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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 7r, page id 00068195:0013
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a+ b = 0 fit aa - bb =0 multiplicando ab per a- b.
sit a +b+c = 0 fit a + b + c - 3a abb- aacc - bb cc 20 nont et ascenditur ad 4
multiplicando per +a -
nam a habet 21 valctes
derivatur et ex praecedenti pro (6) ponendo b + C, nam ita ex aa -bb) fit aa = bb - 2bc - cc =
sit aibret duo fit ad uti seu 2bc, = aq- bb- ce, quod quadiare utrinque oportet, et habetur
desideratum
sit a +b+C+d =0, rursus ad libeamus proxime sequentem, et fiet pro () ponendo etd
 cc -1133- 4aa cd = 0
. ce - 1b dd = 4bb cd,
414
414
au
et fit a  aubb + sccdd +ar ed seu a +  b + ab 156G dabb +64 B
 +cdd
Et quadrando utrabius
6de
-2abb 2abbcc - a b, d
abab abbudD
ab G
2abb
+
1e
= aabb Jircedd
equdd iis Cdd +audd is ed
 (Guod  edd C pantuodus nauecte mious lcede e d
Ccd
aqu.
el
nqu ad d Nna ced
(+ 4a ccdd (+ B aabb .cdd) (+ 16Cdd 45) Cd) - Haa edd - 1b aa
+ 4b7cdd)
16Ccd
bl
Et fit a - 2aabb +6cc dd = +4 na q cd
 + 2 cc dd
seu a - 2aabb + 8cCdd = 14 a47.
bb cd
-4CC
Et quadiando utrobique fit
a + 2ab ab +6aabbcedd
410
quadr e a
+ 4 ab ++ bbcc + 6 aabbecdd, + +C d. quadr. d.  - 2aa bb
4a bb
+64 d.. quadr. de +bcc0d
S- 4bobbec + b ccdd +  8ed iltod r in 1aa bo + 8ccdd
a H2ab
+aeb
+2ab abba
ab
24,
+4a 8 (d4b0) aabbec de
64Cd) H
a
d
cenditur ad a, nam
-gabocl)
+1ba cdd
habet 2 valores
araabb in Be ad
abbec per aabbi
sper aa
c da
ado poratiedo
2
NCd
ue d) CraacdoZ- nalbbecdd
b reo aaccd
2126 1476
58.
522
+gabbcc
V
40
Et fit denique a - +abb + 6ab 58dabbcc dd = 0
( a = 1 b - 1, c =1 et d = - 3 fet a + b + C+ d = 0 po ere a = 3 + 3d = 6564
abb get = 6 (aon aab taur neab u rbb16) + ap  (aa +bb+CC d ( = 1 7 + ( abrC, dd. 3. 9) 2
 a bb = 6+ 218, +27 = 2220; in 4 = - 8880, ab = 3 (cv p G2) +F (_d, - 3. 81) 23 = 246.
et 644  = 1 16
agtbccdd = 9 et 1G= Se
bb  Catiae s, 3,  R S  miberimur vui pu 58. lut 243 + (3d 4 86 1 4. c 1 6 1, 6. 9 d. 9 f 2 86)ab
1udd
(2b )
aubb
3d - b5b
688
60
+0
Et calculu
robatus
is