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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 145r, page id 00068198:0289
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adeeque
AB, X. BC, y si datur momentum ex vertice, dabitur pxydx, dabitur
et  (xxdu.
Videamus an non hoc prodesse possit ad pro-
movendas quadraturas rationales.
sit y = + B (aC + ab XX, :, ah + XX) .+ (aas+ gXX, :, a( + XX). patet
yxdx esse summa invenibilem per quadraturas rationales. Quaeramus v valorem
ipsius XX per y; atque adeo ante omnia tollamus quantitatem irrationalem Fret
Ac tabxx = aF + raafgXX + ggX = (t  F h + Qaa f XX. + gX) y H (aatiht rahxx+ X J yy
4
2
+ aghXX
qu (at + XX)
Jy 29y +gg. ab) X HEahzy- 2ftghsay. + raafg- c- aahb) XX faatihysys -2a fly ta fs- a ch = 0
ah + XX
O
l2Z tam Z + aan = 0 fiet
1ZZ + almZ + (1: 4) namm = namm aaln,: 4, adeoque fiet
unde erit  
Unde hoc loco pro Z ponendo XX, fiet
qu (2ahyy -2 (af + 9h) ay + aa (25g - ac- hb)) 4 (khy y- 2 hhytaass aack, gy. 29y +ggu ab)
arsum- n) - am, : 2l
t
= (2ahyy - 2 (af+9h) ay + au (25g - a c - hb))
ibi examinari meretur pars irrationalis seu vinculo inclusa, quae summari poterit per quadraturam
CX 2
rationalem, et eut
4
t Aaahh 1
 acahh
- 
2, gy - 29y +99- ab
. - 8o
2
-gaagbis
et
y- (C: 3) +6.
4 pabXX + aC
+
e
ubi cum evane scant y et
reliquam calculum inutilem esse
patet
apparet
reliquorum
nam aba
Quadratura rationalis dudum habetur
D + yy -2y7
1y48- 2968+
EE
omittatur D, fiat 43
Jam si sit