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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 65v, page id 00068255:0130
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Itaque ex HvD H. 31 VY + 123. 5232y = 1G. S1Z vZ +100p 500t U-mm
HB. 51, 13) i. 523L H3. 512
2t513  3 5 1M223S
Hmm) 11223. 5123.
10rb destructis jam irrationalibus in aequatione articuli 4 restat in  eadem aequatione pars rationalis
112. 512 vy + 13. 522Zy + e) + 100 p. 500 F + 113. 513VZ =nill oum, ubi substituenus
valores y et  et 500C inventos articulo 6 et 7. jam  100 p = M. H2V + 12313Z: 5123 et
seol=  aq si ul jam 100β = - 12. 112. 513 V + 123. 123, 513 Z,
12. 527 et 5ot permutando 1 et 5. fi
 seu  500 = + 512. 11213V2313Z.: 51223. Ergo 10dp 5oot =. L812 u2IZ vB + 112. siZ 11213. 12B3VZ,: 5122S
Seot - - 312. 113 A~, .
Siz. 123  - 523. 11
Rursus ex artic. 7. est y = 1121y. 5I213V ~ 12313, 52313Z.3:, 11223,51223: Elyo
+II2. 5I2. 51223, 11213.51213VV - 112. 512. 51223, 12313. 523131)
= Bur2z. Snz si (ill- im m)
123.523. 52317. 11213. 51213 --. 4 123.523. 52g1. 12313. 5231377
ubi 123  permutantur 12 et Ncum 23 et Z
12. 512, 11223. 11213. 112B3VV f 1122211225. 112B. 123B ... = 123, 523. 131 2 1291. 123132
l.Fid est 2. 12. Su 12313. 1113)
2312 2se - 51223
jam coefficiens ipsius vo est +112. 512. 11213 (151223. 512I3 = 11223. 11213). A 11. 512. 11213 fa - b) (1. r)- + b) m) seu
fr2. 123)SI2 C N13- sIL. 113) -
as. i 3  4 113, 513 11223. 51223, 52312...
1 su ns, , tr 2.112. 515. 1∞21Z, 12713
2112. 512. U2B3Am + bC) seu- 2. 112. 312. 113a3(112 SI. 13. 3241. 512: 12I
us in quibus siru, hac
et prius quaerat nempe meuorum primum secundum et quartum. Et quibem proprim
 siS qu - 112. S1 (12313. 32343 dat 112. 512. 51) seu H 2. 512: (123. 513 115. 5252),
 123,523. 51223, 11213. 5213 dat 123.523. 512131 seu + 13. 523 (112, 55- 115, 512).
uttermia terminus ( 13. 513. 11223. Axs. 1M23 dat
pro sccuntus terminis qua rumus
+ 1125. 11223. 293 1_B da
112. 523 +SI1) 113. 313
112 13. 12313 =, 112. sey + u3. fIr, tBt H s = siL S23. 113. pE. 14. 113 +
certius denique
+12, 512. 5257112, 523.
=112. 512. 525 123. 512X
= 123, 523. 512, 112. 523
f123. 523. 512 123. 512
+512. 523 112,52)
45(2. 527 125. 51
n2 SI2. 523. 51125 113
3. iEius sasis
(42. 512. 513. 112. 123. 512.523)
seu 2. 112, 512. 525 115. s s M h ar. 12.
. _. 123. is
112. SIL. 125. 5I22
. 12. jur
se 2.512. 523. 112.523
-113.513 si. S25 = 123. 512), 51223
 (12   en. se 1) 11227
SB B- 12223. 5p23. SI22Z 113, 515
11. 525 = 1232 51 + 2. 112. 123. 9n. 523 2 113. 51
Machigue. bes+ i ac FEcitus oege
12) Ergo tandem aequatio explicata sic. stabit
= 2. 112.515. 512. 52. 1B32 ∞V = 2. 125. 525, 512. 51. 113
 12. r3.. 513
11223. 11223. 11213....
4 4. 112. 123. 512.523. 113. 513
Z2. + 2. s12 113 1pi vis. 115
+ 2. 112.123.2
I23 H3SB +4 12. 123. 512. sig. 1B S
supere (t coefficiens ipsius vZ.  quem ut explicemus, ita procedetur
B. HB S
+ 11515]3, 1123. 51223. 12312
seu 4123. 513 (112. 513 - 113. 515), Su2er u3)..
+ p227. 1229. 11213. 12313 seu + 112. 123.513 + 51. 513 11 Q 11223 B
5(2254 51225 + 4. 112. 13 512. 523
et coefficiens ipsius vZ est 25. 5 l1223 S. 113 + 2. 12. 123, sf2 + 4 (1r2. 123. M2. 523. 113. 513.
A st23 + 11225 est 2. 112. 513 + 2. 123512 )eu r. Js E
112). itaque tandem aequatio ex rationalibus explicata sic ctabit
25512. 523. 132 (+IIE. SIE VV
 I223.15. 5B, +125.523 2
 +E(tirS(Sn 6C3. 113
D. Hrar 5 (312. 52 3 113 + 112. 123. 5152) = L. H1223, 112. 123. 512. 51313513
quam aequationem compendio scribemus 120VVI Z IV voaa - 0. Et cum ex
seu dividendo ft 112. 512 VV + 123. 523
 13) Alia similis aequatu fiet ex ex rationalibus subtatis riationatibus valoris ipsius E, d- O, tantum
1 et 5 troturum initialium permatando cum 3 et 7.  quam compendio similiter
seribemus, 220vV 202ZZ+ etvZ+ 200 aa 0; Ias duns aequationes
latere radix esse ( 112. 512V + 123. 523Z et fiet - 2. 112. 512. 123. 523(2 11213. 12313 =  l2X 235(,1 12G. 
se fiet L1c. 523. SI2. S23. 113 + 2= 112. 525 1 123, 515 + 1t 525. A. 1223, 112 1)SIL. 313. 113. 513 =
+2. H12. S1]13. 513... . ..
+2. 112. 5121359. 504.:
B1 en sis quae aquatia q
quae aequabib dividi potest per u2 23 seu per 112. 513 + (3. 512 et fi
.512. 523113 + in 2312. 123.515 + 4. 112. 133.512. 523. 113. 513=0
Et pari re modo
tractando G, D. O fiet 31223. 712723, 315 4 31213. 312. 325. 7132+ 4. 312. 323. 711. 715. 313. 713=0
IVZ = 11223. st. 13. 5231 2(l. m C
l 2. 1123. 112. 123, 512. 529. 113.513
11223.51225 (inise
2. 11213. 2313
quasi ab uno
=11223.51225, 52312 (l mon)
=12. 5I2. SI213. 1313 32313 seu - 1. sir (125. 51 - 15. 113), Su  Mn (SB + sM2, Z13
= 123.523, 51212. 11213. 51213
seu -113. 513 (1123. 523 - 113. 512), 51229 
11223. 13. 51348
Et coefficiens ipsius ZZ est + 123, 523. 12313 (4 52312. 52313 - 12312. 12313) sin 1stus uesn (ib. a f t. )  (B Y a) f19) - - ( c m nus vidi sotas
 sed  b9 + af = 123.523. 113. 512 + 123. 523. 112. 513. Ergo fil coefficient ipsius Z2 -2. 123. 52512313. 11213
je surorest coefficiens ipsius ez. ubi primum excersamus et explicenus ter
ipso omisso, entice
et ordinai
p. S pr13. 123B3 BV +
vq  i edre auimm
uie art asnse