Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 82r
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.82.
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The machine reads it as
- videamus in alia hypothesi evitari possit aequatio cubica
- rev) sadi az
- et saa 3: dZ = dZ+ d0, daZ: (dez ut ddv) 4Z. Ergo d de = (adZ + ddv) dZ: dd Z
- et fic KC y: a seu do: de = de ddz, d Z (ddZ + dd V), sed il rursus ascenditur
- ad cubum
- ad mbum de ssa (Sit tZ+9dv +
- y: a = de: dv.. dy - ddv de: dodo, et
- dy. dx = dx = ddz de: dZ dZ et dy: dx = ddv Azcz. dd Z dudv. sit
- de X:a = de: dz
- jam de = dz F dv,: sdaz: dZ fiet . adZ Lad z v. d + (daz+ ddv adq: d2
- seu t d seu +Z daZe + doc ddZ (daz + ddv) dz 5 ddz: dz = 0
- seu dz + dv 3: Sdaz: dZ = 1. A. 1F dz (daz+ ddv): ddz = de
- sit sit jam data arquatio viqua diaa dy. du Em. Y: a (l3 + ddv) aZ: av ddz,
- st jam data aequatio.
- gy +XX,:aa = dy: fiet A qu (dd Z +ddV) d2dZ: dndo adzue ddZ
- et X: a = (d dZ + ddv) : ddz
- + qu (daz + ddv: dazddZ = ddv : ddZ P
- ut
- adeogue fiet
- seu fiet
- daque ll2 d3d2 + dd2 dez Ldx deque ddZ dZ dZ, t dd dd3 dvdv. + 2 ddze dod dZ
- av av ddZ dav = ddv ddo dudm + dao dd dzdZ +(2 izddo Lodv
- vel sic qu (ddx +1Y, (dZa Z + dvdv), Davdx = adv: ddZ compendu causa
- d242 + dvdo: duxv vocetur m, et ddv: daz vocetur n, et fiet, quln+ 1) n = n
- seu (nn + in +1) m = n seu nn + +(2- )n + (-a + m) = 2 ( ) - 1
- sit n =. 2(2 = m) + (4 (+-+
- 1) et n atque n explicando fiet
- ddvii ddz= 2 d 2d a dedo + ((e du 21 e d
- seu dax
- da
- 2(AX + ded.
- A d f do)- 4 avdxdidz. 4dv dv 7)
- 4dododzd 4do
- 24743 Iut d Zaq - 3d vde
- HL 2n - 1 + Saum -am +1= amm
- (m inm)
- =(4m + 1
- m
- 2m - 1 + S( - 4m),: 2m, sed e cum hoc loco
- n
- 2
- seu
- sit n major quam 1, oritur absurdum nam m = 1 + (dZdz: dudv)
- hoc tamen non obstante pergemus in calculo, nam hoc absurdum calcu non impedit
- seu n =
- analysin, etsi impediat constructionem explicando ergo fiet:
- adv: dazue = 2dZ dZ + 2, dodv= dvdv, + Y (-4dd dZ - 3 lvdv, . 3d vdo + 2d Zd3
- et i jam d0. dZ sit = g d 4. a et du , de = 8 r: a
- et dez: dz = dr: Y, fiet jam sit du; de = co: a
- et dz: de =4t: a
- fiet de dZ dco: dt = 2lt + coco + Y - (4+t +3c010), : 2(c0co + tt)
- sit co: t = q. a fiet ex theorematea noto at: t = (d9: a) (dco : dt) - (9: a)
- jam deo: de habetur per hicper q:a, nam fit deo: dt = 2aa + 99 + f - (42a +349): raatqqu
- a3+ 2 aG
- 29
- Itaque in hypotresi vulorit ipsius de scubamus de -5AZ+ do: Sadz. dz, fiet dead +
- 2a + a99 + a Y- 444-399) = 2aa9
- .
- at
- dq
- 0 (daZ: dZ) (dD +d) + (A + sdF(TddZ + CddV) (dd3: dZ et fiat dZ + Fdv,: sadz: d
- a
- pt
- seute, seu de =(+d) Sda Z + aav. Ia Z: da Z Ergo y: c = ddZ + Aido, dZ:, dudaz
- et X: a = FddZ + Ad,: adque et qua a jam quid y. a erat = de: d et x1a = de: d2
- =a de ddz: d2dz. unde fie
- dyax= s r. ddvd ZdZ: daque duav unde ex aeque xx + ryg: aq = dy. dx, fiet
- en
- fit u - adav: dvdo et di =at
- qui aque + adv): dezZ) et Z a2 (Ava d = (adv: ddz) (d2 d2): dudi,
- .. dvdv (v dv) d2 d Z8: Ax aZ
- et fiet
- dudvo dedoidzaZ vocetur n
- qu (f+ ) = ma seu nn + 2fD + ff = m et nn + 4 (25 -mIn + (f- 4fmtmm)=
- a (45) atm +mm 4Fiq et n = e -2F+m + I(um -4fm), : 2,
- sit = -1 nulla potest evenire impossibilitas
- Av:daque vocetur compendio, n, et
- sit ergo ddv: dazue = f 2+433 L 2f avav + dodo + do X (dvd - 4f 42a Z- +f Av av) CH. (tv
- tidide
- ubo f est numirus arbitrarius, et, si
- Hinc si Sponatur = - 1: E fist dar: daz = dZ dz + 2 dodv + do +(3 dodo + 2 d3 dz.), 5, 2d∞10
- He jam calulus tatis est ut plane perductus sit ad quadraturas ratianales, itaque poterit elaborari e
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 82r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0163?run=74