536 PbtBI ClUXGARI 



liabctur cliam 



(5) [i;i)^_ . . . -i-l("+i)J = [1(1)^ . . . >H-1('-"+i) J 



_f..[l(i)_l- . . ."h_1(x-"+i)] . [i(i(h- . . . ^_1( >■) ] 



^ [l (1) 4- . . '.Vl (r-«+i(] . [i (1 )^, . . . _4_1 (r)J 



_,_[1(1)_h.".-h1»] . 



Ilaec formula mirifice suppediiat solutionem problcmalis, quod 

 statini exponitur . 



Sint in globuli partim albi, partini nigri in urna; prime 

 ponalnr globulos m — 5 esse all)os, et s nigros; postea glo- 

 buli Til — s — 1 siut albi, ac 5-4-1 nigri, et ita deinceps. Glo- 

 buli t-\-s ex urna educi debeant , inter quos albi sint t, et 

 s nigri ; quaeritur « quisnam sit nunierus combinationum, seu 

 " mutalionum . » 



Si in formula superius relata ponantur n = in — -s- — /, 

 X — n = t, y = s-hi , haec aequalitas prodibit 



[W>1+- . . .-»-1('-^-i)J .(.10)-+- . .. -h1(^-h1)J 



m—s — -t 



H-[l(i;^-...-,_1(.-f-i;]; 

 quae formula transformari quoque potest, uti sequitur. 



