A square is a rectangle whose sides are all epual. A rhombus or lozenge, is a parallelogram whose sides are all equal. A trapezoid is a quadrilateral in which two sides only are parallel. A straight line joining two vertices, which are not on the same side of a geometrical figure, is called a diagonal. The side which is opposite to the right angle, in a right-angled triangle, is called the hypothenuse. A circle is a surface terminated on all sides by a curve line returning into itself, all points of which are at an equal distance from one and the same point, called the The curve line itself is called the circumference. Any part of it is called an arc. A straight line, drawn from the centre of a circle to any point of the circumference, is called a radius. A straight line, drawn from one point of the circumference to the other, passing through the centre, is called a diameter. A straight line, joining any two points of the circumference, without passing through the centre, is called a chord. The plane surface included within an arc of a circle and the chord on which it stands is called a segment. The arc of a circle which stands on a diameter is called a semi-circumference. The plane surface included within a semi-circumference and a diameter is called a semi-circle. The plane surface included within two radii and an arc of a circle is called a sector. (See the figure, page 14.) If the two radii are perpendicular to each other, the sector is called a quadrant. A straight line, which, drawn without the circle, and however far extended in both directions, meets the circumference only in one point, is called a tangent. QUESTIONS ON DEFINITIONS. WHAT is that science called, which treats of the extensions of bodies, considered separately from all their other qualities? What are the extensions of bodies called? What are the limits or confines of bodies called? What are the limits of surfaces called? How do you define a line? What are the beginning and end of lines called? How is a geometrical point represented? How is a line represented? How a surface? How do you define a straight line? What do you call a line in which no part is straight? What is that surface called, in which, when two points are taken at pleasure, the straight line joining them lies entirely in it? What do you call a surface in which no part is plane? What is a plane surface called when terminated by lines? By how many straight lines is the simplest rectilinear figure terminated? What do you call it ? What do you call a geometrical figure terminated by four straight lines? What, if terminated by five straight lines? What, if by six? By seven? By eight? What are all geometrical figures terminated by more than three straight lines called? When two straight lines meet, what do they form? What is the point where the lines meet called? What do you call the lines which form the angle? If one straight line meets another, so as to make the two adjacent angles equal, what do you call these angles? What are the lines themselves said to be? What is an angle which is smaller than a right angle called? What an angle larger than a right angle? What do you call two lines, which, situated in the same plane, and however far extended both wavs never meet? When are two lines said to be converging? When, diverging? When a triangle has all its sides equal, what is it called? When two of its sides only are equal, what? When none of its sides are equal, what? What is a triangle called, when it contains a right angle? What, if it does not contain one? What is a quadrilateral, whose opposite sides are parallel, called? What is a right-angled parallelogram called? What is an equilateral rectangle called? What, an equilateral parallelogram? What, a quadrilateral in which two sides only are parallel? How is a circle terminated? What is the line called which terminates a circle? What, a straight line, drawn from the centre, to any point in the circumference? What, a straight line joining two points of the circumference, and passing through the centre? What, a straight line joining two points of the circumference, without passing through the centre? What is the plane surface, included within an arc and the chord which joins its two extremities, called? What is that part of the circumference called, which is cut off by the diameter ? What, the plane surface within a semi-circumference and a diameter ? What, the surface within an arc of a circle and the two radii drawn to its extremities? What is the sector called, if the two radii are perpendicular to each other? What is the name of a straight line, drawn without the circle, which, extended both ways ever so far, touches the circumference only in one point. NOTATION AND SIGNIFICATIONS. For the sake of shortening expressions, and thereby to facilitate language, mathematicians have agreed to adopt the following signs: stands for equal; e. g., the line ABCD means, that the line AB is equal to the line CD. +stands for plus or more; e. g., the lines AB + CD means, that the length of the line CD is to be added to the line AB. stands for minus or less; e. g., line ABCD means, that the length of the line CD is to be taken away from the line AB. X is the sign of multiplication. : is the sign of division. <stands for less than ; e. g., the line ABCD means, that the line AB is shorter than the line CD. stands for greater than; e. g., the line ABCD means, that the line AB is longer than the line CD. A point is denoted by a single letter of the alphabet chosen at pleasure; e. g., the point B. A line is represented by two letters placed at the beginning and end of it; e. g., the line AB. A B |