Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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que arcus percurri, ac proinde pendulum F G, pendulo
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<
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<
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compoſito ex A, B, C, iſochronum eſſe. </
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<
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tem hoc modo.</
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<
s
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">Sit primo, ſi poteſt, major celeritas puncti L, ubi in P
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pervenit, quam ponderis G in O. </
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<
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echoid-s2938
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xml:space
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">Conſtatautem, dum pun-
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ctum L percurrit arcum L P, ſimul centrum gravitatis E
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percurrere arcum ſimilem E Q. </
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<
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echoid-s2939
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xml:space
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">Ducantur à punctis Q, P, O,
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perpendiculares ſurſum, quæ occurrant ſubtenſis arcuum
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E I, L N, G M, in R, S, Y. </
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<
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">& </
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<
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">Unde,
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cum ſit ut L D, x, ad E D, d, ita S P, y, ad R Q; </
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<
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xml:space
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">erit
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R Q æqualis {d y/x}. </
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<
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xml:space
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">Jam quia pondus G eam celeritatem ha-
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bet in O, qua valet ad eandem unde deſcendit altitudinem
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aſcendere, nempe per arcum O M, vel perpendicularem
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O Y ipſi P S æqualem; </
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<
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xml:space
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">punctum igitur L, ubi in P per-
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venerit, majorem ibi celeritatem habebit, quam qua aſcen-
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ditur ad altitudinem P S. </
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<
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xml:space
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">Dum vero L tranſit in P, ſimul
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pondera A, B, C, ſimiles arcus percurrunt ipſi L P, nimirum
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A T, B V, C X. </
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<
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xml:space
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">Eſtque puncti L celeritas in P, ad celeri-
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tatem ponderis A in T, quum vinculo eodem contineantur,
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ſicut diſtantia D L ad D A. </
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<
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">Sed ut quadratum celeritatis
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puncti L, quam habet in P, ad quadratum celeritatis pun-
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cti A in T, ita eſt altitudo ad quam illa celeritate
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aſcendi poteſt, ad altitudinem quò hac celeritate aſcendi
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poteſt . </
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<
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">Ergo etiam, ut quadratum diſtantiæ D L,
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">Prop. 3.
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& 4. part. @.</
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eſt x x, ad quadratum diſtantiæ D A, quod eſt e e, ita eſt
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altitudo quo aſcenditur celeritate puncti L, quum eſt in P,
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(quæ altitudo major dicta eſt quam P S ſive y,) ad altitu-
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dinem quo aſcenditur celeritate ponderis A in T; </
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<
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">ſi nempe
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poſtquam in T pervenit, relicto pendulo, ſeorſim motum
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ſuum ſurſum converteret. </
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<
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">Quæ proinde altitudo major erit
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quam {e e y/x x}.</
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<
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">Eadem ratione, erit altitudo ad quam aſcenderet pondus
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B, celeritate acquiſita per arcum B V, major quam {f f y/x x}. </
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<
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">Et
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altitudo ad quam aſcenderet pondus C, celeritate acquiſita
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per arcum C X, major quam {g g y/x x}. </
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<
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