[56] Loc. cit., Vol. II, p. 94.
[57] Address at Brussels, August, 1910.
[58] For a recent discussion of this general subject, see Professor Hobson on "The Tendencies of Modern Mathematics," in the Educational Review, New York, 1910, Vol. XL, p. 524.
[59] A more extended list of applications is given later in this work.
[60] Abū'l-'Abbās al-Fadl ibn Hātim al-Nairīzī, so called from his birthplace, Nairīz, was a well-known Arab writer. He died about 922 A.D. He wrote a commentary on Euclid.
[61] This illustration, taken from a book in the author's library, appeared in a valuable monograph by W. E. Stark, "Measuring Instruments of Long Ago," published in School Science and Mathematics, Vol. X, pp. 48, 126. With others of the same nature it is here reproduced by the courtesy of Principal Stark and of the editors of the journal in which it appeared.
[62] In speaking of two congruent triangles it is somewhat easier to follow the congruence if the two are read in the same order, even though the relatively unimportant counterclockwise reading is neglected. No one should be a slave to such a formalism, but should follow the plan when convenient.
[63] Stark, loc. cit.
[64] Of which so much was made by Professor Olaus Henrici in his "Congruent Figures," London, 1879,—a book that every teacher of geometry should own.
[65] Much is made of this in the excellent work by Henrici and Treutlein, "Lehrbuch der Geometrie," Leipzig, 1881.