English Title

New demonstrations about the resolution of numbers into squares


Leonhard Euler

Enestrom Number


Fuss Index

41, 74

Original Language


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 selected eight articles by Euler: E445, E448, E449, E450, E451, E452, E453, and 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 chose to publish that one right next to Euler's article, but that made the volume's Mathematics section too long. So, Euler volunteered to withdraw one of his articles: he sent E445 to the Acta Eruditorum instead.

Published as

Journal article

Published Date


Written Date


Original Source Citation

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

Opera Omnia Citation

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

Record Created


E445en.pdf (152 kB)
E445en.pdf (152 kB)