English Title

New demonstrations about the resolution of numbers into squares


Leonhard Euler

Enestrom Number


Fuss Index

41, 74

Original Language


Published as

Journal article

Published Date


Written Date


Archive Notes

Euler wrote this in response to a paper by Lagrange. According to St. Petersburg Academy records it was submitted on September 21, 1772, taken back in 1773, and presented again on March 24, 1774. The following details have been related by Ed Sandifer: on November 19, 1773, the Academy had its meeting to pick the articles to publish in the Mathematics section of the next volume of the Novi Commentarii They picked eight articles by Euler, E445 and E448-E454. Three days later, they received two articles from Daniel Bernoulli in Basel, one of which was very closely related to one of Euler's articles (E447, not on the list) about sums of sines of angles in geometric progression. They decided to publish that one right next to Euler's article, but that made the Mathematics section of that volume too big. So, Euler volunteered to withdraw one of his articles. He picked E445 and sent it to the Acta Eruditorum instead.

Original Source Citation

Nova acta eruditorum, Volume 1773, pp. 193-211.

Opera Omnia Citation

Series 1, Volume 3, pp.218-238.

Record Created


Included in

Mathematics Commons