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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 95r, page id 00068196:0187
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dy: dx = Xx + gy,: aa
sit Y: a = sdz: Z et y: a = sAZR: V
dy: dx (= dZ: v7 :, dz. Z) = Z: V () qu 5 aZ. Z + qu Saz. V differentietur
aequatio S, tiet Zd (210) = siz. dz + silh, az. seut fiet: ponatur
d. 1) esse constans se l(7. v)310 fiet det eleC
14
Hin
vo on v
+ddZe (Zst + L st
per aeq. 5 et 6 tollatur Saz: Z et saz: V
2 (X, Xax + yag = X. + Xyy - y = = X + sxy dy
aa
aa
aa
(X dedy : dx) = X dy y xdy : dx -y
aa da
Z v.
= t dd Z
SX de = x XC- y posito co = aty: de
X3+ sit ceta Y C = ((at + X+), 1
Sit co cd telle YL
dc = +X dx: t(C + ). Ergo posito axila + X) datur SX x: +(a X)
+
1 = VO ded = d0: 10. Ergo si detur fdx YB datur + (xdO: 10,
et viceversa nam est 2x dCd 3 ) = X. C = Sdx VO d XX - 2Xax
dy = pdx + ydx solubilis
P- 1
ady = ypdr + y 9dx fiat y = v et prodit ae D du = v ptXx + v qx
sia C = C 1: n seu aC de  _ Vpdx + v
odx F sit en -et 1=0
seu e = 1., 1-n et fei acd _, Ln adv = v pax + G dx
perto ad =( px +C qux Multiplicetur per
Iliter
porro adco = coF pdx + co cgdx fiat c0 = y eut deo = Y p dus
rf- Y+
o=11I
pdx + cd. odx
sed hic non possum efficere ut alter terminus sit y, quia si faciat
rf-r = 0, evanesert r assumta
 ad = p dx + ci gdx multiplicetur per ed
fiet acd de = pco Ax + C cgdx fiat co = yt, et prodit
er+r-1
a( ary
odx. Ubi vide nihil prodesse e
quia sobi potest adus = ypax + y gdx Solvi poterit proaequatio trium
cum ubique ex, detrahi possit
membrorum talis, quoties cunque duo termint a duae affectiones ipsius u se habent
ut summa et differentia, verb. gr. sit ydus _ = gypdx + y gdx, nam
qdx quod solvi potest
ro ye ponendo Z fiet dZ = Z plX + Zn:
a v du
n