page 309 note * Of Galilei's Discorsi there is a German translation in Ostwald's Klassiker der exaMen Wisscnschaften, and a good account of much of Galilei's work in the English translation of Mach's Mechanics.

page 309 note † That the word “irrational” is merely a bad translation of which here means “inexpressible,” is remarked on p. 248. This remark seems to have been made first by Kepler in 1649 (according to a note by Terquem in Journ. de Math., t. i., 1836, p. 101).

page 309 note We think that, when dealing with irrational numbers and limits, Dr. Höfler might with advantage have introduced such a clear discussion of the logical error involved in defining a real number as a limit (in the usual sense) as is found in A. Rösier's tract Die ncueren Definitionsformen der irrationalen Zahlen und ihre Bedeutung für die Schule (Hannover, 1886).