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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folio 3r, page id 00068033:0005
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addendo invicem EBGHE + HCDGH aequ. EBCdE. fiet:
- 1 +
- 1
+
 est 3ide 1,2 2~ 13,8 4, 4
X
plus
2,3 3,3 4, 34
aequ
+ 11-
ec
etc
memotabile
scopo tamen nostro satius est aliam adhuc commodiorem seriem pro Hyperbola
sit DL aego V. Et aequ. 3 DE Hyperbola aequilatera, vertex E.
 latus rectum b. fier 2b∞ +77 ego vv. unde differentralis
an
aequ desoz
Ergo L aequ v aequ 26q +2 et DE aeqo 207 +22
b+Z
btZ
Deptaque e
b + Z
b +Z
b
v bZ
1Tb+Z
As
 Zay
Est autem V aequ 2bZ +ZZ. proque scribetur aequand quadrorto Z2 + 2Z5 + 
2b22
seu vaeqo 1 +2bs - 2H seu 261 =E5
a 2b -25  2b- 25
26-25 et V aego 2 + (aequ.  +S.
vZ aeqo ZZ + sZ aeque
b-2
quaeritur V aque seu  2bZ +Z2 dq. sit 2bZ (4Z sae qu (2+ 2Z(+s
Pet: Ss aequZ. er due aequ. sit 267 47Z aequ 27 fiet Z25. seu 26 +ZaquZ s
seu fiet  2b2+ bb Z aequ 2s(. seu Z aequ 7, 262
et dZ aego (263CS) +25+) + ds
Eb
 Ss H et dz b3 1bs4
seu fiet: 4bs  est autem v aego Z equ. 2625
2I)(- bb
- 66. Ergo vtque aqu 8b B
Aliter: 2bZ fZZ aequ (2E e 2ZC0 + coco fei coco
aequ Z.
et aZ aequ. co eo +2codco + da dZue aequ d  ergo ae + da
ergo dze aequ 2 co +co d. 2b- 2c0  + 2 deo c0ro
4bb - 8bco + 4c0c0
2b -200
(3+ B
2b - 2co
26 
(2(5s -6b
= 4 aequ a B - aBa
aequ 4b co-2c0l0 dco
G pb - a
2b- 2co + Cd aequ coco + 2bco - 2c0co
seu v aequ 2b00 =c01o et v Z aego sen bco + ∞. Ergo vaque
2b-2c0
26- 2c0
26-216
Eaqu. 26Z +27 Z aequ loco. b - fco aego e. fiet co aequb-e cotd aequ b a e 2bC
2b - 2co
deo aego de et fiei Zaequo b +e- b et v aeqo  + C (b + - e aequ  L e aequ. v.
et dZaqo = e de cy seu dz aequ’  de - b de
Ergo Vdque aequ ( b de -  ede - 1 b + bde sed nnhil hicc discimus.
4 ee
DLago Zaequ. coco dque aequ. co dio vaego cono + co aego 2bco -aro
LD
AZ aequ.
2b - 200
26c0- coco  2b -2c0
b + eo
26. 2c
e aequ
DEaego DE aequ +F
Est autem 
Ergo TE aequ.
2b - 2co
b coro Z
2b -2c0
2bc0-c010.
2bb -2cob + cob
bcocor 2b -2co
2bco- coco l
26 2co
beoco
q 2b - 2bc0 +coco 2b 0 2bb- 2bc0 +coco
2b -co
seu beoco seu L bcoco
4bb 6bco + 2c0c0
aequ
2bb - 2cob + cob 6) bcoco
seu TE aequ bco. Ergo TE dZ aequ
b coco
2b6-2bc0 + coco
2bb - 3bc0 + coco bb -bco + si (b- co
fiet TC _ ago a b - bbe +: bee
luca  be + ee
bcoco
42b- co, 2b-c0
sit b- co aequC
et co aequ b - e
. Ergo Z aequ 3
Quod es
quaerere
cs
Ot
vseu
2bZ127. bz 2
b+Z