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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 200r, page id 00068196:0395
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Eisso per 7 15 116 fit deo - Gt, glogys. ylogr
seu cut
d
seu erit do =) (olog  - y log D + xlogy - Xlog X + X (= vlog d F ylog  - q ixy seu siet
dv = (16) Xlogy - X logX + X - y, :, X - y.
7
lonc
Ex 7 est deo . df logdv: log.lz.
Sed video
Erqu per 15, 16 fiet =  xlogis - xlogX + X - y, :, y logy - y log X + X- 7
jam ips = Y: a. unde sequeretur V: a seu valorem datum ipsius d dy: dx ex x ety
demum sub finem ingredi in calculum atque ita omnia exempla eodem modo tractari
per regressum generaliter
snon sivce
quod parum credibile: Et vel hinc demonstratur quod
res non pottest demonstrari, ique enio aequ. 17 differantpando rediret dy: dx = Y: a
redeundo ad aequ. g. et sres
oportat igitur ut relinquamue. E du
dque logdque dque + haco  d lon dv d. jam deo = Glogd  f log dv: logd Z. Ergo
Hinc explicando
jam datur
(10)
ex aeq. 9 fiet dZ logdz - dZ + h logdv: logdz = de logdo - de
des per dZ et du ex datis, habetu t dv: dZ per logdz et log dv
do: dZ= X y: X (per 2 et 3 Ergo log de  logdzue + log(x: y) Hinc ex aequ. 11 tollendo
seu de = dZy.
durdx de et log du: dz et logdo, habebitur aequ. (14) in qua datur logdz per
superest aequatio una ex duabrs
X et y, vel a, et log. log (X: y) et X: y
2 et 3. nam ambas jam conjaux imus in aequ. 12. sumamus ergo
aequ. 3 X: a = dZ: deo jam seu ex 7, X: a = dz logdz: stogdv seu
F: a = Z logdZ; de (logd Z + log (X. y)) ubi to obt dz: d, tollitur az, ut restet solum
log d+. in aeq. 16) quam conjungendo cum aequ. 14 a tolletur az et habebilus
aequ quaesita qu(7) in qua solum X. y X, y, et log. (X: y)
dy. de 1) X  Xy: aa H: a = (2) du: du
satis simplex
et Xa = dq:deo. fiat  dy. de (4) = dav: ddZ. Et hos tres valores substituendo
Sumamus exemplum pli
In aequ. data, 1. fiet  ddv: ddz= (5) dudz dcodu. definienda jam est valor
ipsia so, seu afsumenda progressio fandamentalis, st ergo dvaz: dcodio = (6) sa seu  logez: logtr
unde fiet ex 5 et 6 fiet ddv: ddz = (7) logau: logdo. adeoque dar logdo = ddlogaz
teodu- dv
et X: a = (3) dz: , et fiet
et quaerando dZ logdzue - dZ + hdco = 18)
dy: ex L X: a sit g: a = video
et hos valores substituendo in aequationedita)
fiet: dav: ddze = C5) dZ: deo definendus jam est valor ipsius deo
 seu deo= log dz. loglv: logd2
dd dy: dx = ddV: ddze
et fiat dz: ded = (6) logo du: log dv
Ergo ex 5 et 6, fit dav: ddZ = logdze: Cg. dv. seu ddv logdo = ddzue logdz.
quan aequationem quadando fit dZ logdZ - dqe + hdco D = dv logdo- dv
ubi primum ponendo  r=0. fit dv: dz = logdd - 1: logdo - 1
12
pono
ex 2 et 2 patet esse bo: dZ =H: Y adeoque log dv = log dz + log ( s: Y
y: X
Ergo ex aequ. 10 fit et 12 fit y. X Ee = log dZ- 1,:, logdze + log)-1 et fiet
porro ex (7 et 11 lit ded = du H. (log(. x: logtZ). quem valorem
seu fiet.
logulu
substituendo in aequ. 3. fiet a: X = , + (log(H: x): log dZ)
log dque  X. log (B: x),: a - x quem vatorem a quando priori aequee
fit ( (Xy) logZ + a - x  X logsY. 2), sed  qua aquatio ab omni
diferentialitate liberata est. Jam aliunde scrimus esse per
247 = x seu =   ya y: X = X: na. Ergo ex 6qu. 18
et loque y: X = log. X = log. 2a. Unde ex aequ. 18 fit
(a - X) X_log X = log. 24) + 2a a = x) = 2 X log X = 2a x log. 2a
(ax 2og X = ax log2a) - exlogX + V logna  2aa = 2 ax = (D ax log K = (Dax log. 2a
quae aequatio
est
seu  2a 2a (a - x),: ax + xX (= loque (X: 2a), petento 
qu
esse identica, quod non est. Ergo redeamus ad
log: )
2 et d est dv: dz itemque e logao- loga
+hM flogty. X): bagdque) =(y. 4) + (Y: X Hlog y. X): logdque  y: X) Bilog ilts si h = 1
X logdz - x + hX log dv: logdq = y log dv = Y
et eil botic
deberet
arete h
ea:d  yix. et
 silio
an
sec logehtesti binte. toria loguin