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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 30r, page id 00068000:0059
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3 dividatur in bina quad rata xx: hh et yyenh
Niha hac
3th B = Xx+yy  unde hh - XX- hh + gu sito. si 
sit Xth X sera)h Y Fh_ (Pia)h sint h = P ( L) + f(y -h)
eton aaas leaa as sed ita connescit h, explicatis X et
et
IhR-
piat be
X =eh +C y = fh + d
Y
3hh = eesh + 2ehc +cc + fl, 2fhd + dd
ac
sit cc + dd = lig et fret 2h = eeh + 2ec + fth +bd, et cetdd
a
=
na
ea
2ec +2fd + ag = cc+ dd
haque ee-5s
99
aa
Ergoe et fngu possunt esse maiores quam e
in erant D vel 1. si sint ambae a fiet vel ifiet
h= rec +sot 2et 2d + ag 2c+ 2d+9 et fit rc+ rd+9- cctdde: q
sit aq = 3aa - eo ff fint 2ec+ 2fd + 3aa - ee- f = cc + dd. sit
3aa ef fint c 3aades2cd+ mm, et fint
m = c + d + e +f. sit 3aa = - 2ef - 2cd 2ef
seu cc + dd + ee +s D 2cC- 26f2d +  +2cd - 2cf- nm
3aa -2de + 2ef + 2cd- 2Cfmm, fint
fia 3aa = 2dC 2 2cd +2cf+2de- 2ef - mm
fietue c+d - e - f = 4m sint _ d et f = 0 et fiet
ramsit f20 et C - a = 1 sint V,d, 1. C = 3aa tmm
fiet d = _m + e+f - c .= 3aa + mm - 2cf + 2ef, : 2e = 2C
Et =M F e -C) +2 qu (P-c) (2f (8- C)) = 3aa + mm (+ 2f (e- C). Hinc potus
sit e-c = l fiet 2lm + 2ll = 3aa + mm, seu
pimi
Cl- m)
inm + ll + ulm = 3l -(3aa sit a(l - a) = b () fiet
a l- m = 3l+ 3a, b. fiet M = - 3bl3 ab + al,: a = bl+ aa- al
seu = 3bbl - 3 a bb (+ abC) = (ab1) + a = aal seu  l = a + 3 abb, :, aa = 3bb
sit m = C3bC+ (ac 36) - 38eb + 9ab + a + 3ac bb - 3a b - 3 ab 2 aa - 3bb
a
seu l= - a3 = 3 abb3 :, 3bb = aa et m = 3, b 3 ab, ab + 26b =2aa,:, 3b6.
seu m = 6ab3 -6ab + 3aabb, :5 aa - 3bb
a
Ihh = xxtgy sit X = eh: a +C, fiet 3hh = eehh + Z ceh + aacc  aay1: aa
f20 fit D =
sit cet gy = hg, fiet 3h = eeh +Z ace = ag,: aa. unde h= 24_e + 9, :, 3aa - ee
5
C
sit a9 = 3aa - ee firt 24ce + 34 lec = cc + yy
siet +3aa = c+ 1gy Cc + ee 2ce + gy +2Cy - 2Cy = Mm = 0
et h = CC+99,: 
+rcg- 28y
( C + y - e = m et 3aa = 2Cy -2Cy - mm
sit c- = l Aet Hy=m et zaa = 2l, mm. unde
Ergo
tollento y fit y = m -l et 3aa = 2lm - Ell - mm seu l-3aa = mm + l -2lm
nem
30a mm - Ely = - zaa nm + yy -ily = ll- 3aa
sit me m =n + a fint nn +gan taa - Ely =. Zua +H = 3aa - ll - 2
nn ll - 2lm = 11- 3a a
3+ pp = 49 3=99 - pp
qu2 qu1
nam -um sit est _ qu (m- 1) - U 3 3 1
4+ p = 3  q. p = 1 sit q e 1tp = 3- p p = 1
M a +n
20