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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 168v, page id 00068198:0336
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4
Aequatio +h gradus habens duas radices aequales
100 C + 101 C + 102 C + 103C + 104 = 0
+3. 101 C3 + 2. 102C +1.,103C
nes apliqus sul. 60 pagina
quae et tato isset ha quae et potuisset haberi ex 1.
2 ex aeg. 2 et 3 fiel +1. 3. 101 101 + 1. 2. 101. 1028 + 1. 1. 101. 103 (4)
0
mulliplicatione Arit hueliea
eg. 4. mulliplicetur per 190 ee, et ab ea auferatur aeq. 1. mulliplicata per 1. 3401 = 24., 100. 102 siel
- 2. 4.100. 102 - 3.4. 100. 103 -4. 4. 100. 107
1. Ac + 1. 2. 100. 101. 102 C3 + 1. 1. 100. 101.103  p. t 100 101. 103C
1. 3, 101, 101. 107
=2. 4, 100, 102 104
-4. 4. 100. 100,104 -44. 100r 100. 104
= 1. 3, 101, 101. 102 = 1. 3 101. 101. 103
Aliter ex aequ. 2 et 3 nova ad e, fieri potest, ullicmos terminos aequando,
42. 4, 100. 10d 102 F2. 4 190. 102.107
scilicet 4. 4. 101 194 + 4. 104 4. 100 C + 4. 104. 3,1012 + 4. 104. 2. 194 = 0 = YF, 4. 100. 104 e +
+2. Y, 106, 101. 102
-1. 103. 1. 101 = 1, 103.2,102 = 1. 103. 3.103
 aequando terminas summos, sit
10CC+ ue + 12 =0 20ee+ 21 ft 3220 SF. 1. 3, 101. 101. 204, 101. 104
, 11. 20C +12. 20 -, + 19. 228+11. 22-= 2. 4, 100. 102, 3. 4, 101. 104.
- 10. 22 412. 20 =0
= 11. 22 i 1012).
= 12. 21
20= p10) C + 2. 102C + 3. 103C + 4. 104
4. 101C =4102C 74103C - 4. 104
= 3. 4. 100. 100.103
= 1. 3, 161, 101. 10)
jungantur aeq. 4 et 5
+12. 20110. 22
11.20
seu
versae
4. 100e+ 3. 101 e +2. 102C +, 103 0 multiplicetur per e, et auferitur inde eq et 1. mulliplicola per
fiet
=10. 21.. = 10. 22 = 12. 200 - 12. 25
et
e
+12. (2. 20. 25
+10. 10. 22. 22
)1.3. 101. 101,. 1. 2. 102. 103.
+ 2. 4, 100, 102. 1.2, 102. 163-.
10 = 1gol. 101
-2.10. 12. 2022 6)
+ 12. 12. 22. 22)=c
102 19, 101. 10
= 4. 4, 100, 104. 1. 2. 101, 1021
4 1. 1. 101. 103. 3. 4, 101, 1021
+ 4. 4. 100. 104. 3.4, 100103..
= 2. 4, 1001102
H = , 1.2. 101, 102
1. 1. 101, 103. 314, 100,103 a
20 = A. 4. 100104
= 1.1. 10l. 103
21 = f3. 4. 101. 104
= 1. 2, 102. 103
faci
(5
(5)
-3. 4. 100,103
- 1. 1. 1011103 = -12102 1031
+ 1. 3, 101, 10). 2. 4. 102. 10c
2. 4. 100.102. 2. 4, 102. 100
= 1. 3. 101. 10]. 1. 3, 103. 103
+ 2. 4. 100102, 1. 3. 103, 103
= 4.4. 100.194. 1. 1. 101. 103
4 1. 1. 101, 103 1. 1. 101. 103
+4. c, 100104 4. 4, 100. 104
1. 1, 101.1634. 4, 100. 10
Et ita tollitur incugnita ex aequatione
habente duas radices aequales.
si in casu aliquo sneciali sit 20 =0 su - 13 20, prurimum contrahetur calculus, et fiet 10. 22 - 10, 11. 21. 22 -0
22 = +2. 4. 10+. 104
= 1.3, 103 103
Hinc e = - 22 =  40
1
10. 11. 21. 22
+ 10, 12, 21. 21
13 = Y 1. 1. 101.103
= 4. 4., 100,104()
+ 11. 11. 20.278
= 11. 12. 20. Y
20 = 12
seu fiet 19. 22 11. 21. seu 4f. 3110l0
Et in pe q. 19 pro 4. 4. 100. 104
poendo 1. 1. 101. 10Z (sb aeg. _2)
fiet 41. 1. 2. 2. 101, 102. 102. 103
ta
1. 104
O1. 102. 3.
2. 4. 102. 1044 (,0) (+ .
∞1. 2, 101, 10]. 1. 3. 103. 102
 2. g., 100. 102. 1. 3. 103. 103
4 1. 1. 3. 3. 101. 101. 103. 10
41. 1. 2. 2, 101. 102. (02. 103
ponamus jam 101 = 2. 1050. 5) 16. 18, 5. 32. 52+ 6  gb2 nempe ex ipsa aeq
(4P. 1. 3.3. 105, 101. 103. 103)
in hroc calculo pro ag. 6. sufficit ct q. 10.
ponamus jam 100 = 10. 50.
et 14 1 101 = 2, 1050. 51
et 102
103 = 2. 30. 51. 52 + 13. 61
104 = 10. 52.52 +2. 62
Cubi 10, 2) fiet
alia sunt
aequ
ro ladiorens
4. 16. 50. 51. 52+2)1 X . S. genus
arbitrio assum
 seu 61 = 4. 10. 59l. + B1262- 251.57) est sine ffam
quamin Seu 4. 105548. 1262 = 251 32Y 125161
 aeqb
11.5
sed pari jurefit 61 = 4. 20.532 +8. 22. 62-2. 2051. 51
 a ipsum quod
obitinere debere
2. 12. 20.51.52 et  divisis abus per 100. 22 - 1812
supposcama
F (2. 35, 52 + 8(2) 62(-2. 10. 5( 52): (12)31
. 12, 2260
seu 61 = 8. 62:51, idque utroque modo atque ita ratculus debet succedere. Sed suppectum
et fit 410. 22. 52 8. 12. 22, 62) - 2. 1022. 51. 52 = 4. 12205248,
fit 4. 52 2517.52. seu 52= 5251. eti 2. Ergo b
quod ita cale 10g12, res, ut saceutu laos ingredtinntur
u
101. 104
4. 14. 104
L1. 3. 103.10
p.104e)
= 3.4, 106. 105
1. 2. 101, 102
F 3,4. 100103
quae aequatio
ci suppositior
quod immenso
2. 102
02. 103
id consecnti sumus
dentica
calculo aequati
evoluto, obtin
onis 6
semus
semr ob sinnt 2
10c
Nempe ubi
ratiolinationi
hypothesis. s
decit
identicam, signu
Unde fecter
quitur a
pro