After multiplication
by
a + b + e = 2s, the equation
(2)
can be manipulated into
the form
~alx -
(s
al
a
~sceJ.
This
expression, in turn, is equivalent to
sin
x §B=
sin ?A sin
1C,
of which triangle (1) is a special case."
5. Acknowledgments.
I obtained references 1, 2 from [157;
references 3,
7, 9, 17 from [2o1; reference 4 from
[51; reference 6 from [11 J; reference 8 from [147; reference 10 from [167; reference 12 from
[131; all the remaining references are my own.
REFERENCES
1. Journal fur die reine and angewandte Mathematik, Vol. 28, 1844, p. 376.
2. Archiv der Mathematik and Physik,
Vol.
15, 1850, p. 225.
3. J. J. Sylvester, On a simple geometrical problem illustrating a conjectured principle in
the theory
of
geometrical method, Philosophical Magazine,
Vol.
u, 1852, pp. 366 - 369.
u. Journal de rriathematiques elementaires et speciales, 1880, p. 538.
5. F. G.- M., Exercises de Geometrie Mame et Fils, Tours, 1907, pp. 234 - 235.
6. Nathan Altshiller-Court, Mathematical Gazette, Vol. 18, 1934, p. 120.
7. A. Henderson, A classic problem in Euclidean geometry, J. Elisha Mitchell Soc., 1937,
pp. 246 - 281.
e.
G. H. Hardy, A Mathematician's Apology, Cambridge University Press, 1940, P.
:111.
9. J. A. McBride, The equal internal bisectors theorem, Edinburgh Mathematical Notes, Vol.
33, 1943, pp. 1 -13.
10. V. Thebault, The Theorem of Lehmus, Scripta Mathematica, Vol. 15, 1949, pp. 87 -
88.
11. Nathan Altshiller-Court, College Geometry, Barnes and Noble, 1952, p. 73.
12. Scientific American, Vol. 204, 1961, pp. 166-168.
13. G. Gilbert and D. McDonnell, The Steiner-Lehmus Theorem, American Mathematical. Monthly,
Vol. 70, 1963, pp. 79-80.
14. H. S. M. Coxeter, S. L. Greitzer, Geometry Revisited, Random House of Canada, 1967, pp.
14 - 16, 156.
15. H. S. M. Coxeter, Introduction to Geometry, 2nd Edition, Wiley, 1969, pp.9, 420.
16. David C. Kay, College Geometry, Holt, Rinehart and Winston, 1969, pp.
119, 348.
17. J. V. Malesevic, A direct proof of the Steiner-Lehmus Theorem, Mathematics Magazine,
Vol. 43, 1970, pp. 101 - 102.