The Teaching of Geometry

by David Eugene Smith

[36] Carson, loc. cit., p. 15.

[37] Al-jabr wa'l-muqābalah: "restoration and equation" is a fairly good translation of the Arabic.

[38] Or be carried along at the same time as a distinct topic.

[39] With a single year for required geometry it would be better from every point of view to cut the plane geometry enough to admit a fair course in solid geometry.

[40] Carson, loc. cit., p. 13.

[41] Carson, loc. cit., p. 12.

[42] From the Greek γη, ge (earth), + μετρειν metrein (to measure), although the science has not had to do directly with the measure of the earth for over two thousand years.

[43] From the Arabic al (the) + jabr (restoration), referring to taking a quantity from one side of an equation and then restoring the balance by taking it from the other side (see [page 37]).

[44] One of the clearest discussions of the subject is in W. B. Frankland, "The First Book of Euclid's 'Elements,'" p. 26, Cambridge, 1905.

[45] "Grundlagen der Geometrie," Leipzig, 1899. See Heath's "Euclid," Vol. I, p. 229, for an English version; also D. E. Smith, "Teaching of Elementary Mathematics," p. 266, New York, 1900.