An Elementary Course of Plane Geometry and Mensuration

Abstract

THIS book is the work of a reformer, not so much of geometry, as of the mode of presenting it to the young. Sciences begin in practical applications, and tend by a universal law to become more and more abstract; and the doctrine of the reforming school is that whatever the science may have developed into, it is necessary in teaching it to go back to practical applications, and to seek for a sure foundation for abstract notions in the familiar experience of common objects. Teachers need to be incessantly reminded of this necessity. In teaching physics or chemistry or botany it is perhaps admitted, though not always obeyed; but in mathematics it is generally not admitted; and when admitted, it is rarely followed out to its logical consequences. Geometry, arithmetic, algebra, must alike be presented first in their applications; and then alone, in most cases, can definition and soundness be given. In most cases, we say, because where mathematical talents of a moderately high order exist, as in the generality of mathematical teachers, this necessity is not felt. And for this reason mathematical teachers who are not also observant of mental phrases, may be slow to believe what has just been pointed out as a necessity in their art. Many of them, we suspect, have a secret sympathy with the mathematician who proposed the health of “The prime numbers, the only branch of mathematics that has not been defiled by contact with the concrete.”

An Elementary Course of Plane Geometry and Mensuration.

By Richard Wormell Second Edition, revised and enlarged. Fcap. 8vo., pp. 276. (London: T. Murby.)