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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 23
# Folio 16r, page id 00068236:0031
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elementis
Aequalio expriene ad curvam currae conicae proportionales
ordinatas habentem est: d +1 +a aequ. Z
2aX + a XX
quod si jam major quam =. seu 9 major quam a, procedit reductio
ad curvam rationolem
seriei infinitae modus nevus item conne
cum investrgatione Mensura seu divis
sit X. X+b aequ ase quae ritur X. fiet Xaequ a reptat
loco
s
seu X X aequ. ax + ab
a + xb+bb
X+b
a + xb +bb
nil fingend Xaequ a omisso secundo X. habebimus Xaqu, a +bb
b
X + b
v
Xt6
X4b
eu
omisso teitro x fiet. X aequ a + b adeoque: X aqu. a  aequ a. a +bb
a + b
omisso quarto X fiet: X aequ q. arbb
Generaliter: X aequ
seu xaequ si a est integer
a
+ a
a
. Ergo X aequ
XX + 4
Ergo X aequ. 
ab + b. a +bb
a. b + b  ab + b. a+bb
a + bb
a. ab + b. atbb
sou xequ
ad. a+ bb + Bab. b. )
erit  investigatio maximae
communis mensurae.
aa
X +2bXY + bb
+ Xa
+ b
si jam a aequ. 1. et b quantitas affirmativa
b+ erit invefigatio conuns B tere
 
xaequ
Cs vel Xaequ-
posit0=
1xa- + b
XX + b
XX + b.
ubi Xa esse aequ. 1. prit aequatio X, X ada
jyterc
ratio extremoe et mediae ratione factoru
seto secsuentorum
rursus Xaego . Ergo XXaqu
XX + 6
Ergo X aequ.
a
+bXRequ a.
et XX gg a = b x
sed haec est identica
a- bx + b b
X aequ
 l a
Xex+bb
et
1
X aequ
xa
seu 
xa v
X
X= + 2b xx + bb
b
bb +2ona
M
b+ p
2b34 abb xx + 2bx+ + aa
continuetur semper divisio, ita ut fiat:
sit  aequ X + a fiet a aequ
+ X
Aebare botrbuta
 b +4bX +600X + 1b X + X
aa aa 
IM seu X aqu
seu
boeb
aa b2+ 4b X +6bb X +4b X +. X
aa na aa
 4b  +6l Xtab EX
+ 2b 3 bb Xx + 2bX + 
+a
quod si talis fingi potest
relatio datarum, ut termni
quotients b. Vb. c. d. C
+
semperfiant integri
t
una com
intumensura