144 ROYAL SOCIETY OF CANADA 
Volumes of parallelopipeds and prisms; of the pyramid. Un- 
necessary to consider truncated pyramid or prism. 
Notion of the derivative. Geometrical interpretation. Applications. 
Homothetic polyhedra. Similar polyhedra. (Programme of the 
Première). 
Problems of the second degree. 
First lesson on regular polygons. 
Work, kinetic energy for a particle. Simple examples. 
Decimal numbers. Operations. Calculation of a quotient to a 
given decimal approximation. 
Resolution of triangles (omitting right angled triangles). 
Multiplication and division of arcs by 2. 
Summary of notions on the symmetry of the cube and of the regular 
octahedron. 
Rabatting. Applications; angle between two lines, a line and a 
plane, two planes. 
Calculation of I. 
Upper limit of absolute error of a sum, of a difference, of a product 
of two factors, of a quotient, of a square root. 
Volume of a sphere. Spherical segment. 
Tangent to a hyperbola. Asymptotes. Simple problems on 
tangents. 
Theory of moments with respect to, a point, an axis. 
MATHÉMATIQUES SPÉCIALES. 
Movement of a heavy particle on an inclined plane with and without 
friction, the initial velocity being zero or directed along the line of 
greatest inclination. | 
Power Series. Interval of convergence. Differentiation. In- 
tegration. 
Series of positive terms. Nature of the convergence or divergence 
drawn from the study of the expression 
Un+1 
pr 
Discussion of the commensurable roots of an equation with integral 
Pilars . 
: Vu, , nu, , numerical examples. 
coefficients. Examples. 
Movement of a point attracted by a fixed centre of force in the ratio 
of the inverse square of the distance. 
_Functions of several independent variables. Partial derivatives. 
Formula of finite increments; derivatives of a compound function. 
Concavity, convexity. Points of inflexion (rectangular coordinates). 
Elimination of one unknown between two algebraic equations by 
means of symmetric functions. 
Normal to an ellipsoid. 
