Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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penitiùs quam cyclois cognita ſit. </
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xml:space
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.</
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qua in hac metienda uſi ſumus, in aliis quoque experiri li-
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buit, de quibus porro nunc agemus.</
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<
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tendere.</
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</
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<
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<
s
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xml:space
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">Sit paraboloides A B, cujus axis A D; </
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">vertex A; </
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<
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">TAB. XIII,
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Fig. 1.</
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prietas autem iſta, ut ordinatim ad axem applicatâ B D,
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cubus abſciſſæ ad verticem D A æquetur ſolido, baſin ha-
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benti quadratum D B, altitudinem vero æqualem lineæ cui-
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dam datæ M; </
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<
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">quæ quidem curva pridem geometris nota
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fuit; </
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<
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xml:space
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">& </
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<
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">ponatur axi D E juncta in directum A E, quæ ha-
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beat {8/27} ipſius M. </
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<
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xml:space
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">Jam ſi filum continuum circa E A B ap-
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plicetur, idque ab E evolvi incipiat, dico deſcriptam ex
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evolutione eſſe parabolam E F, cujus axis E A G, vertex
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E, latus rectum æquale duplæ E A.</
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<
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<
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">Sumpto enim in curva A B puncto quolibet B, ducatur
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quæ in ipſo tangat curvam recta B G, occurrens axi E A
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in G. </
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">ex G ducatur porro G F, quæ ad rectos angulos
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occurrat parabolæ E F in F; </
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xml:space
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ris F H, quæ parabolam in F continget; </
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<
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ordinatim ad axem E G applicetur.</
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<
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">Eſt igitur K G æqualis dimidio lateri recto, hoc eſt, ipſi
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E A; </
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<
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E K æqualis A G. </
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<
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niam B G tangit paraboloidem in B: </
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<
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curvæ hujus facile demonſtrari poteſt. </
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eſt trienti A D: </
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<
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">K H, quæ ex natura parabolæ dupla eſt
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K E, æquabitur duabus tertiis A D. </
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æqualis eſt {8/27} cubi ex A D, hoc eſt, ſolido baſin habenti
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quadratum D B, altitudinem vero æqualem {8/27} M, hoc eſt,
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ipſi A E. </
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K H, ita erit K H longitudine ad A E, hoc eſt ad K G.
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