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The Ontario High School Geometry is intended to cover the course in Theoretical Geometry, begun in the Lower School and completed in the Middle School, as defined in the Programme of Studies for High Schools and Collegiate Institutes of the Province of Ontario.

In deference to the wish of the teachers of mathematics of the Province, this Geometry is divided into Books with numbered propositions.

While the theoretical course is complete in itself, it is assumed that its study has been preceded by the usual course in drawing and measurement. A considerable number of practical problems are given in the exercises. These should be worked out carefully, and, in fact, all diagrams should be accurately and neatly made.

The book contains an abundant supply of carefully selected and graded exercises. Those given in sets throughout the Books will be found suitable for the work of average classes, and just about sufficient in number to fix the subject-matter of the propositions in the minds of the pupils. All the problems contained in the miscellaneous collections at the ends of the Books could be worked through by a few of the best pupils only, and should be used also by the teachers as a store from which to draw suitable material for review purposes

from time to time. While the requirements of class-work have been constantly kept in mind in the choice of proofs, it should not be assumed that other proofs, just as good, cannot in many cases be given.

M306170

Students should be constantly encouraged to work out methods of their own, and to keep records of the best in their note books.

Symmetry has been used to an unusual extent in giving a more concise form to the proofs of constructions.

The treatment of parallels, in accord with the method of many of the best English text-books, is based on Playfair's Axiom.

Tangents are treated both by the method of limits and as lines which meet the circle in only one point.

Areas of triangles and parallelograms are compared with rectangles, thereby not only giving a simple method of treatment, but also promoting facility in numerical computations.

Similarly, the treatment of proportion is correlated with the algebraic knowledge of the pupil.

OTTAWA, June, 1910.

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st. straight. L, 28, 2d angle, angles, angled.

A, As triangle, triangles.

II, lls parallel, parallels. Ilgm, Il gms parallelogram, parallelograms. sq., sqs. square, squares.

AB2 the square on AB.

rect. rectangle.
AB.CD the rectangle contained by AB and CD.

AB
AB: CD, or the ratio of AB to CD.

CD
+ plus, together with.

minus, diminished by.
I is perpendicular to, a perpendicular.

is equal to, equals.
> is greater than.
< is less than.
= is congruent to, congruent.
III is similar to, similar.

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