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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 97r, page id 00068198:0193
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(ydx an aliqua arte potest redidi generiliter summabilis? non puto. 
 X log. a= sd a:  a +1 - posito bg 1= l0. sit y= a. fiet  log. y= X log. a
s seu _8 tog. a. dx = dy: 9+1. seu x = log. a ax a+1 = d a si log a. = 1
fet Ax a +1 = d a seu d, a = a x + dx. Erg. (a de = a - x
itaque si sit aequalio proposita ydx = dy - dx seu (x = dy: 1+ y
x (  = y posito C = F. e V log. X = log. y. a log X +VcX. 1FX = dy :12 y
Ergo d, X = dv togx + dv log. X. X + 1. B, 1+ R,. _tR dex logiX 1+ X + vito dvby X + vdrIEX 1t X.
et X = v log. X + Slog X X do + (X sx: 1FX
sit (X Ax: 1XX = Z et GX an = co
d de sit Za co = M, siet
X I: IAX  p ex = dn et (X = dx + p ap - X  dx (= X  dx) = dm 1F X
X lg. X = log. y. XsAX. IFX = fly: iau seu Xdx: X + de Scx. 1t  = dy: Fy
seu X:  + (ax: 1 X = dus . dx 149 seu d x. FX + dx: (7X = dy . dx adus . cris + 1. tru d dy. ex
(2
X C
X  y
sit ddx = 0 et fiet d dy: dx = ddy: dx
p dx = Cd ergo X = deo: dx et X log X. = log. dco - log. dx. sit  dx constans
Set X Sax: 14X = sadeo: 1+ deo + const. et dx (dx: 1tX + X dx: 1X = d da: 1+ deo
(2
quid si potius fiat  deo constans erit d log. dco= 0. sentfiet X dx FX + Tog. X. dx L- ddx. 1t 
oncen
rursus  aequalionis 3 quaeratur se divisae per x quaeratumr diffeantialis et fre
 hic un omitetur dx essi
parbilis quia adest est tog. 
dx: 1t H = ogeateo B. nxe  (g - log. deo ax: nx (+  lle. 1r lud) + bosta tx ex  - ulx. li tu
jam ex aeg. 6. tollatur - adx: 1+ dx ope aequationis 5, fiet.
dx: ex _ olog. dco  log ax (IX, iEx  log dx - log. deo (a x. XX + X ax): 1X + log. X 
seu fit XX = log ax: da + X + log X XX I+X Unde seq ueretur log. X = X - XX,: 1 + X. FX Unde
X log. X per 3
_
=Xr. 1FXAp
=
X podnde (posito Loga. = 1
Hoec alias disculiend.
interim non videoque vid scrohibeat deo assurat constanterus. Enstopot
sequeretur fore
quod tamen videtur absurdum
si esset X = W fiel v logx = log W et V b. = logto: logs x itaque si
simper posset dari sx toposset semper dari seddx
 = li sil v = log ld
assumcnd pro pressionem c as
(4)
(auv = a
V log. a = lloy dco: dx seu dv log. a =ded: dx. 1+ deo. du
ponauus psas deo idx esse pronessionis Geometircae, fiet et esse d devida = 
Sa du  c a in = deo
possumus autem facere rclationem pro arbitrio inter ded: dx et. d deo idx. sit
Aco: dx= H. _m: a et d dco: dx = dm 1a et sit dm = β it m. a, posita
( constunte et sit d_=ga dv loga = B, sed tunc nihil plud redit quae v = log n
tm faciamus am= ta = ea: in sit B asB= L m. itaque ex aq. q
eio
sit du. loga = ea  B: m: 14 m: a seu dv. log a m + M. a = β At quia M: a = a pr5
iva. 2 quo aequata cdentica
silloga (av. a a + a = _ (per 7.) L (mm: 2a =) a
julum sit vera examinandum. Et latent hic quaedam sublilitates nondum exploratae
+
rutem los. s dv a: + a = a du. dx
sa sit aequalio e dy: dx et copontit 
Z: a quaentur a-
y, Z. Ejusque quaeratur
Cq uatio Esferentialis qo b de est differentio
diffeenta
differentialis in qua aberit a. quaeritur an hoc sit oquatro. diferentio differentialis
diffferentialis () eoanescet et a et habebitur
sil communis ipsi datae 1, a aelliequs et illi quoe fieret ex data si poneretur  a = 0. et
an proprie ipsius aeu. 5 possit noeniri summa summataria. C hoc enu si pere
sit
darefur et entr
xta  x du sit a = d yy  + xdius = X x: x et d O = dx allys y a hxtis a drtur dus t ca natus A datd
=gyy dex - Xdys lex (t Xdx delx G+
= sed jam video si a sit aeg. 0. aliam fieri aequationem et differentio differentialem, quam est
nam il, ex 2 peret dus ytx ay - xdx0 veum replico, rarsus si de ponatur
+X
constons seu adx =0 tunc eandem aequatroneq differentio differentialem prodire ex aeg. _1
et et ex aeg. 5 quas ubi a = 0 nempe 0 = y y +  dy + dxdy + X ddy = XA x
sed hujus summa est aq du yt xayu-xdx = a uam si liceret ouagere cum 4
soloti pb ex er qui reduci t
sabystarieas didivantam et redit aeu 2. sed ita nihil iddurimus novi. Qqvidem aequalios.
 e  tiitu es estirus erittine sto o vero anatia hioter bed
Lignata per aequalirutu 2