University of Virginia Library

3.—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 it 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 our primary

notion of addition; namely, the addition as sensible objects,
one by one. These are dwelt upon, at some length and serve
as the first links of a chain which conducts to the most refined
analysis.—Lacroix's Arithmetic is the text-book.

In Algebra, the first problems are analyzed 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, Legendre is the text-book.

The second junior class, continuing Algebra, and Geometry,
proceed to Trigonometry and its practical applications;
the text-book is Lacroix. Their subsequent course is as follows:
spherical Trigonometry, and its application to practical and
nautical Astronomy, and to the projection and construction of
maps, analytical Geometry, and the first part of the Differential
Calculus; the text-book for which is Bourcharlat. The textbook
for the other subjects are the Professor's manuscript lectures,
with Bonnycastle's Trigonometry for the applications.

The senior classes continue the Differential Calculus, taking
the text partly from Bourcharlat and Lagrange, and partly
from manuscript lectures; and working examples selected from
Peacock and Herschell. The same course is afterwards continued
with the Integral Calculus; which is pursued somewhat
further than is done by Bourcharlat, completes the course of
common Mathematics.

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 given to various problems.

At the commencement of the next session it is intended to
make a partial change in the course by substituting for Legendre's
Geometry, the Cambridge Trigonometry, and the
manuscript analytical Geometry above mentioned, a treatise
of Inductive Geometry embracing all these subjects, and commencing
with an enquiry into the nature of elementary figures,
illustrated by models.