Say the earth has existed 6000 years, the population always having been 800,000,000, and the average life of man 30 years; this being the utmost that could be claimed. Allow then the State of Virginia to contain 70,000 square miles, and each grave to occupy a space of 6 feet by 2; the territory of the State would contain 162,624,000,000; while the mighty army of the dead would number only 160,000,000,000; leaving 2,624,000,000 graves yet unoccupied. How wide of truth then is the position often set forth so positively!
TRICKS IN GEOMETRY.
"Let young beginners come and try
Their hands at our geometry."
The word Geometry is derived from the Greek, and signifies the art of measuring land. The invention of it is ascribed by some to the Chaldeans and Babylonians, by others to the Egyptians, who were obliged to determine the boundaries of their fields after the inundation of the Nile, by geometrical measurements. According to Cassiodorus, the Egyptians either derived the art from the Babylonians, or invented it after it was known to them. Thales, a Phœnician, who died 548 years B.C., and Pythagoras of Samos, who flourished about 520 B.C., introduced it from Egypt into Greece. In elementary geometry, Euclid of Alexandria, as everybody knows, is particularly distinguished. Archimedes measured the sphere, and after him other philosophers prosecuted the science with the utmost assiduity. In Italy, where the sciences first revived after the dark ages, several mathematicians were distinguished in the 16th century. The French, and after them the Germans, followed; while in England, Hook, Newton, and others, carried the science to the highest pitch of usefulness, and through its aid made the most prodigious discoveries. It is not, however, our province to enter into a long disquisition on the subject, but simply to set before the young reader some of the more curious properties of the science, that he may be excited to study it for himself; and we will promise him that should he devote his mind to its study, he will be amply repaid for any amount of labor he may bestow upon it.
GEOMETRICAL DEFINITIONS.
In geometry a point is said to have neither breadth, length, nor thickness. A line is the distance between two points; parallel lines always keep at the same distance from each other. A right line is what is commonly called a straight line. A curve is a line which continually changes its direction. An angle is the inclination or opening of two lines meeting in a point. A figure is a bounded space, and is either a superficies or a solid. A triangle is a figure with three sides and three angles. A square has four equal sides, and four right angles. A circle is a plane figure bounded by a curved line running into itself. Its diameter is a straight line drawn from one extremity of its circumference to the other, and its center is equally distant from every part of the circumference. A solid is any body which has length, breadth, and thickness; and a sphere is a solid, terminated by a convex surface, every part of which is at an equal distance from a point within, called its center.
THE FIVE GEOMETRICAL SOLIDS.