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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 219r, page id 00068196:0433
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tenternus id generaliter in. 2 (X e +.) = uxe ., _C. X +.. 7:, x+ 1), quod
expliremus per Z, ita ut possint tolletermini duo maximi in denominatore, quo facto fiet
ex irrationali esi rmre) = e (. qrenu, (+ m): :
22 +1
+.1) 
ill 1Z+m, 3)(ZC +..:  28 +.., 1Zim). Et rurgus similiter tractando  explicatione
pet.
facta per fY, fiet ex irrationali fiet:
Ret.
re
lvte+
(nV+p)C
=3((. v C+.. (AB + p:, v +..) = - 3)( V +.. ,:,. v.C.) ita res reducta
est ad aequalitatem videamus ju graduum. Quod si um licet tollere primum
teminum numeratoris, et ultimum denominatoris; vel contra;  mutuo
divisores. et ex  facando  2 faciendo  rursus. 
viandum res redibit; ad aequalitatem graduum. Nam esto
X3 + bXx + ac Xtapb.
X+ IxHtmXX + aanX, fiat x = G 2, et prodibit inde:
t
srah
ali ress
aat 2 + ac ZZF _ a bZ + a
=se i hubrhranre C. e1 + a z ranbes t aZ
aanzamzalutab
ita nit  lucramur cum fiat solum permutatio gradus inter mmeratorem
n  + amZZ+ alz +∞ ad;: L
e
et denommatorem. Ergo potius tollamus dnos qerminus temaros in numeratore,
a
retr
 re
id potius considerandum, quia solis explicationibusrem ab. X +. f.
frnctionis v C +..: v)
ed rdaximus ad V +.,, VC +.. Nam adeoque et d ste +.., v
ad  +..  V3C. Ergo vilissim ab hoc res reduci poterit ad X +.: 1+
sed quo Sed quia haec paulo implicatior est via,  nec 
universatis; placet generalem aggredi, quae non tantum omni irratiorali
sed et quod amplius, omni aequationo allect applicari potest, ubi y et x
dutcunque continentur. Sit aequatio g iio + mty + 12 yy + 1139+ et
un ub 18, MI H2, c sint forgulae integen ratio a alquoad x, esi jam X ita
es explicare possit, ut formula tollatur isen it e s
ossuntus terminos quos lubet, tollere.
oms praeter noni  et suo
fuc ergo res redit, ut sciamus
Csi place+
quatenus tolli ressit gradus omulae 10i t. 1X + 12XX +. 13, X + et C = 10
1eG. al e
cralis formula est semper produs a  per constantem (si placet)
divisa est semper productum x XXF3I, XI_I, exc. fiat Hic ut tollumus
autem
Terminis duoque summos Terminum sumenum sint X= lx m in alia aequatione
ex hujus explicatione facta, fiit X 1Z m, enso Ex +21 = 1Z + 21Z + um,;
2t m.  jam ut in producto ex numerato.
ribus evanescet. sumunis terminus Lerortet in eliquo producentium, qualis
zam sin adlemZ trimois
s het
125 seu X= = 21Z:, 2tn
notolters simt ferminum primum et secundum facerem
est (l) Z +21evadesctier
si voluissemgipnmi
analu ta acm
2 ft  4 lZ t au, et fiet
+ 2 ap
ape. Eequane
erifiet talza aan
eque +am, et
abt Aa e hZ + C toinudi: tusu qsam
eo +gla De   ex XtEt fiet 9eZ + 91 a
fiet insre
tullatior. ed
censiderainum
qua
1. 40Z + 21. 
8: 802+8
mplimus tadem gura tollere terminum secundum
cum foparit
ru  Xi.  p
900
novae numerator sit productum
sia: 150aZ + s1a
ea
1 6j 3 51. 40q
+gZ. +g1a ferminus focundus
gone
41 80Z 141. 81
Terminus sunumus erit prodectum omnium ut qua +2180, 90a + 31. 80, t Qat H sed ter
B1. 81
x. 29NaZ1+914
minus secundustrit summa omnium combinationum quales quales fiunt ducendo
sset
,72180Z fentoh
unam et a +21. 81, n omrigu reliquas  unius radices partem absolutam, ut 914+218
a + H. 80
velut in 90 a + 318
praestat autem sem per tollere
alsoltum in omaium caeterarum radicum confficientes ad
summum tantum terminum,; quia. Interim sublationes secundi termini possiumas facilus
+X
et reliquas tales praeter ipsam qua +2.
consequi sure radetos e sormale, aalo sit eum.