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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 64r, page id 00068201:0127
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Ergo per aeq. 42. eut:
Ca
e
ag- f.  - la -lm B
Ga
I-Im- m
3,f3 - agf 40eh, 1 Im -m ag- F C
3Za
a
0
(46) sive compendio, multiplicando per crutem: 03)
si
63
(17 ) estautem D pa lEm + 213m 4+ l n , et 8 - 16 - 3 V m 2ln
4) et fer: 12 m + 2l’ m  + 1 m. E
Cunque nulla alia sapersit aequatio,
-l - 3lm - 31 2  
-ln- 31m  31 ms (da
=m
=
patet unam ex
duabus incognitis, quae nempe supernumeraria est simi posse pro
arbituo, ita scilicet ut aequatio quae inde oriri debet, fat
quantum licet simplex, palet ergo eadem hic opus esse methore
qua in aequationibus numerorum explicandis valore ubsim aliquam
exincognitam ita pro arbitrio assumimus ut explicatione
facta, aequatio residua fiat linearis seu rationalis: ita hoc loco
Cvalore plano
quaeritur ejusmodi explicatio itsupernume rariae
ut, residuae valor fiat planus seu circularis
Ne quis ervort sbsit, aequationes 2. 3. 4 ipplicemus ad Tubum
 ultiplicando in se X+C Nam X+I X+m  x. I-m
ca unde fier: X + lX + Im  X4 X - 1 - m, unde:
+m.
X3 (+IX) (+ lm) X - Vm B0. Hinc sequitur quamdoeunque
verus ergo
+m. - 1.= lm
-l . Lm)
calculus superior m. L mb
= mv.
in aequatione Tubicasecundi
termino carente aequatios tertius
terminus est affirmativus sequi aliquid
nhaginarium, redicem scilicet extrahendam
ex
=12Lem - m. Hinc sequitur nec
alias formas in hanc mutari posse, quia  fieri non possum
aequationes radicum realium, ex aequationibus radicum magi
rariarum.
Si Aequationem 49 brevius enuntiabimu potendo pro- l- In ponendo yk.
v
a
60
(51) fier: Qai aa catm +aym + ma  a
 po  sibstimendo ,  pu 22
((3) fier:
5a
d
2
N 
et pro n substituendo _  B, extracta Radice
O2
av q
(15) Na 1
a
1ds) Ya
2
E5t porendo  p) ve fier: Av, p v ip  v Spa
56). per V
(57)
1fer: V
(5) eut a M po
12
a
62a
11093
sorxa
.Ergo   a0
Egi juncta 50 et 10 eit, b
8ta, cub 1 +4
+lm + m
estra
a3
 adeoque poret pm -3
1H0a- Voa ce
ip 1y10396-1 48a
9 Aub (42+ 43),a.
et divisis ommibus
Ergo
Habitis jam
litusi radicibus, l. et m.
48a cob (474) habetur et a, et habita a habetuor X, nam X + a  pjo, et X1 a,o
m a talt alpi o ex topotres, ne sub fim cduli cvanscare nccspe es aicitiotam Y.
quod signum eris stail elerans calculi veri
1
(45)
lm l m-3m