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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 37v, page id 00068197:0074
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Quaeritur  ex AIxx -bbB, XX - CC) sit X=
biles 
compendio,
c a sl:
es rationales in tegrlas s
siet XX - bb, XX4CC = aa sN = bb 33, aa SSV - CC 13, = a  tbbcc  = aabb se s 27. 
Cujus per multiplicationem producti Denominator est quadratus. Itaque efficiendum est, ut etiam Nume
+453va Ntv + 4a5W AV
+ 4bbcc tr  A+V + 4bbcc V3 )+v
aabtec st, per compe bb +CC per compendium vocetur 99
co
=aadq = -fevB aagot veico a sqo vtr
=aa glico ve-fgatvie
et esic rantatus
Yt- 2afg9 tvc0 LV
24498co10
Et stabit totum Numerator se ex ebb producti ex xx- bb, Xx- ce, ita stavit) Abaa- qq ap
+. a acctq
aaqu l
Posiemnglo 
  
tas
ractito
Haec formula ut ostendatur extrahibilis quadratice, identificetur
quadrato a Latere aa YvZ t
+QPZ
+aE +7
2
gale nempeduno
Y+ vs
hacto 2q
Et fiat e =  c +  Ergo aequando partem irrationales
fiet
+2 ua LV a
-243d V - g 
Qetedeo
+ 4aa -Co2
l+ q
Et aequando partes rationales, fiet:
traa Htoo+ na od a a
+99:
-93.
-4g9tv WoH
c
4
(2 49Z
 aacges vZ
ul tZ
Hic nullum occurrit amplius compendium, nec video divisibilitas
glicuius literae per aliam, seu ad eam reductio effici potest satva generilitate
Tantum ergo superest ut omnes literae quantitates variabiles t v   ,
ed (acrend t iole ut v 2oh+ uh
explicentur per unam, verb. gr. per
=3ot aoh 1- ol A1L es = 50h + 3, t. quibus addi potest litera l.
Hhabemus ergo arbitrarias minimum octo vel novem, opus est autem etiam
aequationibus octo identificatoriis, quia aequatio assurgens ad  gradum
quartum requirit aequationes quinque et assurgens ad gradum secundum earum
rebiqui requirit tres. Itaque spes est rem hac ratione confici posse
sit  V- toci + nh. ( = 1ovd +nh v= 20C +2th = 30co + 3th  - 200 + 41 h.
 Z= 5oci +sch  et + sit 1g 2aa = nim, et   ( M  = 80
F et exaequ. l. fiet a alqque + mmtr + minco  elcdco
40 = (20. 20 +00. e0) 2a -(00 qfbo. 3 sun ( , al 40.  et inimtozermm u
AL∞ +
rator quadratice extrahibilis fiat. Explicetur ergo, i rascorto 33.  aspsto
+aa seY = + f Et bD + aco +67ft vcda
+ bbcc 3 = + buccttve +bba V + 6 bbec tv u 
d
CaabL HVB a a +C3m
=aaes eoco
hac
-00. 00303o rna
 2. 21. 31aa - u umm. , al 40. 51 um 1021 CBVo3I ero
ititr
sta
11. 20
oB S 
L2631
(3(3) - 31. f 
99 + 2aa = qu (b+C) et qu ogequa =nn
11. 50
mmII. 21
hh, al A1 S1
gu - 2aa = qu (b -c) = tum
W- co = () (00-2d)1o 2ia
et , et sit + = 10W +na v = 20W +  a  2 = 0 = 30 10 + 3ia 
8= 5oW + sia Z = 60W +61a, et fiet raa WW= al50. 60Wo + al 50.51 aW + al 51. 61a4
vel ommto
sit cdFZ cd + ip =
2aa I 451)
 + raa qu cot ) - al z vel mnbv- nnco ib  + raa qu ( + Y) = al 
 = al9.
Et ex aequ. 1 fint -mnt Vnnco + 2a a sidlo
se
mm 10. 2
nn -70. 31
+315
mm. 11. 21
Mm. 10. 20
nn -31. 3.
si sumat
nn. 3oh 3
Ex Ulo quaeratur 10, ex aa quaerantur 21: Ei ralores
substituantur in aro et ex a qarm aliqua ex so, st, bebi.
 sed fortasse commodius aliquid reperiri potest, quam ut omnia referantur ad Cor ve
posset e sumi quid +qa. fortasse tame optimum erit pro basi retreri 1d + 1
=2af9974
Sit 89-2aa jen bbtcc- b
uaam
W = co + 1
W= c + quolp ao + 60c0 
Uro =coo + 2a
4eo 1 out
ergo ex aqu. Y
d
slto
FSauptrur) Exaeqirda
aa tvrc p  = lioro 2
ed
Extractio sasti
trrtuo ipsius
cd
99 = bb. + cc
aa = +bc
ub raacs
+aato
ggtraann
at30
raag3 coipse
21=
.31 nn = 51. b1aC7 1
3odizun-Serbt al. 120
21 =.
1omm
pro aeq. 5i possett to, co
hatieas
etoz explicariper
aegeatones forum
coi
pr s ossux+ihsae
W indepenitas ab cdvele