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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 41r, page id 00068196:0081
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 Loguethmicu
AX, X
es
XY, y
X P subriormalis
X+ ctar su ttangentialis
A1 X+
- y =
AH, a, ubi XE0 AB, b cujus - uius log. est 0.
AB, D cujus leg sit 1 = BF = AH BF, b cuius log. AB sit 1.
y = bx seu qua y:a = b. a X.a 10g9 = X. a
_ (i -x) + VF= minim
ly: dx = CCCy: + seu tdy = gax sen dg. y = ax: t. sit Y = (O+ IIX + 127X + 13X et
AB = WV
a
ergo dy. HX dy: dx = 1. 11 + 2. 12 X  3. 13 ~ + 4. 14X = y: t. Ergo fiet
1F. 11 + 2t. 12X + 3l. 13XX + 4t. 14X + ek ∞ 10 + 11X + 12XX + 13X + eec
ib 11 = 16 ex 10. et 12 = 11 = 10, et 13 = 12 = 10. et 19 - 10
Et 1E
tandem g. a =  yea = 1Y 
Et fiet
0
qu (W
Sioa
3+ 1. 24
1. 2. 3. 4+
4
L X + 1 XX + 1 X + erc
1.2 H 1.2.3 13
C) + 14 = + = X + L XX +1
aa
+ 1. 2 H 1.2.3 13
et differentiando ( 1  + 81 X +
in qu (1 +
XX
+
L X
et
1 It 1. 2 +3 1. 2.3 (+
(W-X
+en)
= (min-qu a
+ 70 W0 -x. 2 Y(.
+ 20- X
XK + L X
id- X - Z
sed ita aequatio prodit quam jam hatermus interim
+
10
a
12 It 1.3.3
eat tali aequatione ex dato W daretur X se A X.
X) = _ t
et hhoc reperto
AX
+ W. X = 1 e b. (2x: a). ita ex dato W habetur X X adboque et p
sed dissimules
ponumus binastonantimus lors asytn ptotae seu axis se langere, quod utique
y
habebitur et fier ioqoaa
10 a
1010) a
fieri potest, cum una sursum deosumve moveri possit donec tota infra vel supra
uxa
alteram cadere inciprat fiet qu oX) +
us.
esumendo aequationem
i
(0+ (2)) b
+ 1 x + L xr + et.) minim - e qu
10
1. 2 H
si esset solum serces utque ad  eet+ IX Ci, 1 + 2X + XX = minim-
Y +
H
Lu = LX
1 100 +
(610aa
seu x = _ W - totaa. 10aa + H
idub
a
10aa 10aa
alitr 4 10 aH + 2. 10aatx + I0CaXX = m 10a aH m -iv1o + 2WHX = Et XX
t
XX (+B2. 10aat X + 10a aH (- m) + H Woo
s2W H
1va_ +F
2 WX -X7
10 aa gaa
x = - . 10 aa + 2t + S1ona - W0t) - 10aa (. n 7 ptoa
e
10na + EF
tous 
ergo X incipil esse impostibilis, cum qu (10aa -20L) = (100a (1- m) + 1010) (10aa + H)
Eodem modo sine consideratione radicum aequalium