36 



p :=z an -ir 3 ab -\- 2 bb z=: (a -{- by(a -f- 2 by 

 qz=z 5bb — abz=.b (3b — a.) 

 p _4- 9 m art -4- 2 ai -f- 5 66 



p q zr: aa -^ À ab — bb- 



pp _i_. qq iir ( aa -i-- bb-) (rx -V- yy) 



r-Z=.Â ab -H èbb ^:z Ab (a-^- 2 b) 



s zzz aa -[- Aab — bb 



r _f- .V = aa -h 8 ab --F- 1 bb z=. (a -f- 6) {a -^ 7 by> 



r — s z=z 9bb — aa:m (3 b -{- a) (5 b — a) 



rr — sszzz {aa -+- 2 ab -f- 5 bb) {xx --j- yy). 



L 12. Conjungamus jani singulos factores utriusque formi»- 

 ïae , ac reperiemus : 



pq(p'^—q'*)zzzCa-h b)(a +-2b)b(3 b — a)(aa-+- 2ab-¥ b bb) x 



(aa -H À ab — bb)(aa -+ bb) (xx -+- j«j/) 

 /•^ (/•* _ s*) izi Ab (a-+2b)(aa-h4ab—.bb)(a-^b)(a-^7b) 



(3b-\-a)(3b ~a)(aa-h2ab-i- bbb)(xx-hyi/y, 

 Quod si ergo priorem per posteriorem dividam-us erit 



J>(j (f4--£4) aa 4-&6 



rs (r4— s4) 4 (a H- 76) (36 -f-al ' 



Ouamobrem , ut haec fi-actio quadrato aequetur , ejnsmodi valores 

 pro litteris a et 6 requiruntur , ut ista fractio (a^^a))^;^^^ )- ^^t 

 quadratum, vel etiam ejus inversa ^° '^^^^^\f ^^ ' '1"*^'^ quidem pro 

 nostro exemple utique evenit, suniendo a = 2 et 6ml, tum enim 

 hujus posterions fractionis valor erit 9. Toium ergo negotium 

 hue redit, ut ista fractio ad quadratum reducatur. 



§, 13. Ponamus hic y =: f , ut formula quadrato aequanda 

 sit ^^-'i-^)Jf-^'7 '^ atque methodum prorsus singularem hic sum tradi- 

 turus , ex quoyis valore cognito innumeros alios inveniendi. Hune 

 in finem plures casus , qui quasi se sponte ofFerunt notasse juvabit 

 qui sunt tzzz2, tzzz i, tz^ — 2, t zzzoo, t^z: — 3, t-:zz — 7. 



