page 14 note* Marco Uglieni (the anagram of Luigi Cremona), “I principii della 65 prospettiva lineare secondo Taylor,” Giornale di Matematiche, t. iii. 1865.

page 15 note* Maclaurin was also the author of a work on Geometry, which, thanks to the translation made by E. de Jonquières, was widely read on the Continent. It is a really excellent treatise on the properties of plane cubics.

page 15 note† [Exercitatio Geometrica de Descriptione Linearum Curvarum, 1733.]

page 15 note‡ There is a little exaggeration in the following lines from Matthew Arnold’s essay on “The Literary Influence ol Academies”: “The man of genius (Newton) was continued by the English analysts of the eighteenth century, comparatively powerless and obscure followers of the renowned master. The man of intelligence (Leibniz) was continued by successors like Bernoulli, Euler, Lagrange, and Laplace, the greatest names in modern mathematics” (Essays in Criticism, vol. 1. p. 87, Tauchnitz Edn.).

page 16 note* v. chap. vii. of The History of the Study of Mathematics at Cambridge (Cambridge, 1899), and the article on “The Cambridge School of Mathematics” in the Mathematical Gazette, July 1912.

page 17 note* The materials for the history of certain special epochs or theories have been collected by Halliwell, Todhunter, and Muir; and it should not be forgotten that the Proceedings of the British Association for the Advancement of Science contain a large number of valuable reports on the past and present of other theories and periods.

page 18 note* It is most desirable that these should be collected into an organic whole. They would certainly be of the greatest value.

page 18 note† There are many references to this mathematician in Rigaud’s Correspondence of Scientific-Men. Here we learn not only something of the peculiar characteristics of the man, but that he translated and wrote a commentary on the Algebra of Branker and Rhonius, 1668; that he wrote against Longomontanus (a fact known to A. von Braunmühl, v. vol. 1. p. 58 of his Vorlesunaen über Geschichte der Trigonometrie); that he composed a “Table of Squares”; and, finally, that he published in London, in 1650, a volume entitled An Idea of Mathematics,. which does not seem to have deserved the silence and oblivion it has been awarded in mathematical history.

page 18 note‡ Such hopes are spontaneously expressed in Vacca’s letter quoted above.

§ With one accord all mathematicians are calling for a really complete edition of Newton’s works containing all his unpublished writings.