Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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quarum unaquæque minor ſit arcus cycloidis B N altitudine,
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<
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<
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.</
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itemque minor altitudine arcus circumferentiæ F L; </
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">& </
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<
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ditâ ad F G unâ earum partium G ζ, ducantur à punctis di-
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viſionum rectæ baſi D C parallelæ, & </
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<
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xml:space
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">ad tangentem B Θ
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terminatæ, P O, Q K, &</
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<
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<
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xml:space
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">itemque à puncto ζ recta ζ Ω
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quæ ſecet cycloidem in V, circumferentiam in η; </
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<
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xml:space
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que in punctis ductæ parallelæ ſecant circumferentiam F H,
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ab iis tangentes deorſum ducantur usque ad proximam quæ-
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que parallelam, velut θ Δ, Γ Σ: </
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<
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xml:space
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Η ducta occurrat rectæ ζ Ω in X. </
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<
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xml:space
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<
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xml:space
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ctis, in quibus dictæ parallelæ occurrunt cycloidi, ducan-
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tur totidem tangentes deorſum, velut S Λ, T Ξ, &</
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<
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rum infima, tangens nempe à puncto E ducta, occurrat re-
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ctæ ζ Ω in R.</
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<
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<
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<
s
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">Quia igitur P ζ æqualis eſt F G altitudini arcus B E,
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cui æqualis eſt ex conſtructione altitudo arcus N M, erit & </
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P ζ æqualis altitudini arcus N M. </
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xml:space
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">Eſt autem recta P O ex
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conſtructione ſuperior termino N. </
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">in ea
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punctum V, ſuperius termino M. </
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<
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">Quare, cum arcus S V
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æqualis ſit altitudinis cum arcu N M, ſed termino S ſubli-
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miore quam N, erit tempus per S V brevius tempore per N M.</
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xml:space
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huj.</
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<
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">Atqui tempus per tangentem S Λ, cum celeritate æqua-
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bili ex B S, brevius eſt tempore deſcenſus accelerati per ar-
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cum S T, incipientis in S. </
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<
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">Nam celeritas ex B S, qua to-
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ta S Λ transmiſſa ponitur, æqualis eſt celeritati ex S T
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xml:space
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">Prop. 8.
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huj.</
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quæ motui per arcum S T in fine demum acquiritur; </
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<
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que S Λ minor eſt quam S T. </
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<
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xml:space
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">Similiter tempus per tangen-
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tem T Ξ, cum celeritate æquabili ex B T, brevius eſt tem-
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pore deſcenſus accelerati per arcum T Y poſt S T; </
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<
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xml:space
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">quum
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celeritas ex B T, qua tota T Ξ transmiſſa ponitur, ſit æqua-
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lis celeritati ex S Y, quæ in fine demum acquiritur motui
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dicto per arcum T Y poſt S T; </
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<
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">ipſaque T Ξ minor ſit arcu
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T Y. </
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<
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">Atque ita tempora omnia motuum æquabilium per
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tangentes cycloidis, cum celeritatibus per ſingulas quantæ
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acquiruntur deſcendendo ex B usque ad punctum ipſarum
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contactus, breviora ſimul erunt tempore deſcenſus </
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