RICHELOT, Friedrich Julius. De resolutione algebraica aequationis x^257 = 1, sive de divisione circuli bisectionem anguli septies repetitam in partes 257 inter se aequales commentatio.
Berlin: G. Reimer, 1833. First edition, offprint issue.

Richelot was a student of the great German mathematician Carl Gustav Jacobi who, like Jacobi himself, taught at the University of Königsberg. In 1796, at the age of 19, Gauss showed that the regular 17-gon can be constructed using ruler and compasses only (although he did not show exactly how to do it). Five years later, in his masterpiece Disquisitiones Arithmeticae (1801), he found a sufficient condition for the constructability of the regular n-gon in general: n should be a power of 2 multiplied by distinct Fermat prime numbers (these are the primes of the form 2^m +1 where m is a power of 2). The next Fermat prime after n = 17 (m = 4) is n = 257 (m = 8), so a construction of the regular polygon with 257 sides is called for. Richelot provides such a construction explicitly in the present work. A copy of the work was in Gauss’s library.

Large 4to, pp. [iv], 84. Plain wrappers (not recent) with manuscript label on upper cover, browning and foxing throughout, mostly light but heavier on the first few leaves.