ARNAULD Antoine Nouveaux élémens de géométrie contenant, outre un ordre tout nouveau & de nouvelles démonstrations des propositions les plus communes, de nouveaux moyens de faire voir quelles lignes sont incommensurables, de nouvelles mesures des angles, dont on ne s’étoit point encore avisé, et de nouvelles manières de trouver & de démontrer la proportion des lignes.

DSB., I, p. 291.

First edition.

This work contains Pascal's solution to the problem of magic squares. Written with a pedagogical aim, these Nouveaux Elémens are characterised by a clear and precise exposition of Euclid's geometry, whose theorems are presented in a new order, in the light of contemporary authors, and under Pascal's influence. Pascal, a great friend of Arnauld, had published his Lettres Provinciales to defend him from an accusation of heresy.

The problem relating to magic squares, solved by Fermat and Pascal, consisted in arranging the first integers in a square in such a way that the sum of the digits contained in each vertical, horizontal or diagonal row was always the same. Pascal's research on this subject has not come down to us directly, but he gave the results to his friend Arnauld, who published them as an appendix to his Géométrie.

Light waterstain, pages 199 and 251 have been inserted a second time after page 338.