Opdscula 25; 



t — ha — x — b'^a-^by-\-b'^x=-ba — l^a-ifhy~\-(^b'^—\)x 

 Ideoque 



seu (i^ — 6 — 1) J = (62 — ^ — i)j^ 



Quae aequatLo ut subsistat pro quibuscumque valoribus jt, et 

 y, debet esse 



i,2_^,_,— o 



Hinc i^i+ij substliualur igiiur ^+1 loco i^ in aequa- 



tione 



f = 6a — i2rt-4-&y4-(62 — ,)^ 



el deducemus 



t=z bx + bj — a 

 Cumque sit 



u=^ba — J — bx 



z^= ba — X — by 



erit aggregalum harum aequationum, 



z-^-u + f^-iba — X — y — a 

 seu 



X -^-y -\-z-\-u-^f=:-'xha — a 



br 



Sed x-\-y-\-z-\-u-\rt^ihr; ergo ci.ba—a = br, a=— , 



lib—" 1 



" "462-/, 6+ r 



Ponalur i+i loco P in hac postreiua aequatione, et dedu- 



cemus 



0.5 H 



a2=z:1I_L , et a = ry'5. 

 5 



40. Vocetur M summa rectangulorum omnium , quae fieri 



possunt lineis x,jr,z,u,t binis sumptis, esto scilicet 



1>il = xy'hxz-\-xu + xt+yz+yu+y t + zu + zt-\-ut 

 = xy ■i-(z + t + u)x + (z+t + u)y + (u-\-z)t + uz 

 Sed ex aequationibus superius deduciis habemus 

 z + u + t=^o.ba — X — y — a, M-+-z = aia — (x+y) — i(x+j) 

 = a6a — (6+1) (j:4-j)=:aia — b^ix+y); ergo 



T. II. 33 



