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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 5
# Folio 6v, page id 00068218:0012
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+ bb + 2bc 
Lad
+bb = 2b22-
aa
b2 Dbbcc = 40bcC)
2bbd
+- 2ccda
b+c+d b0 bb + obc nB bx
quadratica
bc +36
+cc
b+ c
b-c
hc =cC
bb + bc
bb H - cc
+bb = 2bc
+cC
b +c -d
+63CbbC 2bc0
Ebec
=le
b7 - 200cc = 8bcde
fiet:
bd + 2b44
b7+bC - 2Du. 2b cedd
186 cde 8bidef.
+4b+ = +9b ccdd +24bbcddee
b+ 6b
tbcdo
=babbuddet
b + c + d + C
6E = b ed 16bbcade
icerummultiplicetur per
b - bbc + 2bcd2
b = 2bbec + 8bcde
163 = bbc + 2bcd
(etiam possunt locli multiplicando
per 60. bc.. sed et productum rurjus multiplicando,
ita assingetur ad sextum gradum. quod forte utile ad
oscendas progassiones
 C 14 (+36) (+, 48)
C40) proba
si sit b+c+d +et f. Attollendo modo dicto prodibit: bd - 4 lcc +6B C E 4b2 cedd - 40bbccdd ee = 128 bbccddet
qua formula multiplicata per 
rursus sublata erit irrationalitas. Atque ita pergi potest in infinitum.
b. bb  b+c. bb cc H b+ c+d. 9 - 4bc
bC
hc
luc
(+ 2bC)
6+cd
+ b =c+ d
+bd + cd - dd
-cb _cc + cd
H - 2bbec
b+c - d - p
bacad, bisca dsi (3) boc = dd p. bbAcc D- dd =+ 2be bbrcc.dd - 2bc
+lbd ad d3 A (xdd
=bbc AC Dedd d
- b3 + bcc + bdd 2 bed
(2)bFC = (Are sib + 2bc - 2de. Scribatur
1e)
b0 b aequ bb.
B (1 bbacc -dd = 4bbce
fet bacid bac.d, bb + cc - dd - 2be 1 +b = 2bbcC
b +C + d
=b3 + bbc - 2 bcd
5
b+c+dte multipl per ab +e+d per
+c
-dd
+c4 - 2b6dd
b + C+d b+c- d  b - c +d b- c - d, +o4- 2ccdd
  le a () cud p +b - 2Cd bacc - dd + 2cd
to
S
A - 2AABB
+ b + c+ d2
b +d
+ b - c- d3
-b - c + d1 - bb + lisc. a
+ b +c- d.
BA = 2AACC. aequ (4) bcC-dd- er + 166  416c)2
C4 = 2ABCC
 2(2) 6c. dd ee
seu A-gAAVE BAAddee + 8bbcc ddee
est autem A aequ bb + c- dd- pe
b+c 0 b -c aequ. H. cc.
b+c+dC b -cad 7bb - 2cd
Scribatu (C. ergo fiet; () tbbucc - dd = 4ccdd
b+cd re  b+c- d -e aqu + bb + 2bC = 2de. scribatur ( () bb tec - dd ex - abbcc - 40de P +B,
egemim
b+ c+ d + e +f 6 b+ c - d - e - f equ
b osuu non
b + bb P - 2cd - 21- 2de 7
oriuntur
 42bc- 2de-2dp 2ef: sed ta rusus quinque partes
Methodus autem commoda haec est: b+cbac, = C bb - cc. sit jam b caequ d+e et loco bb cc habebimus
bb - dd = ex = 2de. quae ducendo in bb - dd - ee + 2de habebiinus. b7 - 2bb dd. sit misus eaequf +9. et erit
ee aeqo H+gg +. 2fg et C aeque f+ 4591ff99
cui
+4ff 2f9
r e 
da 2bb ee
20d ee
et fiet b+ - 2bbdd = 4bb 59 seu fict bt. 2bbddum alil f
= 4bbff = 4dd
26699 + 4f f
Atque hac ratione pergi onstanter potest in infinitur, ut enim 200g
2dd55
+49g f9
hac explicatione ipsius esola restat irrationalis fg. ita ea tollitur subsequenti multiplicatione.
16ff99
eademque muthodus mutatis mutandis etiam locum habebit in cubilis aliisque radicibus, muta fuss
tamen mulandis superunt enim incognilae plures
b + c per bb + cc  bC dat b3+ C3 pontu c argo dy e. fier: + b2+ d +C +. 3de d+e
N.irationa
104c- d
0+c+ d
B Add
1b.
abect
cb = bd
 lid
b8 - 4b cc +6bc + rbEcdd- 40 bbccdd ee.
i l - bb + (2) c+d
+ b, 1c087
+bb - )2)cad
c
18A a
mullipliper b2. iblod +alit. f9
scs