Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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[141] Fig. 22.* 19. Maii.
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[143] Fig. 24.* c a * 27. Maii.
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[144] Fig. 25.c * 31. Maii. a *
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[146] Fig. 27.* 16. Ian. 1656.
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[147] Fig. 28.* 19. Febr.
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[149] Fig. 30.* 30. Mart.
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[150] Fig. 31.* 18. Apr.
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[152] Fig. 33.* 19. Oct.
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[154] Fig. 35.* 9. Nov.
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[155] Fig. 36.* 27. Nov.
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[156] Fig. 37.* 16. Dec.
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[157] Fig. 38.* 18. Ian. 1657.
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[161] Fig. 42.* 19. Maii.
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[162] Fig. 43.* 17. Dec.
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[163] Fig. 44.* 18. Dec.
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[164] Fig. 45.* 27. Dec.
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[165] Fig. 46.* 11. Mart 1658.
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[169] Fig. 50.* 10. Nov.
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[170] Fig. 51.* 16. Ian. 1659.
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239506CHRIST. HUGENII ſive etiam - 3y3 + ayx eſſe affirmatam, ac proinde 3y3 - ayx
eſſe negatam: aut quando 3xx - ay fuerit affirmata, tunc
- 3y3 + ayx eſſe negatam; ac proinde 3y3 - ayx eſſe affir-
matam. Per hæc itaque apparet ex quantitatibus per regulam in-
ventis, quæ erant {3y3 - ayx/3xx - ay} = z judiciari poſſe ad utrum ca-
ſum conſtructio tangentis pertineat; nempe excomperta diſſi-
militudine affectionis in diviſore & dividendo, ſequi ad prio-
rem caſum eam pertinere, hoc eſt z, ſive F E, accipiendam
eſſe verſus A: ex ſimilitudine vero eorum affectionis ſequi ad
contrariam partem ſumendam.
11TAB. XLV.
fig. 6.
Poteſt autem quantitas z ſive FE per regulam inventa, non-
nunquam ad ſimpliciores terminos reduci ope æquationis datæ,
quæ naturam curvæ continet: velut in hac curva A C, axem
habente A D, verticem A, cujuſque ea eſt proprietas ut, ſi à
puncto C in eâ ſumpta, applicetur ordinatim C D, fiat pro-
ductum ex cubo B D (eſt autem B punctum in axe extra cur-
vam datam) in quadratum D A æquale cubo quadrato DC. Si-
ve ponendo B A = a, B D = x, D C = y, fiat æquatio cur-
væ naturam continens, iſta x5 - 2ax4 + aax3 - y5 = o. Hîc
ponendo CG eſſe tangentem, quæ occurrat axi in G, vocan-
doque GD, z, fit ſecundum regulam z = {- 5y5/5x4 - 8ax3 + 3aaxx}.
Quia autem ex datâ æquatione eſt y5 = x5 - 2ax4 + aax3, re-
ſtituendo pro 5y id quod ipſi æquale eſt, fiet z =
{- 5x5 + 10ax4 - 5aax3/5x4 - 8ax3 + 3aaxx}; ſive dividendo per xx, erit z =
{- 5x3 + 10axx - 5aax/5xx - 8ax + 3aa,}. Et rurſus, dividendo hanc fractionem
per x - a, habebitur z = {-5xx + 5ax/5x - 3a}. Quod ſignificat
faciendum ut ſicut B D quinquies ſumpta minus B A ter, ſive
ut B A bis unà cum A D quinquies ad AD quinquies, ita BD
ad D G; atque ita G C tacturam in C curvam A C.

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