(50 



nir d X ■zd V et d r - v d v^ hincquc porro .v ~v' ct r :^ ' i' i". 

 crgo 7 iz: 1 ar Af, qiiae cll acquatio pro ipla Parabohi. Problc- 

 ma autcm nolhuni polhilat, \t innumcras alias eiusmotii cur- 

 vas inuclhgemus, quarum longitudo pari formula cxpiimatur ; 

 fcquamur igitur formuiam priorcm §. 4. traditam , vndc pro 

 pracfcnti cafu erit 



^x V k ^i') — v V{ n — v \ gj 32 — ^'C — P' - f-1'VlA -^ tr) 



io) ) 1 A 1- 81 a i. V (A -»- Bl ' 



quac anibac formuiac infinitis modis intcgrabilcs rcdiii polfunt. 

 Primo fcilicct fi rtatuamus U ~ i-; dcindc vcro ctiam fi fuc- 



rit U ;n / c ; porro quoquc fimiH modo fi fumatur U ziz y v^ 



•\cl Uzziv^r, vcl in gcncrc U ~ "/ c , fi modo exponcns 

 /■ fucrit intcgcr pofitiuus. 



Euolutio cafiis 



qilO U = 1: 

 §. 7. Ilic igitur tofum ncgotium rcdit ad intcgratio- 

 ncm taiium duarum formularum: 



/a c- / (st H- P v) et fv a c / (a -h (3 c). 

 Statuamus igitur / Ta -t- f3 r) — ' ? eritquc 



V = '-L-il' ct d ■; - •_!_!! , 

 hinc crgo pro formuia priorc fict 



pro altcra vcro formula crit 



r, d r, ;/(a -+- ^ .r) - l';^^-! (//-«), 

 quocirca intcgrando clicicmus 



I. /d '.■ /(a + (3 f) := l^' = •u (•=< -t- n ^■/ ct 



II. /'.■ 3 V /(a -H p ^.) = ^^ - '^-^ ^ -j, (3 " - 5 a) 



fiuc 



