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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 8r, page id 00068199:0015
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non successit
ut quna smer my dx t andy + aodx -0 summari pt
etra et phydx taqudutardu summari potest, etiam compositum
pg. myaxtandu  Py7 1x + agydy + aatdx =0 summari possit
summanda est haec aequatio: mydx + an du + apdx = 0 ubi m, n, p, dantur
per X. Hoc variis modis assecutus sum, sed sequens ob consequentias, in primis placet, qui
fit noltiplicando, Multiplicetur ergo haec aequatio per 9 arbitrariam ex X, cum ergo
apqax futura sit summabiais, quae cunque reperiatur q. ide sufficit ut ms inquax + anqdus
summabilis fiat, quod obtinebitur, quod si comparetur huic aadr +ardus et fiet r = ng: a
unde de = ndg + gdn: a, sed rursus dr = modx: aa. Ergo siet du: q = mdx - adn,: an
seu log q + logn = (im dx: an) et posito b esse quantitatem cujus logarithmus sit uuitas
sret,.  nq = b sonax:ant, e q = b A(m x: an) : n.
si proinde fiet
 mydx + andy) = D sorqy a =) ay, b. (max: an)
CCI. Sen dx: an)
Loco y jam assumatur gyu + ahus, posito g et h dari ex x, et fiat inde
nCGgy Fahus) x + an (29 ydys F gydg + 4ydh + ahdy), l. sen lx. an). n cussumna est agyy radhus, b
t
sit jam aequatio data ap ydx + aaqdy + ryydx + aa ydy h m multipli. f. Bsemaxiant
Formula
etur per
fiet afpy dx + aa fgdys + frgydx t afcrydus ∞ rahmyax t aahm dus + mgyydxt   agnydy
0b y dys fiet f - 2 gn:  pursus ob du fiet f = hn: 9, quos duos valores aequando fit h = 294: 0r
aa n ynh
an yydq
Ob yax sis t  hm ax + an dh, seu spdx _ + et qui = hnid x: q et dh: A = anq:,
et dh: h = mq R npaX. _ P - Angdx,: ang. sed ex priori valore est
dhit = 2 (9: N) dg = 2 9d (9: v), : 2g(9. N) = 49 dg + dq: a) = d log9 + d log9: )
superest altinui aequatio ob ydx = n p dx - mgdx: anq
qu~
superest jam
altima coinciventiatio ubi ob gydx et fiet frax = mo dx tan dg, et pro f ponendo
valorem 2gn: V, fiet 2gnYdx = V mo dx + an  dg, seu min = 2rdx - a v (dg: 9): adx
t a
-dlog (9: ), : llx : a)
)-ac a logec. v)  er 
militer reperi rem  non posse
9 velimus multiplicatam ut ibi velimus
sid ita evanescit utrobique dg: 9 vel alog g.
aequare producto ex gy de + afdys, bBd: as) in lytam ubifit aq - p
ootineri, si aequatione pormulam datam in
 
in sic (a 91 +2 βydys) (. sam a , () + sp yax = 8 19) (C. s.  . al : 8), 0
+ n 19, + aby) dx + an f 2gy dyt yydus r ay dh F abtus) p. b. sn dx : ant: H
comp coincidentiantum cumdata apudx + aaquus + 19ydx + a v ydy, f. bsucx. an
onax: an): Avanelcet manebunt m  m, n, g, h, a: β et 7. 8
et primum quaerentur mi ni et f, restabit demum adhuc una aequatio
ita
am aientrae incognita in ubi quaerentur implicatae differentiis  utem
indi indigenus a cet B, reducitur res ad duas a: (3, et  1 Sadx: aβ et
ila et ad (Y: d et s.S pax: ad ast
pro quibus possemus ponere intee lateras
ila vereor
puto necisse fore a ut fet X:
trendentes etores redibit ad f, m: n, g, et sricial
quae evera per ucentur aoduat
 C4 myax + an dy fiat ay V v b fint. 12 lvdx et an vir b + b dv, quod
aqrari debet ipsi Vdr +rde, aa fiit b an = aar Rursus  aar = mbix +an
sit am ydx + aan dy = mbv dx + an vb dr + anbdu =
+dv
aa, vda
nb =at etaadt = ambdr+ ab dn = mb dx  anbdr, sed ita quae situm evanescit
su possumue esfi omittamus compositum u t ubi m et n sufficient
X = b
ne an sp: m) ydx taanch.n)t mVydX +  any dy, b
ubi L et (3. et item Vet
sindx: an
aant mgydx + an 2yu + nosq F n (ea guxR taan d (2 y),
se Myyax. + an rydy +am ayax + aan a dy, pnan. an : n
an y den
(Smax: an: n
fit n = g: 2 m= f∞x am: p = an : 9 = an (9. n)  fit g= m = L v: qu et m: n = 2p: q
p gydx + aqudus + ar ydx + aa n du, da
restat Am (9: m) dx + m d (9. m) = fr dx seu am (26: 4) dx + an d (20: 9) = a ma: p) rax
unde iterum habetur man, quare resgeneraliter non succcedit
n: m = 24 (.9) (r: P)  = 2(V: 1), dx :A (V: 9) = 29: p
nempe. fit
Jyix t.du, na (. snda an Y~   Y L Vdx + ady, s(5 dp. a9)
n
n 5FaX: d9) = b sen dx. 4) 9 = P A PQ b Sindr: an et g -9
e min- a td et n = G. bt ota in b . si s pt ass B