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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 270r, page id 00068196:0535
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quaeritur
ax: XX = a4. Estraatem M: XLa + n: X -a x
Estvantem m: X+ a + n: X - a = 1: XX - aa. fiet
MX = Ma + nX + na, : XX-aa = I: XX - a4
 Ergo M + n = 0 seu r n =-m et
=ma +na  (seu -2ma) = 1. fiet m = - 1: 2a
ex et n = 1: 2a. ergo fret
j: 2a 1: X - a = 1: X+a = 1: XX - aa. Erso
dx : XN - aa = 1: 2a l0g x - a = log. X + 4
seu dx: xx =aa =  1: 24 log X -a: x+ a
Ergo (dx: XX+bb = 1: 2b -1. log X - b r1 : X + bs-1
v = by: X
 si sit 
 et habeatur V = d dy: dx
ile reducitur problema  transcendens affectum
cud parum seu quadraturas. nam bdn ady + Ydx
Ergo dus: dx= b d0.  Xdx - nam bdy = xdo + vdx
Et dy: dx = Xdv: bdx = v:b =  v
Ergo dv : v. b + V = bdx: X
Si sit bv = VX et habcatur v = dy: dx, tentemue
bdv = ydx + xdu et dyc b dv:x = bv dx : XX
et dy: dx = b dv: X dx = bv: XX =
seu dv: dx  V. X: b + v: X
ffine
S aequatio reduci potest ad D. Xx = dy: dx
posito 
vid
XYq quadhaturas
potet reddi pura seu reduci ad
dx: dy = 2xXY = 2ax: 3aa = 2Xy 1
sit 344 - 2Xy ∞ V felia a 2XY - aa = V
seu aa = 2X9 = V. fiet dx: dy = XV: 4Xy - 3V
A
et 2Xdy + 2ydx=
Av et dy: dx  4y: v = 3: X
potest geaeralius sumi aa = MXV + n XX + p yy +qVX + YVy + SBC
s
+25vdv
et M Xdy + m VdX + 2HX dx + 2 p y dy +9udx + qxdv +rvaytryd
honc ∞g.2. jungendo cum aeq. D videamus an eadem opera possimus
collere lX et dx (occbigr. ) N. vel s et dy
verté