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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 5
# Folio 1r, page id 00068218:0001
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sb + HC multiplicari debet per formulam aliam, ita ut in producto tollato sublata sit irrationalitas
b + C in dee aequ. bd + bd + be + ce, aequ. b b + mc. sit daqu. b.
fiet b + bc + be + ce. fiat e aequ. = c. et habebimus: b2 ( b0 ( bc) c
b ed vel carius: b+c in 1b+ 2c, fiet 1b4 1bc + 2b6+ 2C. fiat Z aequ. ()
et habebiious: b et 1 aequ + ( et fiet b= c. Hinc si sb + sc multiplicetus
 b+ per sb - se habebitur  b - c. sed et si b + sc multipliceto
per b - sc. fiet b - c.
=. b Vb + sc+ Id mustiptican formula multiplicanda per aliam formulam, ita ut
 productum sit Grationale. sit b + c+ d multipl. per 1b + 26+ 3d. fiet:
1b + 2 bc + 3 bd
 1 bc
+2C+ 3cd
+ 1 bd + 2cd + 3dd
erit 241 aequ. 0.  + 1 aequo. 3+2 aequ. 0.
Ergo 2 aequ. - 1. 3 aequ. - 1.
sed et 3 aequ. - 2. ergo 3 aequ. + 1.
a aequ quod est absurdum
lig dodratilum
itaque hac multiplicandi ratione Ctrinomium ab irrationalibus liberari non potest
Ergo assumamus: 1b faciamus ergo solum 2+ 1 aequ. 0 et 3 +1. aequ. 0.
fietu et 1 aequ.  fict b 5- d - 2cd, factum ex b ++d in AsC. 
per compendium: b- c d vocetur A. et - 2cd vocetur - B. fiet A-B ducenda
in A+ B et productum erit A =- B. seu b +c+ d - 4bc- 4d (2Cd9 - 9Cd
Ergo si sb + +c+d ducas in Ab- tc- sd in b.cB d  sed
porr Ergo b+ c + d in b -c - d in b2 - c= d + 2cd dat b + c + d - 2b C 2
jam: b- c- d ared dabit b  1- 2bod
1 =c = d
b + C + d - bc - bd - bC - bc - bd +Cd + ed +2bcd
rgo +b per 4b = bc - 2bcd dabit b - 2b
per + b per + b
d
d2
- 2bc  dabit +b - 2 b72
polile per - b + 2bc
cet
+ d.
4 ct = 2 b d
+d4 - 2 cd
dabit. b 4 26
25+ + 2b1g
+ 2 ct d
 idem prodit si pro d ponas bvet c.
sin facias
b per + b per + b +26d etiadabit + b+ - 2b
d - d
+c9  26242
+d4 201
Et generaliter quia:
quia  +b per 1b3- brc +2bcd dat +b - 2b5
patet
=Es
+c4 - 2b4
+d4 - 2c2d2
-2cd - 2cd
Le per  dat - b +c
ideo facil etiam per quam formmlam multiplicari debeat +b+ c- d, vel + b - c - d.
Hanc methodum prosecuti habebrinus resolutionem omnium aequationum
Nam ponamus exempli gratia loco + b - c - d ponamus X - c - d  aequ. 0.
et spalturio tne aquatiarem dum C et d estrogaus a potert au debitam
b + b2 + 2b cd
= bc - 26cd 26