J. 1 4. Pro cafu tertio faciamus n- S > Vt iit x^^^zx Xj 

 et fofmula integralis prior dabit , 



fx xd X cof. x — xx fin. x -f- 2 x cof. x — 2 lin. x, 

 pofterior vero praebet 



' fxxd X fm. X z= — X a: cof. x-i- z x fin. ac -h 2 cof. x — 2 i 

 quibus inuentis aequatio noftra pro hoc cafu erit 



XX :=zx X fin. x^ -+- 2 o: fin. x cof. cp — 2 iin. x^ -1- 2 cof. x 

 -h X X cof. x^ — 2 X fin. X cof. x — 2 cof. x^, 

 liue xx=rxx— 2-f-?.cof.x^ ficque efle oportet 1— cof.xzzo, 

 prorfus vti fupra iam notauimus. 



J. 15. Talis redu£lio autem fuccedit, quoties n fue»- 

 rit numerus integer politiuus , ad quod oftendendum fit ad- 

 huc n — ^ et x''""^ = x^ ac prior formula integralis dabit 



/x^9xcof.x~x^fin.x— s/xx^xfin.x , fiue 

 /x^ 3xcof. X ~ x^ fin. X -+- 3 X xcof. X— 6 xfin. X— ^ cof. X-+- ^J", 

 pofterior vero 



/x^ d X fin. X = — x' cof X -K 3/x X ^ X c<?f. Xy fiue 

 /x^5xfin.x=i;— x^cof.x-H3Xxfin.x-+-6xcof.x— 6fin.x, 

 ex quibus conficitur 

 x^ = x^ fin. x^ -I- 3 X X fin. x cof. x — <^ x fin. x^~6 x fin. x cof. xh-6 fin.x 



-hx^cof x^— 3 xxfin.xcof.x— ^xcofx^^-i-^xfin.xcof.x, 

 fiue x^ ~ x^ — <5 X -^- 6 fin. x , ita vt effe debeat x— fin.x=:o 

 prorfus vt fupra. Huiusmodi autem expreffiones pro cafibus 

 quibus n eft numerus integer, facillime ex notiffimis feriebus 

 ipfius fin. X et cof. X deriaare licet. ^udh 



J. 1 6. Quoniam igitur fatis certi fumus, cafibus qui- 



bus ^<<3 aequationem propofitara infmitas habere radices 



r -^ xea» 



