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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 318r, page id 00068196:0631
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eseries infimta er phibent relationem generalem
inter duas quantitates, v. g. sit y =  X potest poni
 y = 1 X + 12 X + 13X + 14X + t. posito X esse minus quam 1. et
vel y = 1 + 12 = 13 + 1a  + esc posito X esse maj. quam 1
possit et relatio generalis ex primi per continuationem exponentium in infi–
nitum vg. y- xe
n log
xiite
neeses ita lag. y = 1 log a (10X)
etc
XC  (Y)d= X loglogus = log. logix = nX  log 1X
tor
etc
nx
et log (logsloglogus - loglog 10 X) = log. 1X) - log 1X = lg 23 X log (13X). 144. et 
lognX
sed hoc  lommo sed t non ita commod. est haec relatio
ob comprehensiones perpetuas
Quaevis quantitas X potest exprim per   10 4, 2 + 12 2 +1. 5 + 14 4 4 et
ubi pono 10, 11, 12, 13, etc. non posse esse quantitatem nisi 0 vel 1
quonioro
sit jam sit X abscissa et Y ordinata quaeritur dx exprimi possit. Dico non posse,
sed assumi contantem. sit jam g = 20 + a2, + n2 + 23X + et. potest dici y
Sax
30+31 2+322 + 33. 8 + erc A potest poni 30 - , 420 et 31 = + 21 - dys etc
erit semper ovel 1. utcunque appropiaquent sibi ipsae y
drtax = 21. id hic insigne, quod non assuigitur ad potentias
X
jy- 10 + 2. 20 212 + 2. 20. 2 7 + 333
N5
20.2 20. 2 20. B 20
H1.
2. 22 2. 23
22. 
+ 21. 4. 22122 +2.27 2 + 21. 24. 2
15
21.
222)
23.
2026 202
H. 24 22. 25
2324
sed incommodum
hic quod coefficientes
sunt inconstantes.
Sed po  constantibus perdentur melius procedere expressio per
quaenitur summa progress. Har
dyadicas.
esto sum (+ +  +  + 9) aliquousque nempe finita:
y = 10+ 112 + 122 + 3. 2 + etc. posito seriem esse periodicam. Possumus scire credo
 in unteressum, qo quuo sid quam quoo que numer non excedat periodus
+.1 =
100
e
So da
a 100
 108H 100 +2
100
10013
Lu=1 - 2
14 = = 2
 2, = 1 - 2 +4 Y + 16-32
100
100+4
4 - 5 + 16