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

1826:

Mathematics Curriculum

"In Mathematics, there is taught 1st, Algebra: 2, common and Descriptive Geometry; 3, Plane and Spherical Analytical Trigonometry; 4, Shades, Shadows, and Linear Perspective; 5, Analytical Geometry, embracing the construction of algebraical equations, the equations of points and lines in the plane of the two coordinates, polar and polar equations, the equation of the surface of a cone and o f the intersection of this surface by planes, the discussion of the properties of conic sections and their polar equations, and the decision of equations of the second degree; 6, Differential and Integral Calculus, embracing the differentiation of algebraical and transcendental quantities, Taylor's and Maclaurin's theorems, the development of a function of two variables, the application of the calculus to the theory of curves in drawing  tangents and normals, and on determining asymptotes, its application to the maxima and minima of variable functions, and its further application in determining osculatrices, radii of curvature, and the discussion of evolutes and transcendental curves, the integration of [poly]nomials and binomials, rational irrational fractions and binomials by series, the application of differential and integral calculus to the rectification of curves, quadratures and cubatures, namely, to the rectification of the conic sections, the cycloid and spiral lines and the determining of their areas, to the determining the surfaces and solidities of the conoid and the surface and solidity of the solid generated by the revolution of the cycloid about its base; 7, The Orthographic and stereographic projections of the sphere; 8, Surveying, including the use of the Theodolite, compass and plane table, and the measurement of heights and distances."