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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 82v, page id 00068198:0164
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dy y: a = dv: de
dy: dx, (3) = ddv: ddz
X: a, (2) = dz. de sit de constans, erit q dydx )
sit de= dq sdaZ: d2) fit V: a= du fd (lv: de is Ild 7: d2)
tandem ex 4 differentranda quia de constans
et X: a = 61, 1. a 5ddz. 1Z
fiet: adzue + ddzue selitz: dz) =0 ergocum 1 + fdatodque non possit
esse =0. fiet dao quod tamen non licet. posset esse
de (4), de sddz: dZ. firt y: a (5) = d∞. sadz: dz et X = a = (6), (dZ: dv): sclib:
. Ergo per 5et 6
et ex a fiit: 0 = de ddque  n fadz
ex 7 fiet y: a= =
17 ddy
seu (ddzue= duddy
aque
a
a2ddv
et X: a = (0) 4yde dex
dudy daz
Sed ibi esc incom
duddque
modi aliquid ex aequ. 7 vereor, fit eum habetur enim ita prae-
matura relatio inter Z et v nam fit  -ddv: do =
seu
(ddZ: dZ) S (dd z. dZ) seu log 1: dv = log fddz: dZ
l0g (1. 18) = log log dZ quod (nene suto e t licecre panamus
quod an liceat dubito. Videamus an evitari possit seu
an 4 sic assumi possit, ut a non prodeat relatio inter A et d
27 ((ddZ. dZ) fier idze  daZ + 2 dZ ad Z Sddz: dz.
quod non merius priore. Quid si de = dz qu siddZ d2) fiet  e
= 2fddZ 1dZ 0 = 2 ddZe fdaZ: dZ  ddz qu (daz 42),  seu fier
0 = 2 + siddZ: dZ)  Et ita semper Cogarit Emus ea ipsius de
prit coustans. Sed ita etiam ipsa dz erit constans. Et vedeo
 quando logarithmus quantitatis ductus in quantitatem producit.
constantem, idemque est si pro lagui loguut proda opus esse ut
et quantitas et logarithmus st sint constantes. Et iinc etiam
idem esse si potentiaa quantitatis vel logarithimi ad hiteatur
quid si de L dz 5ddz. dZ + do sid ith prodit relatio inter
da et du. sed quid si de = dZ sddz: dz + do fados v, fiet
o = ddzue + ddz 5ddZ. dZ + ddv. Atq hoc s videtur succedere. neque enim
hinc duci potest relatio inter  dz et d0. Itaque resumamus:
V. a  C y: a (1) = do: de X: a (2) - dv. de sit de constans seu .
dde (3to) = 0 fiet dy: dx (4t0) = ddv ddz. Faciamus de = (5to) = du paz: d2) dv
fiet differentiando e o(6to) = ddque + ddque seadz: d2) -ddv. unde ex 5fiet:
fiet de (7mo)
Ta dZ. Et Eta Eecit duti aliquot memsesanno mpliore
da
e
Hoc jam potui l. A fute
dZ - dv. Y. Et y: a (8v0) = dv: dZ ( d v: ddZ) - dz - dv et
trigo ovaoe suin de
dZe (ddv. ddz
Itaque  sufficiunt aequa-
dq intze sen (Eptiid
X: a (9n0) = dZ:) dZ (d dv. ddz) = dz - dv.
tiones 8, 9, 4, suit, it pro aequatione data tractanda
Sit data yy + XX,: aa  (10 mo) = dy: dx et, ex 8, 9 et 4
fiet dq  do do + d2 dz,: (2) (d Z (d dv: d +Z) = dz- dv) = d dv: ddZ, vel
dZ dZ (ddv ddv: ddz dilZ) - 2 d Z d Z (dd v: ddz)  - 2 dZ dv (delv: dd Z) + dz dz - 2d7 dos dudv
= d vdv (ddz: ddv) + dZ dze (d Z. ddv). compendii causa dd dd rdaZ
(12 mo) ve emus Y fiet  fiet c et (ddv ddz) 1 vacemus (13t0) It et
ex i fiet do do + dz dZ. :a  - dv) = e et dodo + dxdZ, 1 d  lterte
com sit pro du, dz, ddo, dazue scribames  m n, dum, ddn, fietgus
mn tnn:, C(. du) du dud Cere La tio) dm an
n0) c0 1Z dco dt et ex aq. 11 fiet 1 Lt, gre (tco)  V) (3ko)d dt
Q( qu. (+(C: dt) - + - a):, 1t + 10co = (13tio) dt: deo. se compendio
(14) E+Co vocemus B, fiet H+coco = vo et AC deo: dt = rr fiet quC Yt + B)   Y
Si cd: + sit 4 et
erag
scribamus
et fit ex aeq. 13 fiet  rnt Mo rYL - B = (4 4)  n: Y
dud: t sit   q sit dt: t =   d9:, q - q ex 14 fit 13-(B. t)Y ~ n. F unde
u
68)) +3C  - s(aCF
( e 4( -
-
90
27 FF)
r= n it + 
adeoque dco: dt 1( (18V0) =  r(Lt + coco) a  + 1
Y. n + 2s... v,t
qua, ut homogeneorum lex segoetur fiet at:  siq
dev: dt = (20m - ssaa +44) + q + a, et d
Iaa tqq +a
et i.. L =q(.AC Saaraqu  Laa + 49 - i scia r9 eaqu)) 8... + . n
A
3io 43
df: +-
dq x
saatqu
A, et pro coponendo
ritque Xra = abin  t lt  1 sed jam pro
Cagno
et pro o ponendo cot: a fiet
de
ne = 1 + 44 et e - laarus
a
it p: t = a + 9;: a
27-4 = 22 (aa +99) - 3 a9
a
posito per 15 p3-a+4, 27 Saarq
x reddamus aC, sprd co, du; et pro aco: t, seu dv: at, Dem qia, ponamus h. de
o