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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 37r, page id 00068201:0073
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de extractionibus Radicum ex Aequat.
X aequ. a + b + Ce M. L aoqu. ab +act be dc. L. aequ. ab
2
X’aqu. a + rab.. Ergo ab aequ. X  _ ab aqu. X- 2a X + a t 146)
et
5
4
4
et a b aeq. X- 4a X + 2a X +  4 a X
qua
e
iga
+a8bX
 16
vel quia X aequ. a erab.
+ 28
4 aX +2ae b+)
Faab
+4
fet X aequ. a +  + 4 a b + 4abc + 4 ab +8 abc
seu X aequ. a + 4ab + +6 a b + abc. ut alionde
Ergo possumus statum scula X8
est autem ab aequ. a b + 4 a bc + abC + 1 a b2
4
Inde aequatio 14b aqu. X 4a X +6a t - 4a, ∞
X aequ a + b + c.
a + b+ Ct aequ. 54.
+gab 12aY2
a+ C+
c4
+ a
+4aV
1E 24 at bCX = 4a bC
idu
- 24467
=12(1bC
X aequ . qX + rX + (+.
abc aqu. 93
quaeritur quantitas a+ ex datis q. r3 54
ro X subslituatur esu intr in aequ. 2. ejus valor ex aequ. 1.
(0) Y12 ex aequ. 4
utique a aqu. s4 b  ex aeq. 3 aequ et a aequ.
Ergo 5+ b
+ b C8 + r 12
144
locum In aequatione 2 substituatur valor ipsius X fiet.
(a + + ab +6 a b + (12 abe 2 a aqu. 9a + 24 ab (.  at s+)
ubi pro a substituatur ejus valor,  ex aequ. 4. fiet:
42 r92b +ab b +6 n 16L
2
Aqu. 9
12 Y
e
bc
b c + 6b
4, 12, Y,  + 4b b +6, 1 Y, bc by +6bc aequ.
o2
aequ. r2, qr bc +2, 12, 972b  2b + 29b=
X  X + lae X + n _ X + pa
Aursus:
d
c
+
+mab + p aeb
+ A abc
in X
+
a
3X3 +7qX HIa X + 1 a
43 ab + 1g ab in X2 - a
ab
+ 23 abc
Sed posterius inutile esse puto quae cujus posterioris multiplicationis productum addi posset priori;
sed jam re recta expensa, puto nos nihil  lucrari per posteriorem multplicationem, nam
multiplicare C in Ft -a, est multiplicare C, x- a in A -g. jum O,X-q potest
considerari ut species formulae D perinde ergo foret ac  si ac si loco D aliam formulam
suntem fiigeremus, mutatis tantum literis (. l. m.  etc. et productum puori producto
adderemus ita enim, nihil lucrabimus, nam si quid lucraremur, nimium mcraremur, possumq
enim similes alias formutas fingere infinitas (N. eae notabilesi ratiocinandi in tabib,
exemplum 3). Et perinde esset si ponamus loco in secunda formula loco D sumta) nos
sumsisse I. utique poterit C+ A assumi pro una cnuantitate. Sed aagendi
tamen arbitrarias uno succurrit pulcherrima gatio si ducamus  in X- g. et
productum addamm ad productum ex D in X-a. Et nusus aliam fingamue formulaque
39X +29 4X + B0 e in X - et denique 41X + 43a in x- aHis omnibus simil
aditis a habebinus utue ad 23 inbinarias idest multo plures quam sit opus e
20 fals 1678
2
abab
aequ.