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 development from the 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
correspondent 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 Venturoli's
Mechanics, the first book of Laplace's Mecanique Celeste, and of
the applications of the principles there give to various problems.