138 ROYAL SOCIETY OF CANADA 
II.——LESSONS ON THE SUBJECTS OF THE PROGRAMME OF THE SECONDE 
AND PREMIÈRE (C AND D) AND MATHÉMATIQUES A. 
Seconde (C. and D.). 
Algebra: Resolution of equation of the first degree in one unknown. 
Inequalities of the first degree. Resolution and discussion of two 
equations of the first degree in two unknowns.—Problems; substitution 
in equation. Discussion of the results.—Variation of the expression 
ax+b; graphic representation.—Equations of the second degree in 
one unknown (theory of imaginaries not discussed). Relations between 
the coëfficients and the roots. —Existence and signs of the roots. Study 
of the trinomial of the second degree.—Inequalities of the second degree. 
Problems of the second degree. Variation of the trinomial of the second 
degree. Graphic representation. Variation of the Expression xt: 
graphic representation.—Notion of derivative; geometrical significance 
of the derivative. The sign of the derivative indicates the direction of 
the variation; applications to very simple numerical examples and in 
particular to the functions studied before. 
Geometry: Simple notions of homothetic figures. Similar polygons. 
Sine, cosine, tangent and cotangent of positive angles less than 2 right 
angles. Metrical relations in a right triangle and in any triangle. Pro- 
portional lines in the circle. Fourth proportional; mean proportional.— 
Regular polygons. Inscription in a circle of a square, of a hexagon; of 
an equilateral triangle, of a decagon, of a quindecagon. Two regular 
polygons of the same number of sides are similar. Ratio of their peri- 
meters. Length of an are of a circle. Ratio of the circumference to 
the diameter. Calculation of =z (confined to the method of the peri- 
meters).—Area of polygons; area of a circle. Measure of the area of 
a rectangle, of a parallelogram, of a triangle, of a trapezium, of any 
polygon.—Ratio of the areas of two similar polygons—Area of a regular 
convex polygon. Area of a circle, of a sector and of a segment of a 
circle. Ratio of the areas of two circles. 
Première (C. and D.). 
GEOMETRY. 
Translation: Rotation about an axis. Symmetry with respect 
to a line. Symmetry with respect to a point. Symmetry with respect 
toaplane. This second kind of symmetry is equivalent to the first. 
Trihedral Angles: Disposition of the elements. Trihedral symme- 
try. Each face of a trihedral is less than the sum of the other two. 
Limits of the sum of the faces of a trihedral.—Supplementary trihedrals. 
Applications.—Inequalities of the trihedrals. 
