COMMENTATIO ad QUAESTIONEM MATHEMaTICAM. 39 



Sit abscissa AP = :« ; P/» = j; BC r= i; AB = « et QO perpendicularis ad P/»j 

 est PB = OQ = AU — AP = rt _ X 

 VC = P& + BC = a + b — X 

 porro PC : Pot = OQ : 0»» 

 \d a ■■{- l> — X i y = « — .T : Om 



Bnde 0« = -V-; — — • J" ; et Om^ = , , ■„ . y- 



Porro AB'^ = Qw^ ~ a^ z= OQ'^ + Om^ 



«rgo 2ax — x^ = y^ . 

 ■}/(^2ax — .ii:"} = y 



ia + b — xy 

 a — x 



a +b — X 

 _ (ja + b — x^ |/(3g.r— a;^) 

 "^ " a — x 



ydx = i — ! i-i-;^ dx 



"" a — x 



_ rja+b — x ) y/jiax—x^) 



ttfydx =f^ ^ -^ d^. 



Antequam autem totum integrale inveniri queat, YQiax — x^^ in seriem convertends 

 est; est vero, uti supra jam vidimus ; 



-,y. 2N I / X2. , X2. X2. ^XS 



*^ ^ ^ *^ 2\/2a ' l6a\/2a 6^a'^V-'> 1024<s3v^ua 



Ut calculus facilior evadat, sumaraus casuiu uhi a =z b et 



,crgo /ydx = f ~ — - .\/C2ax — x^') dx; porro 

 J •J a — X 



et muhiplicatione facta, 



y'" dx [ r , ^ 3 , . s .rl , I ai , 3 al 

 a—x^ ^ z ^ '8 Via ' 32 a\/2a 512 <j^\/2« ' / 



instituta vero divisione, 



J ^ '^ 2a ' 8 a\/za ' 31 «^sa / 



