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

Table of figures

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[171] Fig. 52.12. Febr. *
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[172] Fig. 53.* 24. Febr.
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[173] Fig. 54.25. Febr. *
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[174] Fig. 55.14. Mart. *
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[175] Fig. 56.16. Mart. *
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[176] Fig. 57.* 21. Mart.
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[177] Fig. 58.* 22. Mart.
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[178] Fig. 59.26. Mart. *
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[179] Pag. 574.TAB. XLIX.Fig. 2.
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[180] Fig. 1.C K O B H N G M S * F D A L E
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[181] Fig. 3.E C D A * B
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[182] Fig. 4.P Q O N M L * C R
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[183] Fig. 5.C * V S X T Y
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[184] Fig. 6.
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[185] Fig. 7.
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[186] Pag. 580.TAB. L.Fig. 2.R ♈ L D I T A N ♋ H G E P F K C Q O B M S
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[187] Fig. 3.
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[188] Fig. 4.N Q F C P L E A M H O D f
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[189] Fig. 1.B A
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[Figure 190]
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[Figure 191]
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[192] Pag. 626.TAB. LI.Fig. 1.F E D V S 30 20 10 C L G R H K P A M Z I O X B
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[193] Fig. 2.L K O R E H N I S D G B C
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[194] Fig. 3.A 16 15 14 13 12 11 10 9 B 8 7 6 5 4 3 2 1
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[195] Fig. 4
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[196] Fig. 5.
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[197] Fig. 6.
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[198] Fig. 1.
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[199] Fig. 2.
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[200] Fig. 3.
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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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