Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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tem M K ad M K + 3 K S, ita M B ad M B + 3 B Z:
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<
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<
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<
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erit proinde M B ad M D ut M B ad M B + 3 B Z. </
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<
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xml:space
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">Un-
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de liquet M D æqualem ſumendam ipſi M B + 3 B Z. </
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<
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xml:space
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">At-
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que ita quotlibet puncta curvæ C D E invenire licebit. </
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<
s
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xml:space
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">Cu-
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jus curvæ portio quælibet ut D S, rectæ D B, quæ para-
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boloidi S A B ad angulos rectos occurrit, æqualis erit.
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</
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<
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">Conſtat autem geometricam eſſe, & </
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<
s
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">ſi velimus, poſſumus
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æquatione aliqua relationem exprimere punctorum omnium
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ipſius ad puncta axis S K.</
s
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<
s
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xml:space
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">Simili modo autem, ſi inquiramus in paraboloide illa ſive
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">TAB. XVII.
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Fig. 1.</
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parabola cubica, in qua cubi ordinatim applicatarum ad
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axem, ſunt inter ſe ſicut portiones axis abſciſſæ, inveniemus
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curvam cujus evolutione deſcribitur, quæque proinde rectæ
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lineæ æquari poterit, nihilo difficiliori conſtructione per pun-
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cta determinari. </
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<
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">Nam ſi fuerit illa S A B; </
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<
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">axis S M; </
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<
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">(di-
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citur autem improprie axis in hac curva, cum forma ejus ſit
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ejusmodi, ut ductâ S Z, quæ ſecet S M ad angulos rectos,
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ea portiones ſimiles curvæ habeat ad partes oppoſitas;) </
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<
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rur per punctum quodlibet B, in paraboloide ſumptum, re-
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cta B D, quæ curvam ad angulos rectos ſecet, axique ejus
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occurrat in M, rectæ vero S Z in Z. </
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<
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xml:space
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">Deinde ſumatur B D
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æqualis dimidiæ B M, unà cum ſesquialtera B Z. </
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<
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D unum è punctis curvæ quæſitæ R D vel R I, cujus evo-
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lutione, juncta tamen recta quadam R A, deſcribetur para-
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boloides S A B. </
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<
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xml:space
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">Sunt autem hic, quod notatu dignum eſt,
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quodque in aliis etiam nonnullis harum paraboloidum con-
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tingit, duæ evolutiones in partes contrarias, quarum utra-
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que à puncto certo A initium capit; </
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<
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">ita ut evolutione ipſius
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A R D, in infinitum porro continuatæ, deſcribatur para-
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boloidis pars infinita A B F; </
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<
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xml:space
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">evolutione autem totius A R I,
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ſimiliter in infinitum extenſæ, tantum particula A S. </
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<
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ctum autem A definitur, ſumptâ S P quæ ſit ad latus re-
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ctum paraboloidis, ſicut unitas ad radicem quadrato-qua-
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draticam numeri 91125, (is cubus eſt ex 45) applicatâque
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ordinatim P A. </
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">Unde porro punctum R, confinium dua-
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rum curvarum R D, R I, invenitur ſicut cætera omnia </
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