N E W T O N I

. 52

Caput

Septimum.

Dejignet a quantitatis alicujus partem majorem , b partem mi-

norem : Et erit A i~ —A A . BB quadratum majoris partis radicis ;

■ A ~ — AA ~ Jj]j quadratum partis minoris , qua, quidem majori adnec-tenda ejl cum ftgno ipfius b.

Ut fi quantitas fit 3 +\/8, fcribendo 3 pro a, Sc \/8 pro b,erit v^aa-bb — 1; indeque quadratum majoris partis radicis,id eft 2; 8e quadratum minoris partis id eft 1. Ergoradix eft i+v/2. Rurfus fi ex v 7 32-v 7 24 radix extrahenda fit,ponendo v 7 32 pro a, &: v 7 24 pro b, erit v 7 aa— bb = -s/8; &inde — - 2 j~ — 8 , & — ^ - ■ - , hoc eft 3-v 7 2, Sz ^2, quadrata par-tium radicis. Radix itaque eft J/18-^2. Eodem modo; fide aa+2xVaa-xx radix extrahi debet, pro a fcribe aa\ 8c prob, 2X \/ aa—xx, & erit aa—bb — a^— \aaxx +4V 4 . Cujus radix

eft aa- ixx. Unde quadratum unius partis radicis erit aa - xx,illud alterius xx ; adeoque radix, x + Vaa - xx. Rurfus fi ha-beatur aa + $ax— 2 a \/ ax + epxx, fcribendo aa + $ax- pro a, &2as/ax + \xx pro b, fiet aa-bb - a^+batx+^aaxx', cujus radixeft aa+$ax. Unde quadratum majoris partis radicis erit aa+gax,illud minoris ax\ 3e radix, v 7 a a x \ax - v 7 ax. Denique fi ha-beatur 6+\/8-v/ 12—\/24, ponendo 6*\/8 - A, Le -v 7 12-v 7 24— b, fiet aa-bb — 8. Unde radicis pars major v 7 3 + s/8 ; hoceft (ut fupra) 1 -rv 7 2 ; & pars minor x/3 ; atque adeo radix ipfai -r v 7 2 - v 7 3. Coeterum ubi. plures fu-nt hujufmodi terminiradicales, poliunt partes radicis citius inveniri, dividendo fadlumquarumvis duarum radicalium per tertiam aliquam radicalem,.quae producit quotum rationalem Sc integrum. Nam dupliquoti iftius radix erit duplum partis radicis quaelitoe. Ut in

exemplo noviffimo —= 2, —gg— = 4, -Ps— = 6 *

Ergo partes radicis funt 1, x/2, v 7 3 ut fupra.

Eft Le regula extrahendi altiores radices ex quantitatibus-numeralibus duarum potentia commenfurabilium partium.

Sii