22 Johannes (I) Bernoulli. 



a dm ,.„„ , a 3 f dx 



ent — , = différent, arcus «r 



Vaa-ww aa -xxVaabb -cc xx 



Si jam egr appellatur n, proinde gl = Vaa -nn erit 



„„ , fldw ~ . ., abc-afx 



diff. arcus r£ = — _ : Quia itaque n = 



erit dn = 



Vaa-nn bVaa-xx 



-a 3 f dx + abcx dx 



aab -b xxVaa - x; 



, ■ / t la^bb -aa cc xx + 2aabc fx -aabb cc 



et qma Vao-wn=V/ — rr — n— 



V aa oo -oo ## 



ent 



a an , . »„ ? 



— = arriérent, arcus tr 



Vaa -ww 



-a 3 / dx + abc x dx 

 aa -xx Vaa bb -cc xx + Zbcfx -bb cc 

 ideoque quia différent, arcus h* = differ. arcus kr habetur 

 a 3 f dx -a 3 / dx + abc x dx 



aa -xx Vaa bb -cc xx aa -xxVaa bb -cc xx + %bcfx -bb cc 

 diviso utroque termine- per a dx et multiplie, per aa-xx erit 

 aaf -aaf + bcx 



Vaa bb -ccxx Vaabb -cc xx + %bcfx -bb cc 



vel multipl. per crucem 

 aafVaa bb - cc xx + 2bcfx - bb cc= -aaf + bcxVaa bb - cc xx , 



sumptisque Quadratis erit a 6 bbff -a i ffccxx + 2a i f s bcx — a i ffbbcc 

 = a 6 6o // -2a 4 6 3 /c# + aab^cc xx -a i ffcc xx + 2aafbc 3 x 3 -66c 4 # 4 

 redueta aequatione ad cyphram et divisa per bc, erit 



bc 3 x* -2aafccx B -aab 3 cxx + 2a*bb fx + 2>a i f 3 x -a*ff 6c = 

 vel quia ff + bb=cc erit divisa aequatione per c, 



beex* -Zaafcx 3 -aab 3 xx + 2a*fcx -a 4 //6 =0, 

 vel substituto valore ipsius ff = cc-bb erit 



beex* -2aafcx 3 -aab 3 xx + Za*fcx -a%cc + a i b 3 = 

 dividatur aequatio per xx-aa, et habebitur 



6 cc xx -2aafcx + aab cc -aab 3 = 0, 

 vel (propter cc -66=//) b cc xx -2aafcx + aab ff = 0, 

 quae aequatio, si [28] resolvatur, dabit 



aa f +a/ Vaa -bb 



x = r 



bc 



