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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 1
# Folio 2r, page id 00068214:0003
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ut absolvamus sit aequatio.
et tabe + a)) Bv. fier: C + ab e + a a P- 4 a1
sive e + at  SaD 4a  sive e ⊓ Ya D= 4421 = ad et e Y saeb al - ad
ubi manifestum est, ut valor, hic sit possibilis necesse esse, ut vel A sit cgrantitas negativa quo casa
res semper procedt si  major unitite. vel si a regati ae affirma dva mnot quam B
func si D est negatin res semper succedit Quoniam d non nisi ultimum temium A ingreditur
hinc nihil possiumus in B, ac nequidem semper licet velimus poterimus R reddere negatiolum.
Uolit dicalu gdo so enorem
pone  4 bphol mn 
jam pone +b +d,0. erit bp - d. et bd, d
 ac- d’ quantitas negativa, esse debet
Rem numeris experiri utile ert: sit aequatio: XX +a
X + bX + ac
+
X3 + b X + ac X
X + d
1 d.. + bd. + dac
ac(d13d, dev 27 ( + 12acd 4
sives bu aba. d est major quam ac, et cubus ab a d= ac major quad a dac
e
et quod facili fit sumendo d pro mibituo magnam esto dp1C, et ap 1. et Cp _. fret: 0= ac, 96132
 cujus cubus 32768, rum daC  48 p 20. cdius quad. 100 pel pone dej. erit dr acp 29
102
et cubus
1P
15
vis
1128
225
aequatio ergo erit:
it
quad. a dac, seu a 14, tempe 196.
X2X  - 1SaX + 14 a, et de 7 ergo Xponipoest: ps- y
35 aq Anum + 7  1517  14. X
14b 343 sumamus aliud exemplum. in quo numeri non adeo magni, nempe:
19
 337.
105 d  3 c, 3. ergo d a5,  D - 3,  dB.t. C1. unde d- ac, 16   5
XC nam -64 X + (15, 4) + 4 1 c.
et dac 4 2.
proxponatur cd, ut supra
audices
Aequalionti cug b4  X =a15M4   a An p0. mulliplicems per  2b 2
60
4Cd e _
fiei.
V. mnt (6a60
1tX 1 164
3639V,
 262y  a 4n,0 muttipilicetur pereyse
ab 16  - a 15m 3 P 4V = a an  2Y
t
tre 
X
+ 2a15m 2b .. + 2ea 4n
=aang y +nea an  B.
+ 120 a 13m ..
2 ponemus act Z t ae H 2 Y, tic unde.
e 2Z
et
M
12
a2
2048
3072
sive:
(2768
= aism a
163 -1 8)
cujus aequationis ut tollatur ptertuitm
ponemus
BIBLIOTHBCA
X qua X a X
tb
ua
NOreI
(D