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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 75r, page id 00068194:0149
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Hinc autem correctio colculi habetur, discimusque debere assumi
V = - a + 1 x + 2X + 3 X + 4 x dc nam cum X est aliquid
potest tamn V esse nihil. Et ita calculum prosequi operae pretium
By2 -2b1 VX G+ b v. 8 20. tentenue reducere ad exhahibilem seu comparemus isti
a
bv 2br09 + 89cestt. O = bx
1)b
foret.
fiet bv - 2b ∞ bx9 + b x g= b x Vx  -bV + aXV - ax,
Ergo b X - 26V + axV - a X aequanda quadrat, veo + 2BWsX +bX 
e
eamque aequationem, in duas dividendo fit. BX = ax = 2VCoX +bX et -2bv + axV Vco
fiet ex 5, XC co+ 2b3. a et ex + fier v = N -a x: 2b Vderum, quia ita
nova daretur equatio inter  et x praeter eam quam jam habermus non obtinebitur
res coarcbaretur ab une ad aeqal loco ad lineam ad locum ad punctum Ergo
sic potius scrbendum b2x - 18 S + aXY - a X = Y c _, 2Vc WX 4 WEX
et dividendo in duas fit b x = ax.  2VE WX + WX et - 2b s + axV = oo
et fiet ex 4, v = b X - ax - WVX, : 2COW, et ex 5 het X = 10r + 2b: a
quod si faciamus con, quibus valoribus in aeo unde et habetur do, item dx ilem
= dr: dx. quibus valoribus in aeg. 1. substitutis, habetur nova vel
in aequ  exuncta +bV ∞ + b xs =  vco  + WWX  factuex vens
2 et 3 correcta, per extractionem habebimus tandem aaequationem differentiale
in qua differentiales no assurgatinetra primum gradum
sit b- Z. x - 2 v- 4  = +  et cx aeq. 1. fict: 14 a 12 1 _ 144 3a 1 ga -0
et fiet   o   x
jam de  _ et (9 e (7 sit Y  ex et 7 fit dx ) 2)
4q. 6 fit B  1 seu 2WWV = VX- ax Wx Et 2coW dv. + 2Covdh + 2t b ded
b2dX = 2AXdx= W dx 2XOdW unde facile habetur et dv. sed quitae polut
mohixiora forte a poteum solvere aqu. 1. sine reductine ad rertionalitatem
si faciaau. si assimamus aequationem inter X et p. sed quia in aeq.
20
(21)
  aeq. 1. videndum an sividi possit in du as: _ V - 2X  et b nt - axv + ax = 0
quanm cu prion sis diferentialis videndum an possit derivari ex posteriore; ubi fingum
posrea posia didicidi seu mD + _  X 4 pX in aq ubi fit 2bvC- V
+2aXV8 + 3a X = =O. Et  pro  ponendo v: 2X fiet ex cq. 20. fiet
2b.V a LX aVZ + 2 a X p2) +5aX3 quod non procedit. Quid sitic:
bv - ib 1x9 + l8 + mvG + pV G + qXg + rX G+ +x + W XVG=
et rursus , L+ mo+ ex +gX +urx a +X + WXV 0 sit sC
(er  ert differe atralis ipsius 2 erit. 1tnt 2pr+ g+ irX + 3+XLWXV
11)
2a..
sit jara A + 6C + G9 6 et 38 + K = b (seu = X.  set utique
∞BK. H + GHC: H= seu AH -BKH + GK0 est autem A = b v et 8- 2bV
BB et G= l+ m + pr et  b + ~ axv a H  m + 2p+ ZWXV ek tet
pintubons vditib