Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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major erit ratio K B ad B N quam E F ad F G. </
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<
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<
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<
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<
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major eſt quam K B, quoniam angulus K in triangulo A K B
<
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eſt obtuſus, eſt enim major angulo H E F qui eſt obtuſus
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ex conſtructione. </
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<
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xml:space
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">Ergo ratio A B ad B N major erit ratio-
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ne K B ad B N, ac proinde omnino major ratione E F ad
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F G. </
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<
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">Eodem modo & </
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<
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">ratio B C ad C O, & </
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major oſtendetur ratione E F ad F G. </
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<
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xml:space
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">Itaque conſtat pro-
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poſitum.</
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<
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xml:space
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">PROPOSITIO III.</
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<
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">DUæ curvæ in unam partem inflexæ & </
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<
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xml:space
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">in eas-
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dem partes cavæ ex eodem puncto egredi ne-
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queunt, ita ad ſe invicem comparatæ, ut recta
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omnis quæ alteri earum ad angulos rectos occurrit,
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ſimiliter occurrat & </
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<
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">reliquæ.</
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<
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<
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<
s
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">Sint enim, ſi fieri poteſt, hujuſmodi lineæ curvæ A C E,
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Fig. 3.</
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A G K, communem terminum habentes A, & </
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teriore illarum puncto quolibet K, ſit inde educta K E recta,
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curvæ A G K occurrens ad angulos rectos, ac proinde
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etiam curvæ A C E.</
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<
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">Poteſt jam recta quædam ſumi major curva K G A, quæ
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ſit Q. </
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<
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xml:space
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">Diviſa autem intelligatur ipſa K G A, ut in propo-
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ſitione antecedenti dictum fuit, in tot partes punctis H G F,
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ut ſubtenſæ ſingulæ K H, H G, G F, F A, ad perpen-
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diculares curvæ ſibi contiguas H M, G N, F O, A P
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majorem rationem habeant quam linea Q ad rectam K E.
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</
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<
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">omnes ſimul dictæ ſubtenſæ ad omnes dictas per-
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pendiculares majorem habebunt rationem quam Q ad K E. </
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Producantur autem perpendiculares eædem & </
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væ A C E in D, C, B, nimirum ad angulos rectos ex
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hypotheſi. </
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">Etenim, ducta
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E L ipſi K E perpendiculari, quoniam K E occurrit lineæ
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curvæ E C A ad angulos rectos, tanget E L curvam A C E,
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occurretque neceſſario rectæ M D inter D & </
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