Quotations from the Annual Report of the Board of Visitors to the United States Military Academy made to Congress and the Secretary of War, for the year 1825.

We begin with a quotation about mathematics from p. 135-136, include a portion of a chart from p. 147, and end with some oral examination questions from pp. 148-149.

8th. The branch of Mathematics is next in order, and may justly be considered one of the leading departments in the Academy. The Board deem it no more than justice to state, that the condition of this department leaves nothing to desire. In all its branches, from the elementary rules of Algebra to Problems of great difficulty in the Integral and Differential Calculus, the examination afforded proof of an admirable method of instruction and of rare proficiency. The appearance of the Cadets in Descriptive Geometry, a branch particularly adapted to a Military School, was highly gratifying for the rapidity and elegance with which they conducted their investigations on the black board, requiring long and intricate demonstations and involving many substitutions. In the application of Algebra to Geometry, in the principles of Analytical Plane and Spherical Trigonometry, in the doctrines of Perspective Shades and Shadows, and the Integral and Differentil Calculus, the proficency of the Cadets exceeded anything which the Board have had occasion to withness in any other American Seminary. Nor were their performance less credible in other Graphic and Serrographic projection, and the principles of stone-cutting; a part of the course which the Board believe, is exclusively taught by the lectures of the Professor, with exercises on the black board [[ sic ]], and wtihout the basis of a Text Book.

To give the most satisfactory proof of the progress made by the Cadets in this department, a solution of Problems, contained in the annexed paper marked (B), are submitted by the Board from among many others promptly analysed, drawn, and demonstrateded in the Examination Room without previous preparation.

Specimens of Problems Solved by the Cadets in Philosophy and Mathematicks.

[[ The mathematics problems are preceeded by six in Civil Engineering, five in Military Engineering, and six in Philosophy, i.e., in Physics. One of each type has been selected as an illustration from pp. 148-149. ]]

Selections of Problems and exercises in Civil Enginering.

1st. Explain the practical theory of equilibrium of arches and their abutments, and find, by a practical method, the position and depth of the joints of an equilibrated arch.

Problems in Military Engineering.

4th. Draw and explain at large the detail of Monge's modified front.

Problems in Philosophy.

6th. The centripetal force varying according to any law and the quadrature of curves being granted; find the trajectories in which bodies will move as well as the times of their motion in the trajectories found.

Problems in different branches of Mathematicks.

1st. Make the projection of the screw, and determine the lines of shade on the surfaces of the threads, the shadows cast on those threads, and the shadows cast by the different parts of the screw on a given plane.

2nd. Put in perspective an arch formed by the intersection of two equal cylinders, whose axes are at right angles, also the pedestals on which they rest; find the perspective of the different shadows on its interior, as also the shadows which it casts on a given plane.

3rd. Explain the base and modulus of a system of logarithms, and compare the logarithms of a given quantity in one system with the logarithm of the same quantity in any other system.

4th. Show what the differential of the loagrithm of any quantity in any system is equal to, and the manner in which it is found.

5th. Analyze a curve from its most general equation, find the points of rebrousement, of inflexion, and where the tangents are parallel, or perpendicular, to the axis of abscissa.

6th. Explain the method of integrating monomial and binomial expressions, rational and irrational functions, and the general process of integrating by parts and series.

7th. Find the solidity and the surface of the solid generated by the revolution of the cycloid about its base.

8th. Show the application of the calculus to the rectification of curves.

Remarks:

It is interesting that the second year (third class) cadets are studying calculus from three different books: Lacroix (First English edition 1816), Bourchelet (not "Bourharies" as the table has it), and Hutton (possibly as late as the 1822 edition, but this is very unclear). One wonders what problems this caused for resectioning (was it weekly at this time?). Need to look at these books and figure out precisely which sections were being covered.

If "Lecroix's Algebra," which was used by the fourth section of plebes, is, as it appears, in English, then it has to be Silvestre François Lacroix (1765-1843), Elements of algebra; translated from the French for the use of the students of the university at Cambridge, New England, Cambridge, N. E. : Printed by Hilliard and Metcalf at the University Press, 1818: "... The following translation [by John Farrar] is from the eleventh edition, printed at Paris in 1815"--p. [iii]. The second English edition is 1825. Curiously this work was unknown to Thayer in 1821.

Excerpts Related to Mathematics from Annual Reports of the Board of Visitors to the United States Military Academy

1825:  

Mathematics Curriculum

Page created November 2000.
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