cumference and a diameter, is called a semicircle. The plane surface included within two radii and an arc of a circle, is called a sector. 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 so far extended in both directions, meets the circumference only in one point, is called a tangent. (See the figure on page 9.) 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? How do you define a surface? What are the limits of surfaces called? How do you define a line? What are the beginning and end of lines called? How do you define a point? 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 will lie entirely within 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? By nine? By ten? 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? If one straight line meets another, so as to make the two adjacent angles equal, what do you call these angles? What do you call the lines themselves? 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 so far extended both ways, 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 equal, called? What is a right-angular parallelogram called? What is an equilateral rectangle called? What, an equilateral parallelogram? What, an equilateral in which two sides only are parallel? What is the simplest of all geometrical figures called? How is a circle terminated? What is the line called which terminates a circle ? What is any part of the circumference called? What, a straight line, drawn from the centre, to any part of 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 the two extremities, called? What is that part of the circumference called, which is cut off by the diameter ? What, the plane surface within a semicircumference 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: 1 stands for equal; e. g., the line AB= CD, 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 AB-CD means that the length of the line |