A. When a line falls directly on another line, so as to make the angles on both sides equal; what is the line called? A perpendicular. What are the angles on each side called? A. Right angles. How many degrees does a right angle consist of? as C in figure 3d. A. 90, What are all angles except right angles, called? A. Oblique. How many kinds of oblique angles are there? A. Two. What are they? A. Acute and Obtuse. What is an acute angle? A. Less than a right. What is an obtuse? A. Greater than à right. Of how many degrees does an acute angle consist of then? A. Less than 90. A How many in an obtuse? A. More than 90. Fig. 1. A Square. PRACTICAL QUESTIONS. D What is the length of the sides of a square? A. all equal. How many degrees in each angle of a square? A. 90. What are these angles called then? A. Right angles. How many degrees does the sum of all B the angles in a square make? What is the area of any thing? A. The surface or space enclosed by any lines. PROBLEM I.-To find the area of a square; what is the RULE? A. Multiply the side of the square into itself. Examples for Mental Exercise. How many square feet of boards are contained in the floor of a room 30 feet square? A. 900. Suppose a square lot of land measures 40 rods on each side, how many acres does it contain? 40X40 1600÷÷160—10 the answer Why divide by 160 in the above? A. Because the pro duct is square rods, and square rods must be divided by square rods, square feet by square feet, solid feet by solid feet, &c. Exercises for the Slate. A. Suppose a lot of land is exactly square, and measures on each side 425 rods; how many acres does it contain? 1128 145 acres. A floor in a room measures across one side 25 feet and it is square; how many feet does it contain ? A. 625 feet、 A owns a farm laid out in an exact square, and by measuring, it is found that the distance across one side is 400 rods; how many acres does it contain? A Fig. 2d. A Parallelogram. D B A. 1000 acres. 1. What is a parallelogram? A. It is a figure that has its opposite sides equal and parallel. 2. How many degrees does each angle of a parallelogram C consist of? A. 90. PROBLEM II.--To measure a parallelogram; what is the RULE? A. Multiply the length by the breadth. A garden is 200 feet long, and 10 feet wide; how many feet of ground are there in it? A. 2000 feet. If a board is 12 inches wide, and 24 inches long; how mány feet does it contain ? A. 2 feet. If a board is 12 inches long and 12 wide; how many feet are in it? A. 1 foot. How many feet will a board that is 12 inches wide always contain? A. As many feet as the board is feet in length. If a board is 6 inches or many feet will it contain ? 1 foot. foot wide, and 1 foot long, how A. a foot. If 2 feet long? A. As a board 12 inches wide, contains just as many feet, as the board is long; now tell me how many feet in a board that is 2 feet wide? A. Twice the number of feet that the board is long. How many feet are contained in a board, that is 2 feet wide and 24 feet long? Exercises for the Slate. A lot of land in the form of a parallelogram, is 300 rods in length, and 100 rods wide; how many acres are in it? A. 187 acres. If a board be 30 feet long, and 20 inches wide; how many square feet of boards are contained in it? A. 50 feet. Which is the greatest and smallest angle in fig. 3d.? 180. One angle, in a right angled triangle, is always 90; how many degrees are there in the two other angles. A. 90. In a right angled triangle, what is the longest side called? (See Fig. 3.) What are the two other sides called? By what other name are they sometimes called? A. Legs. PROBLEM I.-To find the side of a square, equal in area to any given superfices. RULE.-The square root of the contents of any given superfices, is the side required. Exercises for the Slate. If the contents of a circle be 160; what is the side of a square equal thereto ? A. 12,64911+ Suppose I have a circular fish pond containing 9 acres, 2 roods, 15 poles, and wish to have a square one containing the same quantity of land; what would be the length of each side? A. 39,179076+ rods. PROBLEM II. The area of a eircle being given to find the diameter. RULE.-As 355: 452: : so is the area to the square of the diameter. Exercises for the Slate. In the middle of a meadow, I have tethered my horse; now how long must the cord be, that he may have the liberty of eating 3 acres of grass? A. 3X4X40X30X452-355 and extract the square root of the quotient which will be the diameter, and half that will be the answer. A. 67,9842 yards, nearly.. PROBLEM III.-The area of a circle being given, to find the circumference. RULE. AS 113: 1420: the area: to the square of the circumference. Examples. When the area of a circle is 12; what is the circumference? A. 12,2798. When the area is 160; what is the circumference? 44,84, nearly. A. PROBLEM IV. Any two sides of a right angled triangle being given, to find the third side. 1st. The base and perpendicular given to find the hypothenuse. RULE.-Add the squares of the base and perpendicular together, and the square root of the sum is the length of the hypothenuse. 2d. The hypothenuse and side given to find the other side. one RULE. From the square of the hypothenuse, subtract the square of the given side, the square root of the remainder is the side required. ypothenuse 35 21 Base $28 Perpendicular |