Pour l'histoire des sept premiers nombres parfaits

Abstract

Until the end of the last century Pietro Cataldi was considered the first mathematician to calculate the 5th, 6th, and 7th perfect numbers. But in two memoirs (1895 and 1899) M. Curtze pointed out that he had found the 5th in Codex Latinus Monacensis 14908, dated 1461, and in Codex Vindobonensis 5203 written by Regiomontanus (1436–1476) during his stay at the University of Vienna. In recent times (1977 and 1980) M. Folkerts pointed out that the young mathematician had calculated the 5th perfect number and also that the 6th is mentioned in the comments of J. Scheybl in his partial edition of Euclid's Elements. We will show that the 5th perfect number was calculated in 1458 by the author of the Codice Palatino 573 of the Biblioteca Nazionale of Florence, which the author himself declares is a copy of a treatise written in his own hand some years before, and that both the 5th and 6th perfect numbers can be found in the Codex Ottobonianus Latinus 3307 of the Biblioteca Apostolica Vaticana composed by the same author “l'Allievo del Vaiaio” in 1460. We will also explain the criteria followed by P. Cataldi (1552–1626) in calculating the first seven perfect numbers in 1603 and show, step by step, how he demonstrated the first of the three well-known propositions on perfect numbers communicated in 1640 to P. Mersenne by P. de Fermat.