science was geometry, which was
first taught in Egypt,--the nurse and cradle of ancient wisdom. It arose
from the necessity of adjusting the landmarks disturbed by the
inundations of the Nile. There is hardly any trace of geometry among the
Hebrews. Among the Hindus there are some works on this science, of great
antiquity. Their mathematicians knew the rule for finding the area of a
triangle from its sides, and also the celebrated proposition concerning
the squares on the sides of the right-angled triangle. The Chinese, it
is said, also knew this proposition before it was known to the Greeks,
among whom it was first propounded by Thales. He applied a circle to the
measurement of angles. Anaximander made geographical charts, which
required considerable geometrical knowledge. Anaxagoras employed
himself in prison in attempting to square the circle. Thales, as has
been said, discovered the important theorem that in a right-angled
triangle the squares on the sides containing the right angle are
together equal to the square on the opposite side of it. Pythagoras
discovered that of all figures having the same boundary, the circle
among plane figures and the sphere among solids are the most capacious.
Hippocrates treated of the duplication of the cube, and wrote elements
of geometry, and knew that the area of a circle was equal to a triangle
whose base is equal to its circumference and altitude equal to its
radius. The disciples of Plato invented conic sections, and discovered
the geometrical foci.

It was however reserved for Euclid to make his name almost synonymous
with geometry. He was born 323 B.C., and belonged to the Platonic sect,
which ever attached great importance to mathematics. His "Elements" are
still in use, as nearly perfect as any human production can be. They
consist of thirteen books. The first four are on plane geometry; the
fifth is on the theory of proportion, and applies to magnitude in
general; the seventh, eighth, and ninth are on arithmetic; the tenth on
the arithmetical characteristics of the division of a straight line; the
eleventh and twelfth on the elements of solid geometry; the thirteenth
on the regular solids. These "Elements" soon became the universal study
of geometers throughout the civilized world; they were translated into
the Arabic, and through the Arabians were made known to mediaeval
Europe. There can be no doubt that this work is one of the highest
triumphs of human genius, and it h