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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 82r, page id 00068198:0163
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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