118 
library of Dr. Aley. Chrystal says the bibliography credited to Mr. Hal- 
sted contains all the references up to its time, save one, giving the non- 
Euclidean arguments. The list is not complete in arguments for Euclid, 
it being impossible to enumerate all the editions of Euclid, edited and up- 
held by the different mathematicians. The list is complete enough, how- 
ever, to assure the reader that there are arguments for Euclid as well as 
against him. 
aff 
1 
10. 
cha 
12. 
T. S. Aldis: “Remarks on the Teaching of Geometry.” 
Isaac Barrow: “Mathematical Lectures,’ London, Stephen Austen, 
1734. - 
Arthur Caley, Collected Papers of, Vol. II, pp. 604-6; Vol. V, p. 471; 
Vol. VIII, XX XIII-V, pp. 409-13; Vol. XII, pp. 220-38; Vol. XIII, 
p. 480. 
H. W. Challis: “A Letter to John Stuart Mill on the Necessity of 
Geometry and the Association of Ideas,’ Oxford and London, 
James Parker & Co., 1867. 
G. Chrystal: ‘“Non-Euclidean Geometry,” Edinburg, David Douglas, 
1880; “Presidential Address,” Bedford, W. J. Robinson, 1887. 
Thos. Cullorin: “A paper on Parallels,’ Quar. Jour. of Math., Vol. 
27, pp. 188-225. 
Edward T. Dixon: “The Foundations of Geometry,’’ London, Geo. 
Bell & Sons, 1891. 
Charles lL. Dodgson: “Euclid and His Modern Rivals,’’ Supplement 
to “Euclid and His Modern Rivals,’ London, Macmillan & Co., 
1885; “A New Theory of Parallels,” London, Macmillan & Co., 
1890. 
Geo. B. Halsted: ‘A Bibliography of Hyper-space and Non-Euclidean 
Geometry,” Amer. Jour. of Math., Vol. I, pp. 261-276, 384, 385; Vol. 
II, pp. 65-70; “Elements of Geometry,’’ New York, John Wiley & 
Sons, 1885. (See Lobatschewski.) 
Henrici: ‘‘Presidential Address,’ Bedford, W. J. Robinson, 1887. 
J. Larmor: ‘On the Geometrical Method,” The Math. Gazette, No. 7, 
April, 1896. 
Nicolai Ivanovich Lobatschewski: ‘‘New Principles of Geometry,” 
translated from the Russian by G. B. Halsted, Austin, The Neo- 
mon, 1897; “Geometrical Researches on the Theory of Parallels,’ 
translated by Halsted. 
