Geometry is a branch of mathematics that treats of figures and
space. The name is Greek, signifying earth measurement. The science is
thought to have grown out of land surveying. It was developed first in
Mesopotamia and in Egypt, both regions in which it was necessary to
reestablish boundaries between fields, after the great inundations that
occur each year. The Greeks were noted mathematicians. The textbook of
plane and solid geornetry now used in schools is essentially that
written by Euclid, a professor of mathematics in the Greek university
of Alexandria, Egypt, who flourished about 300-270 B. C. He taught and
wrote in the Greek language. His geometry was divided into thirteen
books, which were preceded by definitions and axioms, largely as we have
them today.
The study of geometry is of exceptional value in
teaching students to think and to speak accurately. In geometry a
statement is worthless unless absolutely accurate. The conclusions of
geometry are also exceedingly satisfactory. We may say of Nero that he
was cruel, and yet later find it necessary to modify our opinion; but
the geometrical statement that the three angles of a triangle are
together equal to two right angles may be proved beyond question, and is
true for all time, of all triangles. One cannot be absolutely certain
of the spelling of a word, for custom changes. The chemist must be on
the lookout constantly, lest some unexpected circumstance prevent
chemical action taking place as expected; but when two straight lines
cross each other, the opposite angles formed are always equal. They
cannot be otherwise. For this reason geometry is spoken of as an exact
study. It is also exceedingly practical. The builder finds that a
timber forming a triangle with two other timbers is not only a rigid
frame, but the only rigid frame known. Geometry gives the reason; a
triangle cannot change its shape without changing the length of at least
one side. Geometry also furnishes the only method of constructing an
exact right angle, that is, of turning a square corner. The rules of
mensuration are supplied by geometry. Without geometry the rules for
finding the area of a triangle, a rectangle, or a circle, as well as
those for finding the solid contents of spheres and other solids, would
be mere guesswork.
