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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 210v, page id 00068200:0422
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-
Xeus Y dx nva
Ax p eo - dZ
2
dx + dz BCo. dr + dZ H co
 y _B. de + dq ydx A (a ) 4 acu
dx etaa)
Vaxa dx + dZ ponatur relatio Z ad X talis, ut sit
dx + dz quantitas extrahibilis. id est ponatur
2
LX2
y dx ( a Ydx  coax
seu y ax 
X H ydx H. 
V + B2
dx
2β
1bX
2
de B de + idex
ax +(88293+ F
x
(Py
PB dx +
 sit BN X fiet  C et ..  Xdx +.
positoque dx B1. erit y B = + 2x
Vl3 + dx
du
X
2
2 2X
et que aB X + 1 - 2
 de B X Ex + dz, pone XH... cd.
fiet
+ X
a
2
ponendo codo pZ.
  ex Y1. +co
ex
ax + dZ n B 8. aZ  gC
dx
0X
H
s
a
d
e
X - 1
a est data X assumia
datur relatio iphius y ad X
Quaeritur relatio ipsius Z ad X
d2 cete  e y -1 seu dque py- a
Z +   _, dx que
a2
2
2 2X X H 2 2X
et Zp-.:: cd
xAx F, dx y2. seu posito dx p1. fiet
a2
a
+2d Et du + dxps
patet ad inveniendam curvani reujus elemen partes sunt partibus
flnius ordinata Z et
spatius cujus ordinatae y. proportionales; debere quadrari sya
2
Sy a
 à
fiet
yH X+ a. fiet: ZH =a sit vri X + a
ZA = X fa- ~) 
c0+1
X
c0+1
Hinc
yH =  + Y X bX  SH  + bx (+ 2 - 2) seu S1 +bX
yp = +v  y - a  L + 2V
v- a. t supponatur V talis ut sit quadravilis, et
x=2
eo supposito fiat siae elim quadralalis ut si sit Y 12V+ = A = + a. v+  sitax
opes ergo expressione Generali quadrabilium curvarum. X