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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 188r, page id 00068201:0375
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Aequatio X ac. habet 4 radiies. Ae quatio
Aequalia data X = = 13aX + 142 =() =0 habet 4 Radues. Assumatur
alia X + 2I X +22aX + 2aa = (2) = quae habet  tres radices, sed ex quibus una est
communis priori, quaeritur 23 summa productum trium radicum, sed tate, ut, trilem modrum vadicum
seu midorum quilins aequationi X salisfieri pt, ita, ut radix  sit l 6q2 sit
etiam radix aequationis 1. quod fieri pt quinque modis quaeritur jam quomodo
E quot  valores habeant 21, 2 2 21, et 22, summae et summae rectangulorum,
positos inrectanguli seu producti vabrum summam, e et brrectansulorum et trirectam
en lorum summam nihilo aequati seu in posito 23y 24 73 - E
pro 23 substivebindo 23 y  13-y
an
Vic VVroendum quantum um
ratione consequi liceat, aute calculum. Nume calcal pra quod puto
quia et vs est generalis, eadem manente postertore aequa non videtur ze ferpo
quanta sit aequ. 1. sed calculo Ut in aequa ostendit ostensum est si
cqu.  aequ. 1 sit primi vel idi gradus. vid. Act. Cips. ann. rdum
in cta Erudit. Majo 1633.
Sed nunc calculum, tentemus pro
hollendis  tibus aequ  terminis, qui sunt omnes inter medii in aeq. eti
gravy1.
Acqu. 1 mult dicetur per  for (3) mulam X+3IX+a et
aequ. 2 maltiplicetur per for (4) mulam X + 41X + 42 aX + 430a et fiet
X = X 13a X + 14aX
3I
3ea
+ 1331a.. +14. 31 a X 
aequ. (5) at
X,uXaxtaaX
+1. 32a.. +14. 32a
+4 +271. . +2. Ma. +23. H aa XX
42a 1. 32. q aa .. + 23. 4243X
E 43 4a.. + 21 43aa.. +22. 13a3.. + 23, 43a
ita hos sex terminos compa-
rando tollentur literae quinque
nempe 31, 32; 41, 42, 43.
et habebitur aequatio
in qua solum erunt ontae
quaesitae 21, 22, 23, cum
as datis 13, 14
3(= 21+ 41 32 32a =, na + 21. 41, 1442 = 23, 43a) =  13 23 a - 17. 17 - n. 7. 1] - 123. 42
14 a  (+ 13. 2i ead + 13. 41 a  = 23. 41 a + 22. 42a  _ 13, 21a, - 21. 23 a - 21. 22. 41 - 21. 21. 42
imo cnorle
14. 21 a f 14. 41a + (13, 22 a,+ 13. 21. 41 + 13. 42 a = 23. 47a (F13. 22a7 22. 23.  a - 22. 42. 41
sed haec melius praestabuntur regula aliqui assignata Tollamus interm
utcunque saltem ut aestimemus quadum
42 = 13 a + 21. 22 = 23 a g ( 41
42= Ex ida harum Rium fit
+ 14 ac + 21. 23a: 22a + 21. 21
Exprinasil 42 = 14. 21 + 22. 23 41 + 1422 a + 13. 23a - 23. 23a, :, - 14 a - 21. 23
(
(127
 opendo 14. 21. 41 + 14 a 42 + 14. 22a = 0
(30) 
22. 41. 42
23. 23
+13.a 41
=23a
+21. 22
dua 4
1318 13.4
21. 2
1
B. 2
+21 2142 +itaa -
- 22a
(31
13a. 42
23a.
S. si4. 1 7 14. 21 7 14aa7 12a 
121. 233 22. 23) 21.235 21. 23a
23. 23 a
(22
7 21. 23522. 23)
=21. 23a
(33
q. 2ba = 0
tereva
2. 2ha
+,1 4. a 1 1422 a VB 1taa 212) +iua V E.na  a qa Jia 36+18
121. 23.
13, 23 +4.3
a aG) 
S-22af 21. 13.
=(1q. a para atta 2 14aa 22
221. 23513. 23a(- 13a 23a (13. 2)
23. 23a) +21. 22, + 2. 2L
1514 21714. 217 21, 21 1 144a 114 4244 32
222. 13522235 22a521. 23a51321
. . 22a ju. 2IIna  1a
  2za sutra
et 23532. 18c
1+. aX4, 2172t
X2. 23) 2223 5. 22a f2t. 13a522C
17, 4a7 at. 2227 21. 21I 2t. 21) 13a
221. 2391
vaS. nas23C
+(4. a 1a 1
La.130
1+ +7
nat 52a
11. 41 + 10, 42 + 140
copendio L
ta) +. )2I.LIBa 14. 211
30. H. 42 + 323 3a
2141 + 20 42 + 22=0 314 12 =
41 = = 10. 42 - 12a, : 11
41 = - 20, 42 = 22a 3: 21
+10. 21. 92 + 12. 21 a = 11. 20. 42 + 11. 22a
42 = _ 11. 22a = 12. 21a, :, 10. 21 - 11. 20
41 = 10. 22a - 1220a, :, 11. 20 - 10. 21
Ergo
36,10. 2aB11. 1a F 10. Na 1. Na + 3ea 10. a 10. 21 - 0ma 11 20
F1. 20a. 11. 22a = 12. 204. 12. 2a = 12. 20a. 1021 F 12. 30cL. 10. 20
33a, 18. 1 - 2.10. 11. 20.1+11.20
10. 12 3eu
31a, 11. 224. 10. 2] f 11. 2a . 11. 26
+12.24. 10. 21 - 12. 2 a 112
=0 3f 10. 11. 22. 22. 30aa treterrzona
a n. Jira  13a 7
a
2)17.L
=10. 11. 21. 22 31aa - 10, 41. 20, 2232aa
+10. 12, 21. 2),3, aa + 10, 12. 20. 203ca
411. 11. 20. 22 31 a4 + 10, 10. 21. 21. 32 a
=11. 12. 20. 2131aa =10. 12. 20. E.375
-10. 11. 2. 29. 33aa - 10. 11. 20. 21. 33 ac
+10. 10. 21. 21 33aa + H1. 1. 30. 20. 33aa
prss aaquo
aqu.  ex ag. D explicata
sed si aeg. C explicete scribe
vellemus plagula esset
complenda, quod tans
ncenti
iprodeunt 
+10. 12, 21 22.30aa
+11. 12, 20, 52. 30 ac
= 12. 19. 21. 22. 8a0
2a
f1. ta (1.19c2
(22. 1343 33. 2301)+21.
+2
siea 212.
l
2
cnipiie
es ues soastara ) iss ne  dras
n