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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 17
# Folio 2v, page id 00068230:0004
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a + b, a -b = aa - bb
a + b aa - ab + bb = a+ b3
a + b a - ab + db - b3 = a - b
ete ita porro
mia- nsa
mna-nnb
mnulaa -mndab = un 3bb
Ma + nb
ma- mn V ab + mn V ab - n3 + 63
mt a - n b
ma-mn Vab + mu ab - mn Sab +n b
d
ma + n5 b
Ma =nn Vab + mn Vab-mn  a b+ mn Vab = n 
mia +ni ma - 16b
Et ita porro. Hinc enim apparet progressus in infinitum.
Nota: possunt m et n negligi, seu poni = 1, quasi esset tantum Sa + N
Facile enim ex calculo pro solis, sa + ib duci potest calculus proma +n Vb. idemque est
in Trinemiis aut pluribus ad huc nominibus
Qui casculum eundem pro Trinomiis peragere volet,
pro praesenti Algebraestatu
n sextigradus
poterit nunc quidem subsistere in quati gradus irrationalibus
seu in fu
lem A ad or
.Nam lonus procedendo, calculus
ultra
nimis prolixus orietur Nam ad sudeaidas procedendo a
a Ba LY6+ DC
Calculus nimis prolixus orjetur donec Tabulae quaedam combi-
natoriae prius sint praeparatae ad praeimovendam Algebram
po sed
et procedi
 erdoolexe
ad cubicas qe qua
unt pl nassis plurmomiiis in ruditibus quadraticis sbst potent subsisti nis
neessariae praeparentur.
sit a+b +C =0 seu a = 0
fiet (quadralius at - 2aabb = 0
pro tollendis caliuis a + 3a63 - 21 ab c = 0
irvationalibus
usque ad Cubicas; pro pento quinomiis aut
senomiis potert in quadratics radicibus
subsisti
Diguintiais a - 44 64 6a b5- 124 abEt = 0
a  ab + ab
+ d b-- abe+ b
Uo. Haec Methodus tollludi rctio aales
non tantum usum habet pro fractionum
denominatoribus, sed etiam po aequa
tionibus in universum
2
ut MVa+
seu in L
ac
pro quadrimonio sit arb+c +d =0 fiit -a - b = ct d et a + b + 240 = c + d + 2cd. seu arb - c - d 4 2 2cd
6d
et ita res ad trinomium reducta. unde si a +b - c- d boletur ee fint +C
Ex Tabula illa mea combi formarem  reductoria poteatiaum
ad forgas X, y Z es seu a, ab abc videtur haberi pss
Ba
meralis redectid Prationalium. A
torte iiuc melus se sota adesset Z Miirquia X00 firiit o ne pent.  + 2at +b
Nam
pudrato. quadra sicis per solas
a eu
a
y et Z, ut rtitet solum aeui. pro co quae densi eptitibi
hibe
ad 
eito X=0
invenientur
preo quadralicis persolas ac, a, a, pro cubicis persolas a, a, as 1s 2d quarum opetollenda literae  y, L. cdB
suffecert autem rem tructari per modum equationiem, ex quibus tollantur irrationales, Et
imo qua co est smplit abis sipeut 
eamque in rem ex hiberi cheoremata etsi enim methodus tallendi irrationales jam ab aliis est explicata
a X- 1X NZ Hloqu ae sd pu y liamio ajpugendi  ab, tionral s, aqu utit Aes alabid deniq sond tr d a tinemvet 82, EB, eoq9, i atta 5
ipsam tamen sublationem non actu ipso exhibueri
pro quadrinomit