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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 104v, page id 00068201:0208
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Huddonii inveniemus ipsam V.
JX 94 + 3
ope aequationis hujus quadraticae.
V
=SE 13 +20
24
121124
sive Y +
+S a
y
4
2
semt
+gtX
=Y:..
Adioque yp
L
+2124 H. id
+E
um generali emuntratione est.
 y + L p _ A y
r -912s.
+ ZZ
p=2P+Y
+2 P- 9+Z
110
2 23
a
25, 47
8,4
17 (13Z
24) 27
e
+42
ruzis
itaque problema reductum est ad duplicationem cubi. Nam extruhenda
est tantum Radix cubica de 2. qua inventa habebitur etiam Radix cubica de
cuim sit quadratum prioris. Habitis audem 1(2. et +6 4 habetur 7.
et habita Z. de catero tantum e cir Geometriae planae beneficio habebitur Y
protiandi causa, ducamus Z + 4 in se cubiae fiet: Z + 3, 42 + 3. 6Z 64  (128) + 3, 16, (10) E, 4, (10 32) + 4
sive Z + 12Z + 48Z - 164  24 194. et rursus cubando. sed ita ninis alte sspugemu,s 2st brevius ergrita.
132
214 B1, seu 2 +64, 13, 1Z27a ( (126d) (+34 (32 d)  + (3) + 13+ p 132 + 3 , 2 3+ 4
divisisque omnibus per Z+ 4 fat: Z + 2 AZ + 16 p7 132 4 24 3A, 2
a
Ai rectius quadubnmus ab initio, non cubabimus, fiet: 92 + 24Z9 1) 16 1 2   8) +O+
B5 Sutus ita:
ZF + 1(32 + + 4 + ergo
t
+2 pF4 + 5)1.. 4 ut d 3 164 1 3 3 2. 1 4+ 2+ 1
17
Sid rectus ita quia Z+ ps + 4 + V2, ideo erit : 62 q+a = s(2 p 4.. Ergo Zd C, +4. et fiet cubando:
2 + 3, 2)
et s
192
162
14rB
7 64 sivi 2 +6Z + 127)- 120 p0. error. Itaque aliter ron esse oportet,
su
162
scilicet valor ipsius e, est quantitas falsa seu negativa. Nempe C- + ) - s2
H e 4 erit  4 10 - 194. - 4) hic Z+ 4 p. 4 +  sD2 vel 7+ 4 - s a
vel
C4 + D( 4. Unde Z + 18Z 13, 16 Z5 ∞16 p0. 2. - 1B 2
S2
+NB)
quo rursus erroo est, cum ei
= (3)
deprehondea ac quae rere
neceste est, ec proinde primum omisso Z investigemus e,
Nempe e p 4t2 + 104.. E eju e
10 2 N +. averque : et - 3A C) + 3,  C  8 4 102 1 + + 102. sive e. - (2 p, 4.
sue e - 2
-128
132
.o. sive e - 6C 412C - 132 50. Debet
ergo -60 4 12C esse p - 24 e
sive +be  13 quod est absundum nam foret ex 4. i contra hypothesin.
epetindus ergo culculus extractionis: e  - 24C - 132,0.
C N 3) +66 +3844 + (0 66 - Ax 3824
Eritque per regulas Cardani.
sive  Cp 3 28. + 13 4 vel epp+ 4 13) 2 + s 4. et quo minus dubitationi
sit locus oprationem ipsam scipionis Ferai suscipiemus: e  14C + 132. sit er Z + v. fiet
e712, + 3ZF 3Z Z+ v). Et conferendo: 24 , 3ZV. et ZH _. et Z2, 512
et quia Z2 + v 1 12. fiet se + v  132.. adeoque
132f6b. 218
105
o
396
356
512
3814
14
erit ve-B. v2 (+6666) 435 ( (4356 3044. et v -66 162. et v 1966+62 3) n8 13
512
et quia ergo sive v’e 6662. est autem Z2  132 - v. fietque; Z7) 13- 65 +62 5 66 +62
adeoque ZY 13 4. sergo epi s3 128 + 1(3 sive C p  + 4 s3) 2 + 1(3) 4
128
cujus quantilatis cubus, nempe C 464, 23, 16,4 + 3. 4 s3) 16 + 4  seu d24 + 243
aquatitur quantitia ettusm nul 24 P. + 132. H 24, + +3 2 + 24 (3 4 + 132 nempe -
12
192 + 23)2 24, 4 13) 2 + 24 ((3) 4 quae duo aequivalere necesse est: sivi 1925 4, 3 +(3) 2 + 24 104
et diuidendo pes 24 fier: 8 13 +) 2 + 15 4 ergo 8 + 1D2 ei e quod quomoda fieri possit non capio
vidiamus an satisfaciu calculo, an aequutioni nempe 562+2 + 396+C 132 + 3, 8, 1() 4  F 24 8 +24 (3)2 + 132
Unde alia rursus compantio mira. Haec scilicet pertinent au doctrinam de arte ineundi binomiorum summas. Similiter quia
C 121+e
sive e = +() p 4 Ergo 
16.
(1 + H 5() 2. sive eri 4 e- sB. sui e. sin e,
1.
2 ( 4. Ego C. 3,2 + 3, 4 C4 -8 64 adeoque e  6e +12C. 136 49
1B
et spu. C L -1nC. pao. Ego nit:  oc ite + 4 pe + igC sen e. B + +.
i
e
512
6.
512
5
10
Si
334
192
Gt