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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 145r, page id 00068199:0289
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=289
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fyyex datur ex fxu videamus jam
quae sit relatio inter qda
Xxdy datur ex fxydx. Videamus jam quae sit relatio nt
inter
et
xydx et Cydx
 sit  y = a + bX + CXX + dx ext
et
Six sxyixL
le
(ydx = V_ et sxydx = co et Sax sydo = Z seu Z= finosdu
+ fX
yaB  dx, a + b X + CX2 + d ph + ex
 bXx + cx3 + O XE, a de xS
Ca
a X
gax.   h + a X + b X + C. X3 + d X + C X ux dZ. X el:Z - h + K = ( 
xly = dx
Ixydx- Cd = K + Y + a xx + b p + CX + D X
aL. X p. 2pL Co
ax
o
sx) yax = Z = l + hX + a Xx + b x + Cp +  X d, Z. X idx =  + l: Z + h - t
1.2
4.5
2.3 3.4
dz. X = dZ. X = Zax: X et dz = codx Ergo d Z X = co.)
Ergo diz. X idx = B : X - Z2X = CD + l. Z + h - k
sed nobis id curandum est, ut  reperiatur reu co et per (codx
dxsege Y- m + H+ X d x +B sit co  ax scolx: x = 2
ientu lastaman
e
X
1.2
(dx (xgax = 1 - PA saax
X
CH
2.3
3
Et fiet
Ax+ bx + C x+ dx + ex etc
tM  1.2 23
Et sit e
s.b
3.4
45
Et 2X = -K MX + a x + b X + C X + 6)
213
34 4.5
et s-  xtXY - m + aX + apX + C x +D x + eX
ax
 jam Epdx +xdi = V + Sxydx seu  + ec
dX
Ergo 2V + ex C - m +h = V. Ergo exdata Cxydx
Ergo ex
x X sit ex constans. Ergo ex data sxy it sxy datur sy
regularite
jam Exu datur ex data  syus. Ergo ex data _ fyus, et sxuu
Ergo ex data syus et sesyus datur sy
sed res applicunda ad exem
plum nam in quadratura. Hyp. et circ. videtur nimium efficere. si bene
succedit, videtur prodesse  reductioni curvae Conicae.
si verum est thecrema C, debet calculo verificati
x Xyax + Scya+
da
nem pe
XX
quae res succedit, seu dat identicam. Erous verum est Beorema
sXyax = LHXC LXXy =  (XXdy et
S
seu Sydx=  sxyaxe +
1
de
xydx =sydx - L (dx
da
1
Sax dus. Ergu ex D et Q tit
dX
Sxxdy
( eren)+ Sxyte