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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 36r, page id 00068198:0071
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su
a Car +cX = y fit (200) aY + acX
ab + a sae +gx
= yyr sit aabbt ae = af
pro compendio
 et ex aqu. 2  siet aer + a ex = a fyy = aagKyy = 2 aab yy tac +gx. Unde quadum
a ir +2a EIX+ a’ CeXX - Fryy - 2a9r Xyy.
=24cf.... -
Xxyis
4(56)
asu +ratgx ta ggrxy = 4 albe y , +a bbgX y
Unde ordinando aeq. 5. secundum X,  et subordinando secundum y, 
-+ dbbg yt- 2agr yy + 2a cr
+2459.-2acf
++albey +24 fryy - ae rr
a ff.
a99y- 2ac9yy + acc
Efficiamus  si fieri potest, ut fractio coefficiens ipsus X sit deprimibilis
A9gy - 2ac99y + a
seu ut numator dividi possit per latus numeratoris quod est aaguus- ac. ita enim a habebitur
valo ipsius X in irrationali vinculo non habebit nisi yt, alioqui assurget ad it
itaque aaqu- ac multiplicabimus per Dhyy + aK fit (imo) agh a chyu
quod productum debet (800) identificari cum
ergo fit (quof ah = 2a5 - abb et (1omo) R = - 2r
+a gK. - a ck
-qa bb9) - 2a gr yy + 2a er
+21359. -2a cf..
et 12nos exterminis mediis. ch + gk =- 29r - 2cf, ubi pro h et K substituendo valores ex gerte
fiet (12 mo) ( rac f) + 4cbb (=2ag1) = (2agr = 2aCf) sed ita patet fore b vel c = 0,
Quorum nentium licet
Alia ergo rem aggrediamur via, et) videamus an liceat yt et y
tollere vel destruere in quantitate ex qua radix est extrahenda
om pendio pro aq. 6. scribamus:
XX + 1047 + 1ayy + 12a5
20y2421 aayy+ 22
C
= 30aa y +31 9 + gra seu brevius XX + aB = Y aa 
(7mo
20 y + 21a4yy 4 224
ex og. 8 fit (9uo) xx + a0 x + aa  = (7 aa + aa B0
49)
seu
Aaa 43 + aa 0
∞)
45 
Ergo coportet
ex Bah 8 fit (10mo) X = a v23+0C = a0 Quoniam ergo in Y YD  + OC
debet evanescere yd et y videamus quomodo oriantur. Sane in 9)d. D est
125
16. abb. f99 4,6b 99 + ab e  s 99), yt quod debet ponio, et qvanesent
e = 16 abbf 3aa ff 16b 4abb evanet e, et  yd, et pro e restituendo
et
sed
 = id non d
Vatorem ex aeq 8 fiit, 12aas - (1 abbf + (15) b + (4 bb a) ( 4 b) = 0 seu aats - 4 bb af + abi ab =0
q pudit
seu fiet a5 bb Ergo per aeg. 9 fit autt  bb + nc = 2 bb Ergo ac = bb
Rrestat ut in OO + DY investigemus Y firt Hinc in numeratore ips qoefficientis ipsius X
Hinc etiam
eo arscit G. Nam- 40b9 F 2afg est 29, (- 2bb + 2b6).
tabbe =aa eio  seu y in absoluto, erit o, nam fit 4 +b 4bt - +b+
Verum  Ut jam v tollatur in OO + DY patat hinc in () non reperiri y
sed solum in 5+ fergo fiet dG 9924 fr  15 L0. Quod fieri non pblicet
Ergo tenternus efficere ut ex anescat terminus altimus
a
et penultimus
quieu
seu absolutus  qui in O +4DZ est 4acerr  a cerr = quod perse
succed penultiuus seu gy est - 8 agerr - _c fr + 8 acc fr + 8a cgrY =0 quod
sdque iterum per se succedit, quod miror. Unde fat imo et per se evanescit G G
an a BO + 4d Z (166 99 = 16a bb 5. gulu 4 a 5.49 + G. ( abbequs qua Hg,
sed
prodet
(16abb599- 166 499)
et manet in vinculo
Itaque nihil prodest nobis calculus neque enim
une
aa bb + a et ange +2 aab Saetgr