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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 136r, page id 00068201:0271
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Resumta jam aequatione 44. quae erat Co - a H co, - al 70. et
ponendo _cd  Ay. per aq. 45. tunc aequatio 45, y  - e Ry eL
expaa ut supra, ubi explicanda est valor ipsius e per aeq. 56. vel 61
sed ut cortetur calculi prolixitas satius erit hoc fieri in fine. Rursus ergo
ponemus Y H =, X. vel Xp = y. secundum aequ. 19. N sive quod
idem est ponatur ab intio co F,
a X. sive Cd 1 a X: vel X, ve cd
Porro valorem ipsius y vel ed. substituendo in aequ. 45. vel 44 habebitur
aequatio:
(62)
X + - ei H X - ev L 10. loco aeq. 1. vel 20.
a
inde XH S evt + a ex - ev N  Y Cv
2a2
loco scilicet aequationis 2.
latum aq. 3 ut sit
t vt6) - L a5 tass.
4AB
17a8.
Ponamus jam Videamus an
-e v H3 (64) 209672
e.t 1. 27
2C
=2L
27a 4
27 a3
elo
14402
+ L a1252 (65)
ac. ( 1. 2F N
24+
Soer Cov 
+a12
27 a
effecerimus secundum postu-
evL
a0
(66)
2, sive ut
+ 52412
C. 13 et
27a 4
 + a 13- S
e
27a
De3 () H 21
27a 4
Sed jam video nullum ab. e. auxilium
venire posse, ad aequationem 32. resolven
dam, quia ibi b et  aq. 27. et dividitur
per e. et per l, quae e continet multiplicatur
unde evanescit e; nec proindeprocedunt aequatio 52. 53. usque ad s
usque ad 61.
Cum autem postea in absolvenda aequatione 32
haereamus ideoque ita nunc procedemus: Resumta aeg. 2. videamus an
ex binomio ejus extrahi quea radex (ubica: scribendo scilicet:
2) Y + vds=1 conferendo cum 1
3e+
+3tC f-1. ponendo de .
= c
27a 
Quam in rem varia sunt tentanda. Ac primum sonemus v eD  fiet
eq. 73+
 +2-30. et t 6ae ce
282a -79.
 et +, ac 16
2a -r9
et 13 6a56
H 2aea sra
1g- 79
et altera aequatio erit: 6a6)df6 + (C)  18 a (C). ubi faciendo ra - rgH   3,
2a3 f2a
arga =
2a-r9 fier 3, - 18a B + 6a d 160
vel  V, X - 3 a 1) + a d r. ponendo Z
ponendo 3  B 16 ubi tantum opus ut d sit A  1. Quod utique in
nostra potestate est. Ut side aequatio ab initio data fuent
7N 64 et r 136. et 9 2  - 1 V c:
1 d f 28.
et d 17. es. autem YH 1. ergo et d p 1. Tantum ergo B, ra -rq debet
esse quantitas realis quod non difficile, ponendo,  quod non est diffi-
cile, ipsa enim , Y B vel 8, vet vel +2a - r9 semel inventa
peo equaationem realem quippe lubicam,  utique et vadix ojus realis
erit. Pomo inventa, e. habebitur et 9, nam 2
gi 2a - 3. (Ubi efficiendo S 1 2a, quod facitle 19F 3. ergo
errestale est, erit
etiam 9. quantitas negativa vel 615 6 v p 2a ve
 vel 5 p a s: quod itique in potestate est, quia qu
magis augetur d, eo magis augetur B
realem. Erit ergo Pp +
vr (8. d in  = a 1 se
Z habebimus radicem fra rg. semper
136
et 
at . a B 7 ade. Ctg et utoasea B doloni
sit p6
+ LaS