University of Virginia Library

III. MATHEMATICS.

Professor Bonnycastle.—In this school there are commonly five classes.
Of these the first junior begins with Arithmetic; but as the student is required
to have some knowledge of this subject when he enters the University, the lectures
of the Professor are limited to the theory, shewing the method of naming
numbers, the different scales of notation, and the derivation of the several rules
of Arithmetic from the primary notion of addition; the addition namely, of
sensible objects one by one. The ideas thus acquired are appealed to at every
subsequent step, and much pains are taken to exhibit the gradual developement
from these elementary truths of the extensive science of mathematical analysis.
Lacroix's Arithmetic is the text book.

In Algebra, the first problems are analized, with and without the use of letters,
to make the student sensible of the advantages of these signs. In teaching
the rules for adding, subtracting, &c., they are compared with the corresponding
rules in Arithmetic, and the agreement or diversity is noticed and explained.
The text book is Lacroix's Algebra.

In Geometry, the first elements are taught, and illustrated by the use of
models.

The second junior class continue to read Lacroix's Algebra, and Bonnycastle's
Inductive Geometry. In the latter, they successively acquire—the theorems
of Synthetic Geometry—the theory and practice of Plane and Spherical
Trigonometry, with the application of the latter to Nautical Astronomy—the
theory of Projection—and the theory of curved lines and Surfaces. Their
subsequent studies usually embrace a portion of the Differential Calculus.

The senior classes continue the Differential Calculus in lessons taken from
Young and from Bonnycastle's Geometry, concluding the course of Pure Mathematics
with the Integral Calculus, the theory of which is taken from Young,
and the examples from Peacock.

There is, moreover, a class of Mixed Mathematics, for such of the more advanced
students as choose to pursue it; which consists of parts of Poisson's
Mechanics, the first book of Laplace's Mechanique Celeste, and of the applications
of the principles there given to various problems.