Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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tiones B D & </
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xml:space
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">E F, æqualis altitudinis, hoc eſt, ejusmodi
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<
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.</
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ut parallelæ horizontales B C, D H, quæ ſuperiorem por-
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tionem B D includunt, æque inter ſe diſtent ac E G,
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F K, inferiorem partionem E F includentes. </
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<
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xml:space
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deſcenſus per curvam B D brevius fore tempore per E F.</
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<
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</
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<
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<
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xml:space
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">Sumatur enim in B D punctum quodlibet L, & </
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>
<
s
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xml:space
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">in E F
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punctum M, ita ut eadem ſit altitudo E ſupra M quæ B
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ſupra L. </
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<
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xml:space
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">Et deſcripto ſuper axe A C ſemicirculo, occurrant
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ei rectæ horizontales L N, M O, in N & </
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<
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xml:space
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<
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xml:space
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">jungan-
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tur N A, O A. </
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<
s
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xml:space
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">Itaque quum punctum N ſit altius puncto
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O, manifeſtum eſt rectam N A minus ad horizontem incli-
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nari quam O A. </
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<
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xml:space
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">Eſt autem ipſi N A parallela tangens curvæ
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in L puncto , & </
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<
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xml:space
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">ipſi O A parallela tangens curvæ in M.</
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xml:space
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">Prop. 15.
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huj.</
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Ergo curva B D in puncto L minus inclinata eſt quam curva
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E F in puncto M. </
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>
<
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xml:space
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">Quod ſi igitur portio E F, invariata in-
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clinatione, altius extolli intelligatur velut in e f, ita ut in-
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ter eaſdem parallelas cum portione B D comprehendatur,
<
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invenietur punctum M in m, æquali altitudine cum puncto
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L. </
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>
<
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xml:space
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">eritque etiam inclinatio curvæ e f in puncto m, quæ ea-
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dem eſt inclinationi curvæ E F in M, major inclinatione
<
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curvæ B D in L. </
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<
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xml:space
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">Similiter vero, & </
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xml:space
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">in quolibet alio puncto
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curvæ e f, major oſtendetur inclinatio quam curv æ B D
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in puncto æque alto. </
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>
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xml:space
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">Itaque tempus deſcenſus per B D bre-
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vius erit tempore per e f, ſive, quod idem eſt, per E F.</
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>
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<
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position
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xlink:label
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xlink:href
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xml:space
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">Prop.
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præced.</
note
>
quod erat demonſtrandum.</
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<
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xml:space
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">ESto circulus diametro A C, quem ſecet ad an-
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">TAB. IX.
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Fig. 4.</
note
>
gulos rectos D E, & </
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xml:space
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">à termino diametri A e-
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ducta recta A B occurrat circumferentiæ in B, ipſi
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vero D E in F. </
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xml:space
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proportionales eſſe.</
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</
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<
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<
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xml:space
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">& </
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<
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xml:space
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">arcui B D
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recta ſubtenſa ducatur. </
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