncto H, tangentes ſurſum ducantur usque
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ad proximam quæque parallelam, velut Δ Χ, Γ Σ &</
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>
<
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echoid-s1828
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">c. </
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<
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">Si-
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militer vero & </
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<
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echoid-s1830
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xml:space
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">à punctis, in quibus dictæ parallelæ Cy-
<
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cloidi occurrunt, tangentes ſurſum ducantur velut S V,
<
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T M &</
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<
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xml:space
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">c. </
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<
s
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xml:space
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">additâ vero ad rectam F G parte una G R æ-
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/>
quali iis quæ ex diviſione, ductaque R Φ parallelâ ſimi-
<
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liter ipſi D C, patet eam occurrere circumferentiæ F H A
<
lb
/>
inter H & </
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>
<
s
xml:id
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echoid-s1833
"
xml:space
="
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">O, quia G R minor eſt altitudine puncti H ſupra
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O. </
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>
<
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xml:space
="
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">Jam vero ſic porro argumentabimur.</
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>
<
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</
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<
s
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xml:space
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">Tempus per tangentem V S cum celeritate æquabili quæ
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acquireretur ex B S, majus eſt tempore motus continue ac-
<
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celerati per arcum B S poſt N B. </
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>
<
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xml:space
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preserve
">Nam celeritas ex B S mi-
<
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nor eſt celeritate ex N B, propterea quod minor altitudo
<
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B S quam N B. </
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>
<
s
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="
echoid-s1838
"
xml:space
="
preserve
">At celeritas ex B S æquabiliter continuari
<
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ponitur per tangentem V S, cum celeritas acquiſita ex N B
<
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/>
continue porro acceleretur per arcum B S, qui arcus </
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