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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 9r, page id 00068072:0017
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Quid si sic breviorit calculi causa
 Xia = s, dZadv - dodaz,: d bdZ
y: a = du: du dy: a = d7a d v - d vddq, : d2 q
et duyi= sed ita fieret dy. dx = dZ: dv, quod nonhies
An sic g: a = dv: dzue et d  X: a =sddz: dz. fit dy. ax = (l 3 llv - dvllz B,. Ax dy) : (217 24
ob . y: a sumtam = dv: di Z
sit  sit in aequ. data dy : dx = (X: a) = (V: a) et
ex 3 et g fiet (ddv: dd Z) = dv: dz = spad Z: dz) (= dv: d2 sit constans deo = (B) dZ dd y: da
seu dis dyndx 2) (dav: dd Ze) - dv: dZ
S6 fiet dZ: d = (D5 ddZ: dz et ddz: deo = d dZ: az seu dco = dZ et daz = dev
av = dZ (1 = B) Ergo ya foret constans ratio, quod absacue
sit ergo deo = ) dz dd v: dazue et ex set 6 fiet dc: dZ = 5dd Z: dque et deo ddz: de dz = ddz. de
et dZ = do + dco Ergo P  E.se ex
quod rursus absurdum. An ergo sic:
dco= d dz: dav, et exs fiet
 da vadv: adzue db
= dv: dz= d = das: dx quod est absurdum
et davddz  ddv : dco= ddZ 2d
Cdv + dZ) ddv: ddZ v F  S SdaZ: dZ = dutdzue: deo posito (dv + dZ) ddZ: ddv = dee
sed ita fieret dav: ddz
447: dZ = ddo = daZ,: deo. unde dd zidz = dd v + ddz, ddao: (v + d2) dazue seu fiet
dv: deo   fadzue: d
Ergo - dco,
et fit ddv: ddque = dv: d2
ddx, do + 4 = 4 + 1 +
hanc Methodum non procedere, quia scopus
daze ddiZ (dvtdZ) = ddvddo + lvdaz, aZ fiet it
D (( + 
est, ut ante pro quadrabura inveniatur ado: daZe per do: dZ,
ddo: ddz
sed hoc 
ergo calcu Methodus pugruae praecedentes quam hactenus
invento patet ex bb 1 et 3 habitum iri dy: Ax per y: a
sed video generaliter
seri da
apaeramus fantum exemplum tractatu commodum
et y. a L) 5ddZ. dZ fit dy: dx = du: de sit aequatio data
quae est ad sectionem sonicam in fine pagnae primae huus plagulae, nempe
Retinende est
dx: dy =14) 1y: dx = (4) t _ y: x - a:y et fid dv: dq  Glq: deg: Solaz. dv - 1: (daZ. Z
reprobare non licuit
Ed= (dZ: du) ((da Z: d2 - 1edd Erro ddz: dz = daz: dv  Bvaq - d q lav) sclib. 13. 1)
sit ge X: a = ddz: dv
seu dque (dv dd Z - di daZue : (a DitZ) d velv:, du dazue- d27 cax = s ddz. dz.  ubi non licet ponere
adv = 0 et generaliter in hac methodo id permissum non est, nam alioqui haberetur
Cdd7: d7
foret constans quantitas
et haberntur do per do: dZe sum
assumatur dco = di dav: duZ et ex ea fiet
habereturque praeterea sine quadraturis x aequatione
Aco dZ, v. dZ): (d- dqe B(d v. d) (a0 - dzue. H av: du)): aede dv - deo = sadz: d
evanesceret, et ddz
seu dodo dz de ique  dudo - d vdzue : d Z  duaz = deodz = 5 ddZ: dz
video difficulter assumi posse deu
siet aosd (dvdq . deo dq doddo - dxtaz- didax) - (d vao - eodi B, av altztay auo - do t)  daz
Se C2 (vdod ddo = avavd z a X - du d 3 dz ddv E.l cod Z lv lo + duvtrar at deduly dam
2), dodz - dco dz
= dudiqu  duavazu dao evar
dvavardaquet dvuez tav  duaz aeo daz
et pro deo substituendo valorem ethaliqua absolvendo fiet
(2), dudz - dcodZ
+ Z d Z lZ ddv dax (ctd2) - 2 dZ dzue dx dd v dd veld Z
do3 ddz
Av do dZ (13) ddqu ddzue - 2 dvd lavaiz + d. d dldvado
Az davao - 2Z  dv ddvddav - d vellaz adz = dvar, due dazaaz - 2rddz av da XF dey delvaldx
dento ee t
daqe cu
seu dar
Et fiet Lud
d (r2
et seu d dez=
d + dos
d st + 24Z1 7 lv C az rd v)
dodv (21 (dz + dv)
de +2 d 7aZ + dz Ld 2d Z + 2 dod Z + 2d0 dv)
2d2dZ C a 1MavBE a +do)
d7+26
d  12
etti X
etq + 2dxdo)
v 
xdz + dodo
dv, dody d (1+(1 + 2. 4
d
ilo  hotis- quadratu, C 
Avaro - dx s( + 2du +2
+dodg et fiet do =
ag =) des des - q dqu. 17 d2 =
12 (1- 4 12
Edvdv) = (d 12
ita reducta quadratura foret ad rationatem
et latd+
M 19dg = d2a2,: at
2 1 -a 12)