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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 10r, page id 00068199:0019
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(, aequatio data sit dyB +dx A = 0 posito A et B dari rationaliter 
ex X et y. sit Assumatur L =0 quae rationaliter data ex x et y
determinata fit duL dydL + dx AL =0 seu -dy: dx = dL: 4C.
ubi in L et  dE y assurgit ad eundem gradum, sed in aL ad inferiorem
unitate jam - dy: dx = A: B, sit dL B = LA. haec aequatio
est ordinaria excedens ipsam L0 proat L altior quam A vel B. itaque
aquatio L=0 esset multiplicanda per arbitrariam. Quod
libenter evitarem. Assumal loco L assumatur
L + .  b(_ NY CC B l - L +b is, fiet
du +L + dx  L + dy Nb (nCD + dx dNb tm Y +  (c M dy + GdM ax) N bIM)
Ergo - b Fn3 = L : N = dy d L + dx dL,:, dy d N + dx  N + N d M dyt Nd M dx
seu A L: N = b
seu Nd L + LdN, :NN = dM. L: N seu N dL + LdN = LN d M
d esset N constans, et
dL +FtC   Ex + ey = 0 sit cLdx + et dyt dus d L+ dx dL
t ita evitatur ductus arbitrariarum in se invicem,
dy (el + +L) + dx (CL + + L) ~M du B+, dx A, e) quod ut suceedat.. 2bi
L
aute omna destructionibus efficiendum est ut et + dL, et CL+ dL
tantum differant gradu, quantim B et A..  deinde multiplicatione
ipsius
per MeHrcienda est comparabilitas. sit B grad termini
ecurim
temmini
in L gradus
sit in A y gradus f in Bgradus 9
temtini
fertuim.
de eaunt arbitrariae Z+I,
eL + d L gradus Z et CL + d L quatus g
quarum sed ut f- g evanescat in Ct + aL ,super supererunt Z+ 1 -f+g
711 in MA gra G + 9 = ZH. st9
in MB, _ quad V +G 
literae arbi
v aequationes comparatiae erunt
literae compari equasiones comparatatitiae 27, nam destrncti
ergo
sunt ergo coparrationes
computo contero etiam eas quae aequa gradus qui destruuntur
oporleret esse M E M grad terminis aequare Z quod fier nequit
quia M + fvel M dB - 1 non potest excedere Z