Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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etiam V A ad A Φ longitudine, ut F A ad A H. </
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xml:space
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<
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.</
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itaque M N ad O P, eadem erit quæ F A ad A H, hoc
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eſt, propter triangula ſimilia F A H, F H Σ, eadem quæ
<
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F H ad H Σ, ut dictum fuit. </
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<
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xml:space
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">Itaque dicta ratio temporis
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per M N ad tempus per O P, componitur ex rationibus
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F X ad F H & </
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<
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xml:space
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">F H ad H Σ, ideoque eadem erit quæ
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F X ſive X H ad H Σ. </
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<
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xml:space
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">Sicut autem radius X H ad H Σ,
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ita eſt tangens S T ad rectam Q R; </
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<
s
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xml:space
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">hoc enim facile perſpi-
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citur. </
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<
s
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xml:space
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">Igitur tempus motus qualem diximus per M N, ad
<
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tempus per O P conſtat eſſe ſicut S T ad Q R. </
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<
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xml:space
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">quod erat
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demonſtrandum.</
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<
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Fig. I.</
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A B C, cujus vertex A deorſum ſpectet, axis
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A D ad borizontem erectus ſit; </
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<
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">ſumpto in ea
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quovis puncto B, ducatur inde deorſum recta B Θ
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quæ Cycloidem tangat, occurratque rectæ horizon-
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tali A Θ in Θ: </
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>
<
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">recta vero B F ad axem perpendi-
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cularis agatur, & </
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culus F H A. </
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<
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">Deinde alia recta G E, parallela
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F B, ſecet Cycloidem in E, rectam B Θ in I, cir-
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cumferentiam F H A in H, & </
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>
<
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in G.</
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<
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">Dico tempus deſcenſus per arcum Cycloidis B E,
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eſſe ad tempus per tangentem B I cum celeritate di-
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midia ex B Θ, ſicut arcus F H ad rectam F G.</
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<
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xml:space
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">Si enim hoc verum non eſt, habebit tempus per arcum
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B E ad dictum tempus per B I, vel majorem rationem quam
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arcus F H ad rectam F G vel minorem. </
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>
<
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fieri poteſt, majorem.</
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