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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 164r, page id 00068199:0327
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dit aequatio data 100 + 10y + 101 dy + 120 yy + 111 ydy = 0
appet Aissumatur v todo +Y _ =0 ipsa v existente mgy +ny, fiet aequatio nova
 Y+ ny + + myu
per y fit r = 100t.)
+Gany x quay +qun yy + 29 dy
100L+ 110 Ly + 101Fdy + 120tyy + I1 F ydy
er ydus sit g = lIt: 2m et per dy fit g = 1oct: n, quos duos valores aquando fit
IIIn = 2. 10c M seu n~M n = 2. 101 M: I. Ob y fit n + gdn = 1ot seu explicando
a per n, sit E + nn + 101E dn = 110Fn, adeoque F =  nn:, I1On = 101 dn. Eodemmodo
ob yy fit m + gdm = 120F, seu 2mm + uIF dm = 2. 1otm, seu F = 2mm:, 2: 120 11Id m
ut siet 
N
-
1IOn = 101dn
3BIM
2 mm
2. 120M = III am
IO βm = 101 d Bm = 101 βdm
 2+0 jam 2. 101: I1 compendio vocatur B, cognita
e2 Mm.
siet n = BM, et fiet
ubi feliciter evanescit mm, et fit
2. 120m - 11I am
+ 2. 110 β3 m = 2. 101 _Bam 1 = 0 adeoque tandem
Lm
_. 1220BB + 101 d β - 110 βB
11I (3β = 2. 101 (3
sit sit jam data aequatio aax XXdx + yydX = aadue fiet 100 = xxdx et 10 = 0 et 101 = - aa
B
= 2. 101 aBm
= 2. 120 βBm +. 111 (3β mS
Z N
infinitu
fiet
dD: 1I
quia 181 = = et 1II = 0 fit (3=
Adx  idaased dur: m Aadx. aa seu X logm = 4X: aa
et (20, = dX et 1II = 0 s. fept lur p27
u et
oacvura hyp.
scit et fi vel B
B= 0. sed non B ergo 1
seu M = b(+X. aa 7 t + = 2 btBX :aa : 2 b(4X 1a = e B F2X: a4F
seq ita dmim quarq
et do
M. 2M
Ergo g 1
Ergo dm: 2m = sed ita fit dm: n evanescit
iaque ut habeatur supplement cm ex 44. data frat. eit
X = yZ et dx = ydZ
sit 7 = hv + W fiet Xxdx BB +hh vodx + 2hWvax + 20W dxaat rdzaa vah
= aa ) hdo - aa Vdh F aahvdV + aaW don
nga D an
fial ut  WoWdx +aa dv= 0 fiet 10= aadv
et ciet
sit v = B A ny min ny m t M + ny tly,:y, et ex b+ qdv + r fiet
Edsiet  100(+ 110y + 10rdy + 120lyy
fiet Ce q= 2ot. m = 11ot =m: dn
et fit C∞0- 120F dm 10 tm nm, seu L = mm p. 1O n- 12od p
tqnus ( gnydue andus e
1
O
B. X X dxa + hh V dx dx + Ergu fit x de Xx Vda thh vdx Zhaad V - a a Vdh
ex
quaesitum siesset f-x = aa B. W seu cxagescet a sed nit inde
es habebitur
Ai m+ nyu + qudus
per d
2
: V et yy = 2Z(. vV et dy: vaz + 7do ergo fit Cxxdx WB + ZZ ax  aa vaz taaziv
 -  y =
+4
C
fit = u ob Ao lut  + = - 9m : 11. Ergo ob fit H M + gdm =  1109M:1
+ryusqnydu
=gm: 120 per y fit + = g4m: 100. fit dm: m = - 100: 120 Set habetur et _ C: 9 = =m: 121
M ob y fit m + gdm = pomgitzo, et fit g = - 120m :, nom + lodm. Ergo pomanel narbitraria
fit t
ino potuset esse n20 Fresumamus pagina vers