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49 ╞ф└╠┴І - ... syntax; (3) abundant easy exercises, designed not only to fix in the memory the forms and principles of grammar, but also to cultivate readiness in the reproduction of natural forms of expression; (4) the reading of from...
54 ╞ф└╠┴І - ... quadratic equations, both numerical and literal ; simple cases of equations with one or more unknown quantities, that can be solved by the methods of linear or quadratic equations ; problems depending on quadratic equations ; the binomial theorem for positive integral exponents ; the formulas for the nth term and the sum of the terms of arithmetical and geometrical progressions, with applications.
51 ╞ф└╠┴І - INSTRUCTION At the end of the advanced course the pupil should be able to read at sight, with the help of a vocabulary of special or technical expressions, difficult French not earlier than that of the seventeenth century ; to write in French a short essay on some simple subject connected with the works read ; to put into French a passage of easy English prose ; and to carry on a simple conversation in French.
53 ╞ф└╠┴І - Fractions, including complex fractions, and ratio and proportion. Linear equations, both numerical and literal, containing one or more unknown quantities. Problems depending on linear equations. Radicals, including the extraction of the square root of polynomials and of numbers. Exponents, including the fractional and negative.
54 ╞ф└╠┴І - The formulas for the nth term and the sum of the terms of arithmetical and geometric progressions, with applications. It is assumed that pupils will be required throughout the course to solve numerous problems which involve putting questions into equations. Some of these problems should be chosen from mensuration, from physics, and from commercial life. The use of graphical methods and illustrations, particularly in connection with the solution of equations, is also expected.
54 ╞ф└╠┴І - The usual theorems and constructions of good textbooks, including the relations of planes and lines in space; the properties and measurement of prisms, pyramids, cylinders, and cones; the sphere and the spherical triangle. The solution of numerous original exercises, including loci problems. Applications to the mensuration of surfaces and solids.
50 ╞ф└╠┴І - The second year's work should comprise: (1) the reading of 250 to 400 pages of easy modern prose in the form of stories, plays, or historical or biographical sketches ; (2) constant practice, as in the previous year, in translating into French easy variations upon the texts read; (3) frequent abstracts, sometimes oral and sometimes written, of portions of the text already read; (4...
54 ╞ф└╠┴І - Permutations and combinations, limited to simple cases; complex numbers, with graphical representation of sums and differences; determinants, chiefly of the second, third, and fourth orders, including the use of minors and the solution of linear equations; numerical equations of higher degree, and so...
54 ╞ф└╠┴І - Definitions and relations of the six trigonometric functions as ratios; circular measurement of angles. Proofs of principal formulas, in particular for the sine, cosine, and tangent of the sum and the difference of two angles, of the double angle and the half angle, the product expressions for the sum or the difference of two sines or of two cosines, etc.; the transformation of trigonometric expressions by means of these formulas. Solution of trigonometric equations of a simple character. Theory...
51 ╞ф└╠┴І - ... to put into German short English sentences taken from the language of everyday life or based upon the text given for translation, and to answer questions upon the rudiments of the grammar, as defined below.
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