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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 2
# Folio 4v, page id 00068204:0008
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fB Pa
ad curvam aeliquam sit. d ZXC.  f
X
ordinatim applicata termino diametri seu basis Z
(1 ( Nosmaliter noistens: ubi literae. d, C, f, denotant
Saq2m Con. = 0
Cd = E+ f Z
quas libet quantitates datus, _D, n, X indices potes
tatum sive dignitatum quantitatum quibus affixae.
Adq eo. f  ) Sunt: fac 8f1
itaque
5
it
4L∞
X+ X= 8,
s XC +f=
CL, et Nn - n = X, et area curvee erit 2 in
2
5
r. 1 x E A
s- 1
2- A V C∞
LH
+
X =2 Y ED
5= 2
2y = 2 3Y ec
S 3
s =
)
5= KC. Citeris C, B, C, D, _e. denatantibus
tr ferminos proxime antecedentes, nempe  terminum
in
S
B terminum.
2.2
s- 1
X EA
Ke. haec series,
subi r fractio est vel numerus negativus, continuatur
B
infinitum: ubi vero r integer est, et affirmativus
in continuatur ad ot terminos tantum quod sunt unitates
en eodem Y, et sic extibet geometrucam quadratu
inmussram Ccervae. Rem exemplis illustro.
= h. 3= 1.  Cpe. 1. Proponatur Darabola, eujus ordinatim app
-1v. vMata sit V az; haec in formam Regulae neducta, fit
Asit (. . C  X O = a ZZ: Quare. est d = 1. 0 =0. E = 0. f = a.
 1. adeoq 2 = 1. 5-=- 1  Z à Xa E)Z. N =0
nDin bed E arca quaesita
aXa ZIZ in F, hoc eot, 2 = Vaz
ita nona, posit 1sm et sic in genere. Si cZ) ponatur ordinatim applicata,
prodibit area
-
5
n+1L
7 =1
Ex. 2. Sit ordinatim applicata.
a. 4Z
Cs= 2CCZZ + ~
haec per reductionem fit a AZX cc -2 = 
etiam a A= 3
- 1 1 Cc=2
est d = a. t. 6= 1. C = cc. f..
adeoq X= 1. s=- 1. Z
a4
A
vel.
Jnprioi casu
1. H = = (2
 RcC ZZ
X= +2.
hoc est
2cc- 122 N = 0. Et area eurrae = R in Z0
id est
a
RCC = 2Z=. In secundo autem ca su est
Cd=  a 1 O = - 3. e1 f- cC. n = - 2. 7 -2.-
1- 5 = - 1: Z = a 1
2cC X
1 + cc Z2) 15
id est.
= a 1Z =
aet aari
Ae = fh. Z- dZ
Z= co- E: f (t. t)
 = scon E) es
ita res reducta ad crninos
um
sit in homus hh= 9 AI
O-5, 1d t (91. Co. dio
unde si a st integer
habetur solutio absoluta
tis vege hic scriptiorioxa
si loco q assuisit
D=5, c- Egl. Co, IJora 
ergo si q rationali,
tunc fdG g. b+d 3 E+ 5Z
randiour ad aliquot finitas
1, b + d. c, eC.  C
Haec maximi momtati
sit  integer polu
set
mibus
non
icem
sum
ediuis huraro
(+ 5. 8
Nin _E_ = f. Z
et
FZ- vbi. n - E. fl t
in 0D= C,:f( 0.
dA 1Z. Zm (+5Z1 k.
esse integrum, obtenta est
depressio mo gentraliter
sattiet si h sit 1,
adhibili quodcung
quantitate sub irvationalis
tenta resoluta in plunes
dicisores, et unum ex
irrationalem povendi v,
habetur deprossib
tetanez
 cit.
u v