MATHEMATICS. 
Phares 1, 2 3.4. 5. 
Martuematics is the science which treats of quantity and of the various 
forms and combinations of magnitudes. The idea of magnitude applies to 
everything which either actually or abstractly admits of increase or, 
diminution. 
Mathematics is divided into Pure and Applied. The former derives all 
its ideas and conclusions directly through the understanding, without 
requiring the least assistance from the experience and knowledge obtained 
through the senses, while the latter applies the deductions of the former to 
the various objects of experience and of the external world. Pure Mathe- 
matics distinguishes two kinds of magnitudes,—continuous, and interrupted 
or discrete. A magnitude is said to be continuous when its parts adhere 
closely together, so that the ending of one part coincides exactly with the 
beginning of the next; to this species belong the magnitudes of extent or 
space, e. g. a surface. A magnitude is interrupted or discrete when its 
parts are separated one from another, as the individual stones in a pile. 
Pure Mathematics is therefore divided into two principal sections, Geometry 
and Arithmetic (in its wider sense). Arithmetic, which includes Arithmetic 
proper, Algebra, and the analysis of finite and infinite quantities, offers 
from its very nature hardly any material for pictorial representations : we 
must therefore confine ourselves to geometry alone 
Geometry (earth measuring) derives its name from a single application 
of the science, which will be treated of hereafter ; and, as before remarked, 
has reference to continuously extended magnitudes, or magnitudes of space. 
As there are three different directions or dimensions of extension, so are 
there also three different kinds of magnitude or space,—lines, surfaces, and, 
solids; of which lines extend only in one direction (length), surfaces in two 
directions (length and breadth), and solids in three (length, breadth, and 
height or thickness). Lines are bounded by points, surfaces by lines, and 
solids by surfaces. Lines are divided into straight and curved; in lke 
manner, surfaces into plane and curved. Geometry itself, nowever, is not 
divided according to the three kinds of magnitudes, but only into two prin- 
cipal sections,—Planimetry (Plane Geometry), and Stereometry (Geometry 
of Solids). The former treats of such magnitudes of space or combinations 
of magnitudes as are found in a single plane, or in which only two dimen- 
sions occur (length and breadth) ; the latter, of those in which all these three 
are found (length, breadth, and height or thickness), and hence it refers to 
ICONOGRAPHIC ENCYCLOPAZDIA.—VOL. I. 1 1 
