University of Virginia Library

III. MATHEMATICS.

Professor Bonnycastle.—In this school there are commonly four
classes.

Mathematics, in its present state, is divided into many distinct branches
—of which we may enumerate.

1st. Those few simple rules which have for their object not to assist any
process of reasoning foreign to number, but merely, to determine such

numbers as occur in domestic life—commerce—or other departments of or
dinary business.

2dly. That very extensive—general and exact logic—which has sufficed
to reduce at least three fourths of the propositions of which human reason
is conversant, to propositions either of pure number, or that can be
solved by means of pure number.

3dly. The rules of mere calculation required in some of the branches of
practical mathematics—as in surveying—navigation—practical astronomy,
&c.

The very enlarged views—the increased power of reasoning—and the
exercise of mind which the second of these divisions affords—renders it
incomparably the most important as a branch of general education—Yet
to give effect to its great powers in this respect, it must be taught in a manner
very different from that formerly adopted, and which whilst largely
followed in Europe, is to be found in none of our text books, and in few of
our schools. It is this branch of the subject which is especially studied
in the University—and the great objects which it proposes to attain, and
the simple—general—and closely connected methods whereby it attains
them are kept constantly before the student's view.

The first junior class 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 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 students sensible of the advantages of these signs. In
teaching the rules for adding, substracting, &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.