ANALYTIC

A.

z 9 8ec. dividendo per hos

t z%a'

i, ~ “ To> ^ C * ^

^Itiinum terminum per hos ordine numeros, 2, 3, 4, 5, 6, 7, Scc. ?^ hanc, z-\z* + rT ^z s -j^z + 36 * 88 *

2x 3? 4x 5, 6x 7, 8x9, 8ec. Et hanc a + — -

^ c * multiplicando per hos y, -p^ aliis ( b ).

8a 3 + :6« s

iz. Cseteriim in inventione primi termini quotientis, et non-^nquam fecundi tertiive, difficultas etiamnum enodanda fuper-Poteft enim valor ejus, fecundum praecedentia quae litus, elfe^ Ur da, live inextricabilis, radix aequationis multipliciter af-f e ^ae. Quod cum accidit, modb non fit infuper impoffibilis,l ^Um litera aliqua defignabis, dein operabere tanquam li cog-bl tum haberes. Quemadmodum in exemplo y l + axy + a z y-x l —2fl3 =o, li radix hujus jv 3 + ^ 2 ^-2« 3 = o, fuilfet furda, vel ignota ;^Xilfem quamlibet b pro ea ponendam elfe, et refolutionem.(k>uta ad tertiam dimenlionem quotientis) ut fequitur per-fe cilfem.

y 3 + aay + axy — za 3 — x 3 ~ o. Sit cc — 3 b + a .

, abx a^bx 3 x 3 a 3 b l x 3 a s bx 3 , a'b -'x 3 „

■v—b -- + —r— + — + - g -— - -I -— &C.

C l'“ C* C c

II

+

+/

+ axy+ aay-x 3— za 3

+ b 3 + 3^/+ $bp % +p 3

4- abx -f- axp+ aab + aap-x 3— za 3

— abx , __

- + i —P

CC

f

4- axj>

+ ccp-x 3

4- abx

a 3 Px 3 „

— -g— &c.

3 ab 3 x z baPx

+ —rS, S-c.

(T C

(fbx 1

— —— + ax i

c

— abx + ccq-x 3

4- abx

, bab x\ a 4 bx z a 3 b 3 x 3 fa*bx x . a 3 a 3 b s x 3

‘-+“ „) +*’ + + c - + c .

Scribens b in quotiente, fuppono b+p=y, Se pro y fubftituo utv ide$ ; unde prodit p^ + 3p"b + Lee. reje&is terminis ¥ + a z b-^aySui nihilo lunt aequales, propterea qubd b fupponitur radix hujus+ ay-2a>- 0 . Deinde termini 3 b z p+a~p+abx dant qtio-

^nti

apponendum, Se

— abx

,+ ai

+ q fubftituendum pro p.

3 b' \ a'

( b ) Vide Analyi', per yEquat. Infinit, Cap. VIII.

Fff 2

Brevitatis