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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 9
# Folio 5r, page id 00068104:0009
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seplem fr. 1690
Ope
de Quadraturis ad alias reducendis
Anralyseos
Omne mea calculi infinitorum, reducitur quadratura proposita
ad alias variis modis. Ex. g. sit (X sat bx de fit 
sit , sa+ bx = v fit sexdx. jam sexdx + (xxdo = _B XX
jam do = bdx:  V
Ergo
bX sa+ bx ax +  Sib XXdx: Vat bX = XX SatbX
Ergo si datur  una Quadratura datur et altera. sit atbx- eca
fiet dx = deo: b. et X = d cd: b = a: b et XA  2a
et XX = a coco: bb - 2aco: bd + a 4: bb. Ergo ex D. fit
bb in scoc du -(2a0 deo +(adco. datur ergo D, adeoque et C
as.
icua
in genere
similiter sesset
fiet D=
si 8
Sed
sco
X Iae +bx ax = O faci (eet =
e
X V x
(X dv. et C+5 = xet v. itaque generaliter
SX Vae+bx dx reducitur ad
a + bX = c ad
et+ = F: 2
Zb X dx. VaerbX, seu faciendo
22
P e-1- 1.2
c da   dio + cd
deo etc.
semperque finitus est numerus, si e sit integer. Quod si e sit fractus
verus verb. gr.  eo ipso pro dit series infinita quo quadratura
Circuli Hyperbolae aut Ellipsebs; idemque est pro fractionibus aliis
quibuscurque est autem
Cvet1 -1. 2 = Coe2-1.2. et ila porro
e+ 2- 1:2
Itaque quadratura curvae Cujus ordinata est X Sa +bX, reducitur id hanc
redeseriem:
B
et 2- 1:2
Cd
e+2- 1:2
et 1-1. 2
Cd
e+1 = 1: 2
+
C - 1.2
C0
- 1- 1. 2
= Cd
0
e- 132 C- 1 = 1:2
∞- 2- 1: 2
+ Cd
∞ -2 - 1:2 et
quod servit ad interpolationes Wallisianas demonstrandas, et reddendas generales
patetque simul quod in casu fractrum fracti valoris ipsius e, mo et irra-
tionalis re redtuca ad quadratur A Cariam dividendo enim
totam anen per esis d
Et dividendo totam seriem per cos patet
hinc dari methodum incundi per quadraturas summam seiet talis
cd
1 1.2
 = Cd
(+ 1+IL
1.2
(+1: 2
at
C0
C = 1. 2
= 1- 1. 2
Cd
e - 1- 1: 2
+
2 - 1. 2
Ce
ek
ea 2 = 1: 2.