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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 84r, page id 00068198:0167
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luide fua pog. derse)
Videtur autem in  semper effici posse ut in. mvot aan + abdv =0 sit
n: m constans. Ponamus aequationem fuisse fyZ+ ag aaq + at dZ = o fiat
= lvra (l: a)v et dz = dll:. a) v + l.: a) dv et prodibit ut
mlull ve + a p + aakalv + aast do
et n: m = constanti Ergo g: IUf: aa) = costanti seu aag: Uf = constanti hia Ergo erit
H = ag = Ufh, et H = aeg: fh et prodit aequatio:
ag: fh) VV taag + k al v + dpk (dv = 0, m = ag: fh n = g, b- klia
Kdl - , fiet meov + aan + acv + R do = 0 sit jam v = (y 1g
+aanyy
+ac pyy
sit jau v= (p: a) y + q et fiet
+ acaqus mov =m(pp: aa) yy + 2msp. 49y + m 99
+ acdpyys 0 = L acV =
aan =
Cabdv=
+pC y + acq
+ aan
bapy tabdq + bpdys d
ib si asolulus temunus esset destinendus fieretque t9 = 0 seu q constans fieret
qq + ac: m) 9 + aan: m = 0 seu gq + (ac: m)9 Haacc: Amm)  aacc - aanam,: Amm
seu q = a N(cc - amn): 2m oportet cc-ame: amm esse constantem
et redeundo ad aeq. (l f: aq pr + aa g + KdlD + KIdV fiet c = kal: a m =: aa
ad = 4 inm h. a +W fh: a
seu _ A Ca Haldl = 4  Th + 4 au59 seu aadl e = 2 sasy rallos 9)
hunc si esg ag +  hfl constans seu ag:hf constans, procedit
quadratura sed h est constans ergo debet esse dF. Et redimus ad prius.
nam sustrapostulabur m:n constantem
si in 57Z+ aag. + a k du fecissemus Z- v + q fieret
 -aq: v fieret faqe + aag = ak9 do 
Z+ Xx  + AK dz. dx sit x. _yaR
y-
nam x = an
v0
dmin + aann  K (aadu aamdo): (a dn = ande)
a mm + aannve + 
si
on
7Z + V ∞ + ak  d 1p: dZ
L
va
sit Z
2V3
nov
CXRa 1L+ 10y 29 - 31a430y
2 +y  21+y
Z4 ( PdZ + ak di = Z = n a +10y p = 39 a + 30y, et fiet
 Va +31Ia. 10y+ 3. 11a 10y + 1831 sit 10 estans
WYdZ - 31 a +3. 31. 30a9 + 30gy, a du + 10 dy
zez adu taduidys +e ade 0) gy + Hlaio dys F 1a 10 ydy + 31 y dy
3 aadpt
et debet esse Uf: aa = m et g - n
sielque ute rua yys + y +  eo  
raM p
C
=Pytag. iy