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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 2
# Folio 5r, page id 00068204:0009
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A = 0. Et area =X n = hoc est
Areu his casibus diversimodo extribetur, quatenus computatuur
adiversis finibus, quorum assignatro per hos in ventos
valores arearum facilis est.
Exempl. 3. Sit ordinatim applicata a5
25 V= + Z2
hoclest, perreductionem ad de bitam formam, vel
a7
b + Z2 Vel a5 4
X1 + b = 2 et erit
in prioris casu d = a 5. 0 = - 2. C = b. f. - 1. n = 1. X = 2
2
a deog. r-
de; quare eum x non sit numerus
affirmatiuus, procedo ad alterum casum: hic est, d = a5
7.
e
1. f= = b. n = - 1. X = 2. ad eoq Y = 3
a5
6XY + b= 1
BZ. X
= 2.
2, Seu = - a 5Z + a 5b
et area =Z in Z
1ZX 2Z
= O
32
bX. Z
X 3200 hoc est
30b6 + 296= = 16=Z Y
10566=Z
.
- 2
-
a5Z + a6,
62Z ZZ + bZ
Exempluq. sit denique ordinatim applicata.
o
c-3aCC22 + 3aa cZ3 = a3Z7 haec ad formam Regulae
reducta, fit 673YC aZ3
O= 3. e = c. f- - - a. n -
Z
:5C
56
2)=
=2aZC a
5. Indeq est d = b.
5. X = - 3. r = 2. 5 = 2.
5. N = Z: et areu = e
=7a, id est -- 30abZ3 + 756c
28aa
152 =
XC- a25
X
7.
Quod si res non successisset in hoc casu, existente r vel frauione vel
numero negatiuo, tunc tentassem alterum casum purgando terminum
=aZ3 in ordinatim applicata a coessiciente 2, hoc est reducendo
ordinalim applicatam ad hanc furmam bZ = i X - a + CZ 3) 7: et seg
in neutro casu fuisset numerus integer et affirmatiuus, conclusitlem
curuum ex earum numers etse quae non possunt geometrice quadrari
nam, quantum animaduerto, haec Regula exhibet infinitit aequa onibus
areas omnium, Geometricam quadraturam admitlentium curvarum,
quarum ordinatim applicatae conseant ex pocestatibus, radicibus, vel
quibus libet dignitatibus binomii cujus cungue.
At quando hujusmodi curua aliqua non potest Geometrice cun
sune ad manaes altia Aeore matae pro compaeratione. suro carmu conscero
a 1ZZ
LC - 2CC22