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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 18v, page id 00068022:0036
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Cum hoc sit maximi momenti, erroris vitandi causa de integro assumer
operae pretium erit.
Esto GBE. Hyperbola. Cujus centraa A. vertex B. Radius ut
ita dicam AC. vel CB. a. AD  cD vel CH
vel CF p y. AD, a - y.
vel AH
AF 4 a+y.
DE, a
-y
CF ( AFp
EF HL, a
  + L +  +  + = et c.  spatio in infinitum
11 - y + y - y + yt - y etc.
eique summa omnium HL ad CF. applicatarum erit.
-
aty
Eg D Ergo posita a , 1. eut DEp 1 + y + y +, y +7 etc.
et summa omnium DE, erit applicatarum ad AC, erit:
Posita producto, ACBEm,
Sed HL p a 1
1+y 1
=
 E + 3 + = - = etc. spatio CFGLB
5. 0
auferatur spatum CFGLB a spatio ACBEM. restabit:
et  a
25
fret.
(9 L ( +) + = (+ 2) +  ( ) +  ( ) er
sive 2 2 2 ex  1 Z  etc.. qua demon-
2
stration quod satii mirabile est, et ostendit summam ipsius seriei
2. = erc esse infinitam, et pronide et aream spatii.
A 1. 2
AC BGM. quandoquide finita a CBGF, ei ademta, ider
2 +2, +2 + 2. quod aequatur spatio GFCAM BLG
Hujus duplo = 4 +  + 4 + =. erc. auferatur area
et opposito Hypetom, circuli, cujus dicmeter CF., nempe radius CF. quae est.
4 - 2 + = - 4 + = etc. fier inde differentia haec.
8 + = + 8 et c. et si addatur area Circuli ejusdem
si Aadi si diumeter  sit 1. Eircumfrentia est: 2- 2 + 4  
Ergo si diameter 2. seu si radius 1. etit cicumfernta 8 - 8 r 8 - 8
ergo semicricumferentia, et -  += etc. quae ducta in radiam
1. dat circulum, ergo circulus et == + 4 er. Ergo quadrans
circuli 1 -  +   erc
Anferatur Quadrans circuli
a spatio c FGB. restabit resen restabit: fier:
+ = -
relinquit.) seu nihil notatile adimit. Hoc argu mento concluditur, Re
infinitum non esse totum; nec nisi fictionem, alioqui enim
foret pars aequalis toti. Si ad spatium 1.  L.  er
addas 1 = 2 + = - 4 +  -  ex. fier.
potiqus illi spatio pote
fiet: _ 8 + 8 + 8 et.
c
35
sumta bilicet