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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 74r, page id 00068199:0147
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ay = (1) (ba + CX Y) + (ma + nX). Hujus quaeritur
momentum ex tangente verticis, seu initio ipsarum X.
quod dupliciter obtiner potest summando Xxdue et
summando, VXdx. jam yxdx summari posse manifestum
est per quadraturas rationales. Ergo et XXdy, ex quo
quid fiat, videamus.
2d
aayy = +ba + CX  + 2 N(bm a +bn a X + et
maz nX
e
cma
e seu compendo aagus - Fa - gX, 2 = 4bma ete
4 a ubi f = b+ m et g= c+n 4
c
(5t0
1fate y = 2fa yy - 20099yX + 259aX + 9gXd= 0
4
bn a X = Cn X
Osit g90 cn =0 seu ce + nn +(D en (= Cn =0
El
=Cm
ey
et fiet CC + FB + ~ nn + CN +Z c = ZCC- CC =
4cC
seu n + EC = = C 1 - 3 su  (R etiam f. bm =0 et
ne seu n: C = (0 - 1 + 1 - 3, : 2
fs - bm = 0 fietque m : b = - 1 - Y- 3, : 2
et fiet a y = 2 Ybm a yy = 2 aVCn yy X + 2bemb) a X = 0
et
e
sit quoque
seu XX
du em 2a ibm
e
e d
e
D. bn a X
ema
2 on Gy + bn ax
quod rursus reducibile ad quadraturas rationales sed
a
+ Cm a
= 2ubcmn
idem obtinem
forma tam imaginari
interventu imaginariarum quod singulare
quam
rationali quae comparandae inter se et videndum an non
ubi minum
per eandem quadraturae gradum
sid imaginarium  tollatur formaliter. Nam virbraliter
quidem tolli per sepatet xx pro X ab aeq. 1 mostam, fieret
et a pro a
rfaegus-2(  HXX t 2fga  
Rx
si fuisset
ce
ex eg. 5. t s V
BX
ua
 seu
=Cm qxx
ubma sed s. Hubri in rellaquamus quanbtatem in
sit jam
sed si ef- bin relinquamus quanti tate in indeterminatam
+fac 
hiet
XX =
27ayG + Aab- bma
haagyys +bn a tema
quod haberi potest per quadratura
rationaem summari et lices inter
ventu inneginariaru