page 309 note * Of Galilei’s Discorsi there is a German translation in Ostwald’s Klassiker der cxakten 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 “&λоγоs,” 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. Rösler’s tract Die neueren Definitionsformen der irrationalen Zahlen und ihre Bedeutung für die Schule (Hannover, 1886).