ARITHMETICA UNIVERSALIS. 53

. , KE

Sit quantitas a ± b. Ejus pars major a. Index ™ , g

trahenda c. Quare minimum numerum », P cnmbuta

.... r vnGilun & fit quotus C OMpUIU

Diditur per aa — bb Jine tejiauo , J 1 .

V a + B X \/ q_ m numeris integris proximis. Sit fitque

av/q. per maximum diviforem rationalem: Sit quo ,fq

n

r + —

Reductio

DICA-

~~r;— m numeris integris proximis t. Et erit -— ggg— rCiL f lX d ua -~Jita, fi modo radix extrahi potejl.

Ut fi radix cubica extrahenda fit ex-^968+ 25; erit aa - bb- 34 3 ; ejus divifores 7, 7, 7 ; ergo »= 7, qj=i. Poiroa + bxv 7 q_, feu v 7 968 + 25, extradla prioris partis radice, fit paulomajor quam 56 ; ejus radix cubica in numeris proximis eft 4.Ergo r — 4. Infuper av 7 q_, feu v 7 968, extrahendo quicquid ra-tionale eft, fit 22\/2.. Ergo v 7 2, ejus pars radicalis, eft r; 8c

—, feu -h-, in numeris integris proximis eft 2. Ergo t - 2.

Denique /r eft 2-v 7 2, v 7 ttss—n eft 1, & v 7 ^, feu v 76 !, eft 1. Ergo2V 7 a + 1 eft radix qusefita, fi modo radix extrahi queat. Tentoitaque per multiplicationem fi cubus ipfius av 7 2 + 1 fit s/qfiS + 25,res fuccedit.

Rurfus fi radix cubica extrahenda fit ex 68 ->/4374; eritaa-bb= 250, cujus divifores funt 5, 5 , 5,2. Ergo n-$ x 2 = 10,

<^-4. Et s /a + b x n/qj feu ^68+V4374 x 2, in nu-meris proximis integris, eft 7 = r. Infuper a\/q_, feu 6 8^/4,-extrahendo quicquid rationale eft, fit 1 z6x/1. Ergo s~ x,

r + T

~—, feu in numeris integris proximis eft 4 — ^ - ergo ;

ts - 4, v 7 ttss~n =*/6, St </q^= ^4, feu ^2 ; atque adeo radix;

tentanda ~i-.

Iterum fi radix quadrato-cubica extrahenda fit ex 29^6 + 41^/3 \efit aa — bb — 3, adeoque n~ 3, c^— 81, ^ — 5, -t ~ t ~ t,-

= v/ 6, v 7 jf/jj - » = s/g ^0,= v^81 feu v 7 9; atque adeo radix

lentanda —diTiV9

Cxtcrum