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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 47r, page id 00068201:0093
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+
C + bm X3 f
+ Cn
+ du
+ eco
9 A
h v2
2Co
3 Mn
4 mv
p + 26) + E- p +, sep
+n dD teld
d
5+ 3E
d- p 3 +
E l 3-p -. 9
+
7- p +
a
Guo Gnschlbire
t
ti
X ( I +n + v.
A
1 +
24
I4. MN i
4mv in
+nv 
fpne 29
liem
piy se
Agin
+ 4 ma v.
+n 2mn
2mB
+amv n
mn
n
+quid n
Trisectio t Radicum,
XY me rmn
d
bmn
6m V
612D
ex
2n
n
C8
20
X m 3mam +6m nD
ast
63 3mv m
13mnon +Emnv
3muv ma
3mn v in
znom
12mn V
= 4mnV V
3nv 
v4
Ad mux quio
sive
cupplendo  nx
(Em e 2mn
v 2 mo
n
2_X
sive 2M X
2n
2
Amnv m
n
2mn
-21
94
vn
-2n 2
+
s
dumma
X F X 4mn X = mnV X
poba, 81 e
nv:
108
) 45 X
X n
priorem
 
= 24
2
= 8 muv X + m
Y X
2y
set fiet:
em
2n X =amuB. X - 4mn
er
+12mnv X 16 nin
2m
+m
4
2m X + gmuv X + 2mn m
3
su
den 2u 1G- n n
nor ∞4
9o
PA +m +quen. Ego 2neuu H q +s.  rect
ix
ergo
c
Possumus jan hanc aequationem quadrato, quadraticam
rX +si
affectam datae cuidam comparare, dividendio
aequationem ex comparatione duorum X valorum
factam statim abinitio in tres alias, aequando
scilidet terminos terminis. Nam Sed et nonnihil immuta
possumus ante comparationem, praedividendo primum
in partes duas. nempe:  qX + rX +S TnndS
F 4S X- dmunX + mnto, dividatur in duas partes
26
nempe C4 SX 1 4X sive 4 X HD; et posteriorem . DmmB X + nht   r +s
Ergo si si q At  si s sigesumma rectangulorum sub singulis binis radicis partibus, ducatur in se fiet
16
fiet (8) D + Emm mv EnvrB, sive CmX. (D + EmnoX B 4. Multipluetur
45I
haec aequatio per quantitatem quamlibet, ut Z  et latus ejus unum uni, alterum alteri
(10
aequationis 6 lateri ad scribatur) fiet:  - 8 mnvX + In tn + V  YX +
(13)
+62.
2 D
ib
ponnique 2   2. fiet - 2muB. X + n A Y X + s. quam rursus dividemd in duas
(14)
(16)
fiet e mnv r Z. 9 m n 2 + BE  S +  c per supa dicta nn + mv + no rI Q
(9)
jam  Me nv Fe  = nn D. nv + 9. Ergo junctis 17 et 18. exit HB N 1 2 - mn + q. Inserantur
2m
iiventi ipsarum Mx RB, me vabores, in eq. 16 fiet: mn + F - _n + q, Y p 9 quae est identica
valores aequando fiet: +=
2m
eM
27
B, quos duos  19. et 20. ipsius mD
in adeoque tern - am n + gmn  - erm
24
jam ex 16 erit 4 - mn, c0m an. et ex irerit amen-qua 2t Fimta. Ergo duos ipsius
in tn valores aequando, fiet: quama ( amn -gum. quae aequatia explicando ipsam v eos - Y per 14, fiet
+v 11
EY (27)
im
nusus identica aequatio. Uta nur ergo tertio, maci ; inserendo in 16, fiet. --  + - r (ad) a
Em A 
et sublatis fractionibus, et explicata muo redibit aequatio 16. Magna erg quaestio est, quomodo intercta
aequatione 15 ultra iri possit. d Ab aequatione 22. abest v. itabuimus vE
Emn
milus ext 19 erit vF  2 = n + 4, et aequando 26 et 28. fier: 2nY - 4m n + 9mn Erm ut aute
4 mn
aequando 2826. et 27. prodibit idem denius aequando 27 et 28 fies 2MY + 2nY, - 4Mn = 4 m n + qu + quon
H 9m - amn. aequatio de a quante. Ian etiam v1)  i + 4. sed mamifestum est priora semper
reditura: videamus an non asni esse postit, quod r summum residuarum incognitarum ope ili hujus invenimus
nempe: m+ n F 4m nt Latun sam n s  jum N + In +n- 2mn + amus2
_s
et tetat, nt ex p stat r
rem. Ergo.
4
=8N N
Supplementa
-8mv
-8nY
en
=AmnV H
v
-4muv m
in
=g mnv X
2M H
reV
=2 WX