## E581 -- Plenior explicatio circa comparationem quantitatum in formula integrali $$\int\! \frac{Z\,dz}{\sqrt{1+mzz+nz^4}}$$ contentarum denotante $$Z$$ functionem quamcunque rationalem ipsius $$zz$$

(A more complete investigation into the relationship between those quantities contained in the integral formula $$\displaystyle \int\! \frac{Z\,dz}{\sqrt{1+mzz+nz^4}}$$, where $$Z$$ denotes a rational function of $$zz$$)

Summary:

According to the records, it was presented to the St. Petersburg Academy on August 14, 1775.

Publication:
• Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1781, 1785, pp. 3-22
• Opera Omnia: Series 1, Volume 21, pp. 39 - 56
• Reprinted in Institutiones calculi integralis 4, 1794, pp. 446-464 [E581a], ed. tertia 4, 1845, pp.446-464 [E581b]
Documents Available:
• Original Publication: E581
• Alexander Aycock has made draft translations into German and English, available online at Euler-Kreis Mainz.