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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 20
# Folio 15r, page id 00068090:0029
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Ad Adt. decembus 1695. p. 353
Aeqdata a dy= ypax + 93gdx quaeritur solutio sit y = v. fiet
-1 (3)
n
(
a C v do = v pax + ve t a C. V du = v. pax + V gdx. sit e- 1 = en. sit
L
( = 1:, 1-n fiet aedv - gdx, V = V pax seu ae do- gdx = V pax
Ex 3 per 3 fit a: ( B B
(8) 1+1 -
M. 7 C= M
1.ni s1
gax seu a:, 1- n dv = qdx + B
e.1 = F. (n + = 1 -1 +n, 7,  seu a:, 1-n do= gdx + v. pdx
m
1
vid si fuisset data aequatio adu =  pax + y qdx sit g v fiel
di
ac
do
me
(
V Pax- sit ady: y= pdx +
jam Sdy: G = fdy. y= i at
m(3
-M. (4
Ergo y= Cd
1-m
im
1: (=M 1)
15)
oux
=c 1: cm C
n. m :: 1- ra
1: 1- m Ergo ex 2 fist a: c- m deo = pdx + co
gax seu
faciendo n - m, :, 1 -n = Y. fiet  a: -m deo = pdx + co. cdx sed hujus
quodsi aq. 1. faisset adu = G. pax + G. x ex t solutio desiteratur
data esset aeq. qualis g. scribumue. bdco = pdx+ co gdx
unde fiet bcodco = copdx + ct gdx sit coeo=  W fietque
ebau
adu = y pdx + y que sit y = v fiet  a e ve he u
a e v
do = v pax + v gdx seu acdo = v en - et1,
n
em
e-1
en- et1
pax + V
sed  video nihil inde posse duci, nisi vel m vel n sit  1. vel saltem
do = h + _ 1: V
e
Gx
si daretur adu =  pdx 1Y adx F y. 9dx qualiscunque esset posita 
esse numerum certum, daretur solutio etiam pro oi alio easu, ut si dai
a
si daretur ady = pax + yy qdx, dacetur elim a adu = paxt y. gax
Datur ady = pdx + y9dx sit y ~ 1. y fiet sit dg.y = ve fiet
y = fod sav: v. et fiet ado = vpdx + sdv: v 9dx
 G = ∞ b fiet dy: y = d  logb. av. v et dy = log. b. B. du: v
et siet a tog. b. b de = pdx + b 9dx
mo
ib
a b ady - y pax + y qax sit y = b fit alog. b b. do = b pax + b gux seu
a logb = p a logb ( ne dx = pax + (nv - me qux sed ait hinc