15. An OBTUSE ANGLE is greater than a right angle.

16. Two straight lines are parallel, when they lie in the same plane and can

not meet, how far soever, either way, both

may be produced. They then have the same direction.

17. A PLANE FIGURE is a portion of a plane bounded by lines, either straight or curved.

18. A POLYGON is a plane figure bounded by straight lines.

The bounding lines are called sides of the polygon. The broken line, made up of all the sides of the polygon, is called the perimeter of the polygon. The angles formed by the sides are called angles of the polygon.

19. Polygons are classified according to the number of their sides or angles.

A Polygon of three sides is called a triangle; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon; one of ten sides, a decagon; one of twelve sides, a dodecagon, &c.

20. An EQUILATERAL POLYGON is one whose sides are all equal.

An EQUIANGULAR POLYGON is one whose angles are all equal.

A REGULAR POLYGON is one which is both equilateral and equiangular.

21. Two polygons are mutually equilateral, when their sides, taken in the same order, are equal, each to each: that is, following their perimeters in the same direction, the first

side of the one is equal to the first side of the other, the second side of the one to the second side of the other, and so on.

22. Two polygons are mutually equiangular, when their angles, taken in the same order, are equal, each to each.

23. A DIAGONAL of a polygon is a straight line joining the vertices of two angles, not consecutive.

24. A BASE of a polygon is any one of its sides on which the polygon is supposed to stand.

25. Triangles may be classified with reference to either their sides, or their angles.

When classified with reference to their sides, there are two classes: scalene and isosceles.

1st. A SCALENE TRIANGLE is one which

has no two of its sides equal.

2d. An IsoSCELES TRIANGLE is one which

has two of its sides equal.

When all of the sides are equal, the triangle is EQUILATERAL.

A

When classified with reference to their angles, there are

two classes: right-angled and oblique-angled.

1st. A RIGHT-ANGLED TRIANGLE is one

that has one right angle.

The side opposite the right angle is called the hypothe

nuse.

2d. An OBLIQUE-ANGLED TRIANGLE is one

whose angles are all oblique.

If one angle of an oblique-angled triangle is obtuse, the triangle is said to be OBTUSE-ANGLED. If all of the angles are acute, the triangle is said to be ACUTE-ANGLED.

26. Quadrilaterals are classified with reference to the relative directions of their sides. There are then two classes; the first class embraces those which have no two sides parallel; the second class embraces those which have at least two sides parallel.

Quadrilaterals of the first class, are called trapeziums. Quadrilaterals of the second class, are divided into two species: trapezoids and parallelograms.

27. A TRAPEZOID is a quadrilateral which

has only two of its sides parallel.

28. A PARALLELOGRAM is a quadrilateral which has its opposite sides parallel, two and two.

There are two varieties of parallelograms: rectangles and rhomboids.

1st. A RECTANGLE is is a parallelogram whose angles are all right angles.

A SQUARE is an equilateral rectangle.

2d. A RHOMBOID is a parallelogram whose angles are all oblique.

A RHOMBUS is an equilateral rhomboid.

29. SPACE is indefinite extension.

30. A VOLUME is a limited portion of space, combining the three dimensions of length, breadth, and thickness.

AXIOMS.

1. Things which are equal to the same thing, are equal to each other.

2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal.

4. If equals are added to unequals, the sums are unequal.

5. If equals are subtracted from unequals, the remainders are unequal.

6. If equals are multiplied by equals, the products are equal.

7. If equals are divided by equals, the quotients are

equal.

8. The whole is greater than any of its parts.

9. The whole is equal to the sum of all its parts.

10. All right angles are equal.

11. Only one straight line can be drawn joining two given points.

12. The shortest distance from one point to another is measured on the straight line which joins them.

13. Through the same point, only one straight line can be drawn parallel to a given straight line.

POSTULATES.

1. A straight line can be drawn joining any two points. 2. A straight line may be prolonged to any length.

3. If two straight lines are unequal, the length of the less may be laid off on the greater.

4. A straight line may be bisected; that is, divided into two equal parts.

5. An angle may be bisected.

6. A perpendicular may be drawn to a given straight line, either from a point without, or from a point on the line.

7. A straight line may be drawn, making with a given straight line an angle equal to a given angle.

8. A straight line may be drawn through a given point, parallel to a given line.

NOTE.

In making references, the following abbreviations are employed, viz.: A. for Axiom; B. for Book; C. for Corollary; D. for Definition; I. for Introduction; P. for Proposition; Prob. for Problem; Post. for Postulate; and S. for Scholium. In referring to the same Book, the number of the Book is not given; in referring to any other Book, the number of the Book is given.