The lectures on mathematics form of themselves a continuous, closely connected whole; consequently, the same teacher who gave instruction in the first cœtus is to retain his pupils in the second, so that each of the two teachers commence with the first cœtus in alternate years.
For the third cœtus there will be a selection made of those students who have made themselves noticed in the second cœtus by distinguished ability, special application, and peculiar talent for the study of mathematics, and have thus raised hopes that they may be conducted with success into the higher branches of the science.
They form a separate division, whose number should always be small if the selection be guided strictly by the contemplated purpose. All the other students of the third cœtus form a second division, in which the entire field of what they have already been taught in mathematics is again gone over, with a view to its application; and at the end of this course some other subjects necessary to the Artillerist and Engineer are to be treated, without, however, mere scientific speculations.
For each of these divisions a separate teacher is appointed.
A. THE LECTURES IN THE FIRST CŒTUS EMBRACE,—
I. Arithmetic and Algebra.
1. Algebra, with sums, differences, products, quotients, whole numbers, roots, powers with real exponents and logarithms. The qualities of fixed numbers, fractions, decimal and continued fractions. Extraction of square and cubic roots in figures and letters, practical use of logarithms.
2. Algebra, equations of the first and second degree, with one or more unknown quantities, proportions, and the higher numerical equations.
3. Arithmetical and geometrical progression, calculation of interest, theory of combination, binomial theory for real exponents, series for powers and logarithms and analytic trigonometry.
4. Cubic and biquadratic equations, pure equation of the nth degree, reciprocal equations. (4½ months.)