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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 8v, page id 00068199:0016
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data, _ Z yylXx +2a 9dy, ss rax: an summari potest, fiat r: a = M: M
Ergo in jydx +2am ydy, bsmaxian in etiam summari potest, et alterutra harum n vel
est arbitraria. sit jam proposita summanda formula C quatio
Vsax+ 2aa Bdes + ap Bx t acquds + aatdx =0. Multiplicetur
p fiat Y = p: a = m:n et multiplicetur tota aequatio per n
fiat v = Cy: a et du= edus + ydejia, et fiet
+ Y eeyyax + 2aa ee ydys + 2aa y yde + ap eyax + auqe dys + aatdx
a a
raceyy de
aa
 adqy de.
ita
d
Lyyax pVYdx + aq idy + ar ydx + aatdus + aa vdy + aatax =0
da
multiplicetur per Li b sispaxitia, et protuctum dento subtacto aatax, fi b sndxiaa
I. Sndxiaa
aequetur ipsi N (9yy + ahius dx + a a d (ggy +ahius) C
se et fiet pyydx + agydy + ar y dx + aa a dy, f, bsnaxiaa o
Fahnydx
sndx: aa
aayydus raaghydus +aaaydh + ahdy, b
ngyy dx
per ydy fit af q = aag seu f = 2 a9: 9 per dy fit aaf sv = ah seu f = atr: . Ergo
liet g: h = g: 25 F. pdx = n 9dx + aadus seu 2 agp: 9) = n gdx + aadgue
seu aa dg: g = (2 a (p: 4) = n x dx seu n = aa dg l: g) + 2 a sp: 9) dx 3: dx
restat aequatio frdx = hnax F aa dh = _ alisr: a) dx seu n = a : p5) Ax - ccact h(. ti), : dx
Ergo aa log (g: h) = s px (2 a p : 4) = alr. 1)) = aa log (9: 20)
rclatio
quae aequallo ars
ea
in merdx + aande dx + apvdx + aaqdv dto prae si al v = egia
possit, videndum est
alius modus determinandi
atax
Y vedx + 2 aa vd
itfiet meeyg ex + aneegny taapegax + aeqe du + atdx
une yyde
fiat mee dx + anede 
+aqy de
aapedx + aequle seu Cadx adde=
aeqe
laciemus ergo ex altera tera determinatione
an ee
seu omelxt agnde = npedx +nqde
sed ita destructo agnde utinque eram scit e
ne aa tognerede
24m x +aande - noedat nade = aullynaa ede  -  aloy q C ad de
anqe
sed ita iterum evanescente utrinque de, evanestit et e
Haec igotur via non procedit
my + andy + apdk = 0, sit (m ydx + andys) (smarian + ( p Ls mex an AX)
fit mydx +an dy + apdx, L l. mdx: an
(mgax + sindx) dy + an dy) - ) mdx +
ay bsmax: an + (a p bsmaxian dx) = 0
si an = snax sret = c; res pro cederet
smaxdy
Ptan idys
 sincX).
non loret sciliert PCf a dn = M ax
sed odet edq = pedx + gde qui
= M ydx + ady, bs max: auF
n P, mydx +an dy. L Smx: an) = ay b sindx: an
 myax + dCy bsmax: aui
sit aequatio pVG + a9y dy M  a (mylx + an dy) Q bsindx: an fapy ax tagdu + pyysx t, aquay) a (. s pl: aq
itaque abs si jam sit data itaque
sit a Haec utique est summabilis. videamus an inde confici possit data per arbitrariam p
multiplicata a  a selydx + afrdus + ryyax + gr ydy fiet maa bsmex an paa j spa: aq L : e
et a = ap spax: aq sed cum ita tantum adsius quantitates p. 4 et min
u
G
non lires salis facere = aa  sedxiaq. sed quia non nisi duae suntae quantitates
aa (b. smdx: an + b ApaX : ag)
artutiariae min et d p. q, non possunt salis facere tribus lequationibus