114 



D E MUTUA 



I N T E G R A L T U M a U O R U N D A M 

 INTER SE RELATION E. 



A U C T R E 



C. F. K A U S L E R. 



Conventui exhib. clic \i Maji 1808. 



5. 1. la commercio epistolico ccleb. Lamhcrti clar. 

 HoUandus, litteris praematuia morte infelicitcr ercptiis, sa- 

 gacissimo amico idcani pioponit, qiiaedam Inttiz,ralia , si 

 quidem Lanquam teimini cujusdani sciici spcctantiir , ex 

 aliis cjusdcm seiiei tcrminis, vcl intcgralibiis cognitis, de- 

 terminandi. Ad probandam possibilitatcni , quod dcntur 

 huJLis modi Intcgralia, seiicui : 



3x xdx x~dx x'^—^dx_ _ ^^^^^ 



y(Fx~=^l^)> Vib^T^l^)* v'ibiT-^) r'Xbx-^x^)' V(bx — x^)' 



considérât, ac methodo satis mgeniosa valorem y -^^^—^^^ 



hoc modo expressiim exhibet : 



Quodsi niinc m m i assimiamus, intégrale y ^-^-j-—^^, abit 

 ^^ fvibV^x-y cil jus valor, iit constat, est _ Arc. sin/^^ &~ > 

 proinde/^,^,-^ erit := ^ Arc. sin. ^^^^-^-^ - /(bx - x=^). 

 Posito itaque m en 2, 3, 4 etc. prodibunt successive inte- 

 gralia f ,--"i^~-ry fy^fj'^i) etc., quae omnia ex intcgrali 



