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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 211v, page id 00068196:0418
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=418
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sit aequalio X + px + etc = O
abs
sit quadratur ex +Ex+ ese
D, et DD=  B+ 3)  exralubilis quahatiae go=
C.
aequ quiaddatur utrobique fit O + N = quadrato G fiet
=tt
ergo est C productum ex Z+D in F-). itaque res eodem redit, ac siquaerati
( productum ex duabus aequationibus gradus 3Hi
si culica extractio quaeratur, reducitur res ad productionem ex duibus
aequationibus una gradus quarti, altera idi. Nam sit exx+ Extg
)
+ 73.
, sed C + 7 debet esse extrahibilis Cabice
ergo  fit C) + 93= F, et O = t 3- ). Ergo C productu extiti +GD+)
C
= D, fiet
in + D ti - D. Ergo perinde est ac si fficiendu sit ut  possit
Qoidi per Fr-). quae est aequatio 2di gradus.
si quaeratur ut FC sit divilibilis peraequationem edi gradus aiscendetur
in quaerenda altima tucognita ad aequationem 15 gradus, quia sex
radicum in aeq. bti gradus possunt institui combinationes 15.
sin quae ratur ut  sit divisibilis per aequationem estii gradus ascendetu
ad aequationem graduum 20, quia sex radicum sunt 20 terniones.
u.
1S. biniomes 15
54. temines 20
Cert dgd sib - gq (soct (i) absib = dkS14t + vo (BBBnoc Certaque BH Stit, H(Ssodb r gesAt  D _ I = (odt sevrs) AtiB
9Ct Certaque no  V. cet) Sad dem. (Sor +dd de   + lent dus) us b = (eet prcit ba
3
qa
S(sat nS+ (5D+ AA) p. C
t 
dinguosua sovgna une rat
nb sid (O +6d, V +Rsvo= linSt ( =, tb  it sibsst (uv sB
Hotonont 
ISe = f +d n su: c(su + B12- A
esse  eeror 7. sot:  su - 4)52 + X1) +t
e
no siv: jyso +Yy) G9D evi +) Vuso- ygn dy so  = f yf + HHm = Yet 1 y, t Ysu 41 yfit 
q
+sy - 5  = v: C7v = d) +
so Si
0045tHeuot 
t
In hopysu sio 3H + 9) Y) s q. Cos s + ys = P. v)   + et = et etqu 5: j5 - 3 = 3d 9 15)
etaque
A 
(Be
t0
quo
Ho
usr+
secysent seet
7: S +3 = v: ) 3 +y qu S: H X7 = v. 33 - gy = g
Vo est rmga ed erctio Bunus
it 3F). (B2Fdq ab = eet D +bq 1 L H3 Cf5 +59 Dp. 502 +).) =H, +h (33tqu) s 2: 682 + d9 =4
(H + 4) p B, _ (34+ 2 = ( mul. Xd. yu tucur prnt 6. et v adt rA iud 18
’et do
a
21N
v)ut
3 -9y = qu qun 4X - B 5 1) qu
yg = 33t qu 4 p, (f + (9 Cnt q) pE. 1 for + 19C ec + dqe c et de  + (H+Sq C33 + qu) p2 = de2+ for + a7
p (e+ 4+ (3t5,S. BdC +79) ab = d0 + ser, +si