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[ARCHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 139 
Homology: Parallel plane sections of polyhedral angles. Areas. 
Polyhedra: Homothetic polyhedra, similar polyhedra. Prisms, 
Pyramids.—Summary of notions on the symmetry of the cube 
and of the regular octahedron.—Volumes of parallelopipeds and 
of prisms. Volume of the Pyramid.—Volume of a pyramid truncated 
by parallel sections. Volume of a truncated triangular prism.—Ratio 
of the volumes of two similar polyhedra.—Two symmetrical polyhedra 
are equivalent.—Sphere: plane section, poles, tangent plane. Circum- 
scribed cone and cylinder. Area and volume. 
Mathématiques A 
Arithmetic: Common fractions. Reduction of a fraction to its 
simplest terms. Reductionof several fractions to a common denominator 
Least common denominator. Operations with common fractions.— 
Decimal numbers. Operations (considering the decimal fractions as 
particular cases of ordinary fractions). Calculation of a quotient to 
a given decimal approximation.—Reduction of an ordinary fraction 
to a decimal fraction; condition of possibility. When the reduction is 
impossible, the ordinary fraction can be regarded as the limit of an un- 
limited periodic decimal fraction.—Square of a whole number or of a 
fractional number; nature of the square of the sum of two numbers. 
The square of a fraction is never equal to a whole number. Definition 
and extraction of the square root of a whole number or of a fraction to 
a given decimal approximation.—Definition of absolute error and of 
relative error. Determination of the upper limit of an error made in 
a sum, a difference, a product, a quotient, knowing the upper limits of 
the errors by which the given quantities are affected.—Metric System. 
Algebra: Monomials, polynomials; addition, subtraction, multi- 
plication and division of monomials and of polynomials. Equations of 
the second degree in one unknown. Simple equations which are 
equivalent. (The theory of imaginaries is not developed).—Problems 
of the first and second degree.—Arithmetic Progressions. Geometric 
Progressions. Common Logarithms. Compound Interest, annuities. 
Trigonometry: Circular Functions. Addition and Subtraction of 
arcs. Multiplication and division by 2.—Resolution of triangles. 
Applications of Trigonometry to various questions relative to the 
elevation of planes. (The construction of the trigonometric tables is 
not to be considered). 
Geometry: Inversion’. ‘Applications. Peaucellier’s Cell.—Polar of 
a point with respect to a circle. Polar plane of a point with respect to 
a sphere.—Hyperbola: Trace, tangent; asymptotes; simple problems 
on tangents. Equation of a hyperbola with respect to its axes. Plane 
sections of a cone and of a cylinder of revolution. 
