- If a board is 12 inches long and 12 wide, how many feet in it? Ans. 1 foot. If a board is 12 inches wide, and 24 inches or 2 feet does it contain? Ans. 2 feet. How many feet will a board that is 12 inches wide always contain? Ans. As many feet as the board is feet in length. If a board is 6 inches or foot wide and 1 foo: long, how many feet will it contain? Ans. 1 a foot. If 2 feet long? Ans. 1 foot. 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? Ans. Twice tho 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. What is a triangle? Ans. Any three cornered figure bounded by three straight lines; as figure 3d. Fig. 3. Fig. 4. сн Does the greatness of an angle depend on the length of the two lines which form it, or the width of their opening? Ans. On the wideness of their open, ing. Which is the greatest and smallest angle in fig. 4. How many degrees are all the angles in any triangle? Ans. 180. One angle, in a right angled triangle, is always 90; how many degrees are in the two other angles! Ans. 90. In a right angled triangle, what is the longest side called, as A B in figure 3? Ans. Hypothenuse. What are A C and B C called in figure 3? Ans. legs. What is the rule for finding the area of a triangle? Ans. Multiply the base of the given triangle into half its perpendicular height. Required the area of a triangle whose base, or longest side 30 inches, and the perpendicular height, 14 inches? Ans. 210 square inches. To find the content of any regular solid of three dimensions, length, breadth and thickness, as a piece of timber squared, whose length is more than the breadth and depth; what is the rule? Ans. Multiply the breadth by the depth, or thickness, and that product by the length, which gives the solid content. A square piece of timber, being 2 feet broad, 4 feet thick, and 9 feet long; how many solid does it contain? To find how many solid feet a round stick of timber, equally thick froin end to end will contain, when hewn square; what is the rule? Ans. Multiply twice the square of its semi-diameter in inches, by the length in feet, then divide the product by 144, and the quetient will be the answer. If the diameter of a round stick of timber be 12 inches, and its length 20 feet, how many solid feet will it contain, when hewn square? Ans. 6X6X2 x 203144=10 feet the answer. · Te find how many feet of square edged boards, of a given thickness, can be sawn from a log of a given diameter; what is the rule? Ans. Find the solid content of the log by the last rule: Then say, As the thickness of board including the saw calf; is to the solid feet : so is 12 (inches) to the number of inches required. How many feet of square edged boards, 14 inches thick, including the saw calf, can be sawn from a log 20 feet long, and 24 inches diameter--12X12X 2X20-144=40 feet solid content. As 11 : 40 : 12--384 feet the answer. Repeat the denominations of Linear, or Long Measure, with their corresponding Square Measures : Linear or Long Measure. Square Measure. 12 inches 1 foot, 144 inches 1 foot, 3 feet 1 yard, 9 feet 1 yard, 6 feet 1 fathom, 36 feet, I fathom, 164 feet 1 rod, 2721 feet l rod, 55 yards 1 rod, 301 yards 1 roa, 4 rods 1 chain, 16 rods 1 chain, 40 rods 1 furlong, 1600 rods 1 furlong, 320 rods 1 mile. 102400 rods 1 mile. In the above tables how are the several denominations in Square Measure, produced? Ans. They are the squares of their corresponding denominations in Long Measure. For example how is 144 produced? Ans. 12x 12 144. How is 2724? Ans. 163X164=9721. DUODECIMALS. By whom are Duodecimals, or Cross Multiplication used? Ans. By artificers. For what purpose? Ans. In measuring their several works. What else may it be applied to? Ans. To the measuring of wood for fuel, &c. Repeat the table 12"" fourths make I third, 1 second, 12' inch.orprimes 1 foot. · What do feet multiplied by feet, give? Ans. Feet. What do feet multiplied by inches, give? Ans. Inches. What do feet multiplied by seconds, give? Ans. Seconds. What do inches multiplied by inches, give? Ans. Seconds. What do seconds multiplied by seconds,give? Ans. Fourths. RULE. How place the multiplier? Ans. Under the multiplicand, so that feet may stand under feet, inches under inches, &c. With which denomination of the multiplicand do you begin to multiply? Ans. The lowest. What multiply it by? Ans. The highest denomination in the multiplier. How place the result of each multiplication? Ans. Feet under feet, inches under inches, &c, of the factors, and in the sereral products. How many carry in all cases? Ans. One for every 12. How place the product of the multiplication by the next highest denomination in the multiplier, and so on to the last? Ans. One figure further towards the right for each multiplication. How are the several products to be added? Ans. As they then stand. Is this method of multiplying confined to carrying by 12? Ans. It is not. EXAMPLES, Multiply 23 feet by 24 feet? Ans. 6 3 0 64 sq. feet. 6,25 sq. ft. You have said that feet multiplied by feet gives feet; do you mean square feet or not? Why are duodecimals so called? Ans. From duodecimus (Latin)-signifying 12, because in multiplying we carry by 12. Is it confined to twelves? Ans. It may be greatly extended. In multiplying pounds, shillings, pence, &c. what do pounds multiplied by pounds give? Ans. Pounds. What do pounds multiplied by shillings give? Ans. Shillings. What do shillings multiplied by shillings and so on give, Ans. Twentieths of a shilling, &c. £ s. .' Multiply 2 5 2,25 by 2 5 2,25 |