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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 73v, page id 00068198:0146
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Cavcd =  log2p = C0 loq V et div: W = co dv : V + deo log V
dip  seu d (ve = vi Coldv: v + deo logv
6Z
2
et fiet
l
sit aequatio data h = _ Z. V et fiet B = V dq +ZV de +ZV codv: v
e
dt
 et dividendo per v fitdh d 4 Zdco loq v + Z0dy. v  seu fiet,
hujus um facilis est summatio
habetum quanfitas summabiles
dZ + deo logp + codv: v sed sodeo nihil 
sit enim hac Nam quantitas hac est summabilis, sed eadem
multiplicata per D Z est etiam summabilis.
quaeeadem
duae quantitates sit data quantu Nam
sint ergo
(IdZ + dcologv + codv: v)
 logZ + co logv, et ((V (dz + dco logu + codv: V)) = ZV
vel Z. v + b. Hinc videtur Moctus dari Z Summandi formulas quasvis
sit ergo quantitas data XX + yy, ex  = aadus. Ergo debet
summari XX F yy, dx. sit dx = dZ + deo logv + codv: v, et
fiet X = logZ + colog V. Bursus sit XX+ yy = Z. v seu
gy -q vo 5=C  qu (loget co logv)
2d
tandem aay =  7 vo seu
seu agy = 22. v bc
C (( Ergo tandem fiet ZZ. V.: a = Z. V, = qu (log Z + co log D,)
yy
Nec video quid pohibeati hanc methodum applicari ad aequationes
Tangentiales omnes. Et habet hoc motabile, quod simul
res omnis reduciturad quadratu as rationales seu ad
aequationes exponentales
12
se
sed 1B
(posito loga 20
Resumamus
et utrobique quadrando fit a d v. 1 = co dv: v + a logv. du, seu fiet
difepentiando s.
Adip =  codvi + Ep logB da seu d. V = v codv. B + logudco:a
jam d, q ued = ve dque + Z dv. Ergo tandem fiet
y qu = 110 eq + Z (co dvix + logrdes =
d, L
Z. V, dziZ +codvio Hgl
A, les.   seu log. Z vo = (Z + c0 logu = logz +  colog v
a
so
quod verissimum esse minifest patet.
1
20 a
Caeterum ita habemus duas quantitates summabiles quarum una alteram dividit
id
va
Nam dz. Z. +codv:  Flog V dedia est summabilis, dat enim logz + co logv
Sed Z. V dz: Z + codv:  tlogivdco ex deo loquevia est etiam summabilis dat enim Z. V + b
sit Z co- sit 58 dlvges= c ut coastat
Hinc venit in mentem resolvi posse omnes aequationes diGaugentiales seu differentiales
vel ( b20) dat, B. VD. +h 2) 2t
primi gradus. Sumamus Unam ex simplicioribus in Reciem, sed resolutu difficillimis super qua
dnifraties Remondii me consuluere. sit a aadu- xx + gy, de
sitHanc formulam
dun fuctam summundam reslvamus in producentes comparendas nostris  si
byg, a
adec
Ftnd nitr nostris aetandas, fiet _ l. dz: Z +codv: V tdco logu: a et
DXX+gy, a  _ adeoque N: a = logZ + cologv: a. XX tys A = Z. v: . 42
d posito aF). vel omisa a, it XX LYy = b 3. fCo) et gy  Z V qu (10gZ rco logv)
Z. N 1b = 1  y. adeoque erit
ee
t
Ergo fiet Xx ps Ux extyq 
ve gu log. Z + aloge Y
ut ante B jam video
(utii ut co sit constans, et quidem Unita
2b   yu vec
et fiel bb F2bZV. + ZZ v: aa = Z a luae putlin + e la qu logoZ. sed na omnia
yu =
inus maxindeat face
iterunt reducta ad unam quantitatem, eem v. sed hoc non nocet, Nam
Et hoc  nceret, nisi hinc Cinte datur etiam y et X quod quidem et in Hyplibola
verum est, nec ideo minus ea est curia.  Sed in eo incommodum, quod ita ZV = y. Et
cum ex novissima aequatione ZB sit determinata equeretur etiam y. e de terminatam eodem modo fieret
X determinata, et video nihil savare etsi sumamus 7. v, nam et haec quantitas fiet determinata
1
in sirbio fiet Z B qu (2 5) = L B qu. (log 210