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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 19v, page id 00068196:0038
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A sdq + lytm + e y  + h(dy + Pysdy + l + m +y = 0 fiet
haga +distu + rdys + s  rdy sdy+ ydr sdy + d +dm - Ady + ndy + ydn
et quia fdy = l+ m + ny, : , h+ ry = hdy + (Y+N) dus -m dus + _ dn + dm + dl: her.
video optine poni m =0, et fint h lrdus + ly dr + ldh + nrydys + nygar +nd h = mdli + mrdys + mdr
= hhdu +h(rendus - hon dys + hydu + ham- hdl + hrdus _r(rra) ydy- rmdy + rypdu Frdm + 19 dl
Sed vides nimis alte assurgi. Et sane n variabilus est mutilis et m _ frat =0
et fiet h sdly = rysayu +l , 8y = 0 et  hidy + ih sdys + xdys + rdys say + ydr say rdl +ly ∞ 0
et sdu V-h dy erdy + dl + dys:, dh+ rdy Fydr = l+ y,, h+ry, unde
hh dy thrdus + rrydus + habe hdy+ rydus F hdl + ry al L.
yydr
=rydus = ldh l at
=0 oporles resse constantem
seu aro
oportet ar dr esse constantem seu dr-0, iter esse atrut as sed ita non potest tolli dyt Ergo calculus
un d 
A sic _ _  _ B (yt +  fy ny + p = 0
jam d b  facile habotur quia  si b = W f e bogb = legu. et de logb erori C db: l = dW0 e W seu du = de log b. bC+ C fe. db: B
pricr. malus.
not dh + h (Mdys + ydm + dh) (m9 4
et lipt o
seu qua
logl H (my + k) smvat dl: l + nay + ydn + dso =0
-na dh - pah - hnymau -htiys ydm - khius dh - lis ndus - tisi pam - t s d h - hny at nu -hay th -hpalsuy - h p al t lefi y
inde- nith - pdk dtm hdtnus val
et fint  test h loge maynus + hloglmpdus +legl. natydm + nydh +pdh
hndy holngu al +hlogE nyah
hinc ut destraatur dy dx fiat logl dm + m Alil = 0 fen
+hloylsyam
+te ny db
+ hlogl pdh
+hhpdt
- hap
sit jan aequa bio data hmtan gaus + Bhimmndys + Y timmn gax + Bhmmnax = o et fiet Hminp = ( )emmn
seu logM = loglogl seu m = logl et ab: l = dm
+ Empysal
seu p = fn: p) (n: mm) + Bn et n dh FhmBdh + tmpam Fhmnam + tmpam-hdn = gummnax
et denique pah + mpah + hapam - hdp = Bhmm fit - fit M = pah. + honpa h +hihpdm - hap, : Bhmm HX
F mmji, Bimm + 1 et siet pih +hmpah + hhpdm - hap + Bmmpdh + Bumtimpah + Bmm hhpam - Bmm h d p = Dhrmmm Bi pdX
sed si in assumemus pro constante malim tolli p, nam fiet dp= dnac
=hdn - Y tmmndx dytem dm n (+ B) = 0
sed cum ope duarm
arum aequationum tollantur dt  si et A per rationem dh:h id dn:n desinetur in aequatione
ubi evanescat dm, fiet nah + hmncth + i madi 
mM
+) - hudB = Aummndx.
quae non est in potestate. itaque praeter calculi prolixitatum
sit -h, 3 + byy tamys + aan = 0 fiet 3yys dy + aly dy + gy dl + a
pet -3syy dy + 2 lydys taamdy +ayy dl tay dm +  dn A - h dh
-3hh yydy + 2ahl 1s dy + aahm dy + ahyus dl taahy am + ah d n = 0 sit aequato data aydus + β3 dy +. Vy dx rab aX
et fret
3tih gydus - 3hh (3y dus L
+aclgy dy +aaβ9 dy
algus dp taanyah + oinah
al yus dh -aamus ah + an dh
3hihV py dx - 3ht BGylx
ta ) gydx taa fgatx) = 0
qua multiplicetur per , et fiet
habentur
hhA y +aG ifiet
ergo g et M
et m = 2aβl + 3GβB: aa
in  ob dx fit a han + andh = 2 a βBdx + 3h(3βF dx. sed quia ad huc duqe reslvendae
et ex dy firt g = hm: β hinc ex ydys fit 2a β3fil + 3h BB= aa fim.
 pmpth 4 ny + p =0, fiet: arqualiores, timeo difficultatem
et g = R2 al + 3hh B,: aa seu g = 2ahl + 3hh β, : aa
ob un d fit 
my+ A 
ny dg2
Redcamus ad priorem:
nyth (mdy tydu + hl)  g
= pu-
p
mo (my +h) dl F ndys + ydn + ap = 0
p
Lmnygdlit + Rydu
H,  yy dm +leyl. nyat
+llylipyda
+mpls
-dm: nm = dl: 1
.Et frebus foret
sed si lesset constans, et g qu
log. li Mnydys alogl. Mn B dy a loglma ydus + bgl. mab lx
fiet de utrique destuendo gydu, fiet dm: m = - dlologl
+ Pdg: g =0
 phal:l
si jam y dy  st logl. M
seu log m=
logloge. seu log i = log.logl seu  = log. l
in milogt = 1. jono unc ex ay
seu p = nB+ et ex dx
poro p
pagig utei g.9+ hatit) - pa B. B
seu log) +hlog l - logs(3+,) = logn = (D(. β341) ex posito h esse onstantem
seu
seu dg: g. = hal: l - dp. p =  B( DHi, BF id x
L9: g t d + (3+1) dm: m + h dl: l + (3+1) dl- dn : n =
dg BC: 1 B1) dx + 
dn = nBdx
inperest aequatio
Ulil =dn :n = Y dx
seu togM F toy. = Jog. log l. + log. log l + E lX + dB - Vdx
(+ dus= hal: D + (β+ 1)dm: m (+ hal: D + ((3+ 1)
ed cta evanesscunt assumlae ergo mon ticet facere
et ex y iex faciaram hane: Ag: 9 X dh: M A(Bm 1) n.m
si Ddx+dB +da +ri.
qe redecus ix
= Vdx
at: M Lan:M = Yd
Fax+dC
asunsitia
x + B =  ex, quod eeciet non
(L Ba) x hat: ) +(.+1M: N Ergus rursus omne
eplupotetale