gained $386; what was each man's part ? Ans. { B's, 185,202 4. Two merchants entered into partnership for 16 mo.; A at first put in stock to the amount of $600, and, at the end of 9 months, put in $100 more; B. put in at first $750, and, at the expiration of 6 months, took out $250; with this stock they A's$200,797. 5. On the first of January, A began trade with $760, and, on the first of February following, he took in B with $540 ; on the first of June following, he took in C with $800 ; at the end of the year, they found they had gained $872: what was each inan's share of the gain? Ans. A's share, $384,929; B's, $250,71; C's, $236,36. MENSURATION. 1 LXXIX. SQUARE MEASURE. Q. What are your ideas of a Square ? A B A. It is any thing which is as long as it is wide. Q. What kind of a figure does this on the right appear to be ? A. A square figure. A. Because the side AB is as long as the side BC. D A. It has four equal sides, and four equal angles. Q. In the above figure, if each side be 1 foot in length, what ought A to be called ? 1. 1 square foot. 3 feet = 1 yard. itself, give ? Q. If the sides of a square be each 1 yard in A 3 feet = l yard. B length, as in the figure on the right, whai ought it to be called ? A. 1 square yard. Q. In this square, I perceive there are several smaller squares contained in the larger. If you count all the smaller squares, allowing each one to be 1 foot, how many square feet or square yards will they make ? Q. Why? D C A. Because there are 9 small squares, each containing 1 sq. ft., which make 9 sq. ft., i. e., 1 sq. yd Q. How many square feet, then, make 1 square yard ? Q. If we multiply 3 feet (the length of 1 side) by the width, 3 feet, making 9, the same result is produced as before. What, then, will multiplying the length of any square by the breadth, or the length' into A. The square feet, square inches, &c., contained in the figure. Q. How many square inches in a figure 2 inches long and 2 inches wide ? A. 2x2 = 4. Q. How many in a figure 4 inches long and 4 inches wide ? 12 inches square, that is, 12 inches long, and 12 inches wide ? 8 inches square 6 inches square ? 20 inches square ? 30 inches square ? Q. How many square feet in a figure 1 foot, or 12 inches, square A. 301 sq. yds.; because 54 yds. X 53 yds = 301. How many square feet in 1 square rod ? and why? A. 2721 sq. ft. ; because 161 ft. (the number of feet in i rod in length) x 164 ft. = 2721. Q. T'his figure on the right A B is called a Parailelogram: what, then, are your ideas of a Parallelogram? A. That it is a figure which is long-F D E C er than it is wide ? Q. We see by this figure, that there are two kinds of Parallelograms, viz. ABCD and ABÉF. By inspecting these they will be found to be equal : how, then, may a Parallelogram be defined ? A. It is a figure which has its opposite sides of equal length, and its opposite angles equal. Q. If this figure had been square, and each side 2 feet in length, it Is plain that it would have contained 4 square feet; but, allowing the longest side to be 2 feet, and the shortest side only 1 foot, it will , of course, contain but it as many square feet: how many, then, does it contain ? A. 2 ft. (length) x 1 ft. (breadth) = 2 sq. ft. Q. If a figure 1 inch in breadth and 1 inch in length contains 1 square inch, how many square inches will a figure 1 inch wide and 2 inches long contain ? 3 inches long ? 4 inches long 8 inches long? 12 inches long? 20 inches long? Q. If a higure 1 foot wide and 1 foot long contains 1 square foot, how many square feet will a figure 1 foot wide and 2 feet long contain 3 feet long? 4 feet long? 8 feet long? 10 feet long Q. How, then, do you proceed to find the square feet, inches, &c. of a square or parallelograin ? A. Multiply the length by the breadth. 1. How many square feet in a room 10 feet long and 2 feet wide? (10 X 2=20 sq. ft., Ans.) In a room 8 feet wide and 12 feet long? 20 feet long? 2. How many square rods in a piece of land 4 rods wide and 8 rods long? 10 rods long? 11 rods long? 12 rods long? 10 rods long and 4 rods wide ? Q: When a piece of land, in any shape, contains 40 square rods, what is it called? A. l rood. 3. How many square rods in a piece of land 40 rods long and 2 rods wide ? 4 rods wide ? Q. When a piece of land, in any shape, contains 160 square rode, what is it called A. 1 acre. 4. How many square rods in a piece of land 20 rods long and 2 rods wide? How many such pieces will make an acre, or 160 square rods? 5. How wide must a piece of land be, which is 80 rode long, to make an acre ? 40 rods long? 20 rods long? 6. How many square feet of boards are contained in the door of a rooni 10 feet square ? 20 feet square ? 10 feet wide and 20-feet long? 20 feet wide and 30 feet long? 7. How many square yards in a figure 3 feet long and 3 feet wide ? 6 feet square ? 10 feet long and 9 feet wide? 6 feet long and 2 feet wide? (2 X 6=12-9.-1} ydson Ans.) In a figure 10 feet long and 4 wide ? A. 45 yds. 8. How many square yards in 9 square feet? là 108? In 72? In 99 ? In 27 ? In 80? In 37 ? square miles Coutadning 25 square milos. Q. How, then, must square feet, square inches, &c. be divided ? A. Square inches by square inches, square feet by square feet, &c. 5 square miles. Q. We are now prepared to angwer that interesting question which occurs in Geography, viz. the difference between miles square and square 5 miles square. miles. The figures on the right are introduced for the purpose of its illustration. Examine them attentively; then tell me, for instance, What is the difference between 5 square miles and 5 miles square ? A. 5 means 5 miles in length and only 1 in breadth ; but 5 miles square means 5 miles in length and 5 miles in breadth, making 5 times as many miles as only 1 in breadth; that is, 25 square miles. From these illustrations we derive the following general RULE. Q: How do you proceed to find the contents of a Square or Parallelogram? A. Multiply the length by the breadth. Exercises for the State. 1. In a room 16 feet long and 11 feet wide, how many square Peet? A. 176. 2. How many acres in a piece of land 560 rods long and 3 rods wide ? 560 x 32=112 square acres, Ans. The pupil must recollect that square inches must be divided by square inches, square yards by square yards, &c. 3. How many acres in a piece of land 370 rods wide and 426 rodo long? A. 985 acres, 20 rods. 4. How many rods long must a piece of land be, which is 80 rods wide, to inake 1 acre ?-2. How many rods wide to make 4 acres?-8. How many rods wide to make 200 acres ?-100. A. 410 rods. 5. How many square feet of boards are contained in the floor of a room 40 ft. 6 in. long and 10 ft. 3 in. wide? (Reduce the inches to the decimal of a foot.) A. 415,125 ft.=415$ feet. 6. How many acres are contained in the road from Boston to Providence, allowing the distance to be 40 miles, and the average width of the road 4 rods ? A. 320 acres. 7. How many square feet are contained in a board 12 inches long and 12 inches wide ?-1. 12 inches wide and 24 inches long ?-2. 3 feet long ?-3. 20 feet long?-20. A. 26 feet. 8. How many square feet in a board 1 ft. 6 in. wide and 18 ft. 9 in. long? A. 23,125 ft. =28} feet. 9. How many yards of carpeting, that is 14 yd. 'wide, will cover a floor 21 ft. 3 in. long and 13 ft. 6 in. wide ? A. 25), yards. 10. How many feet of boards will it take to cover the walls of a house 30 ft. 6 in. wide, 40 ft. 9 in. long, and 20 ft. high? and what will they come to, at $10 per 1000 feet? A. 2850 feet; cost $235. 11. How many shingles will it take to cover the roof of a barn 40 feet long, allowing the length of the rafters to be 16 ft. 6 in., and 6 shingles to cover 1 square foot? what will they cost, at $1,25 per 1000 ? A. 7920 shingles; cust, $9,90. 12. What will a lot of land, 300 rods wide and 600 rods long come to, at $15 an acre? A. $16875. 13. What will a lot of land, i mile square, come to, at $20,75 per acre ? A. $13280. (LXXX. SOLID, OR CUBIC MEASURE. Q. When a block is 1 inch long, 1 inch thick, and 1 inch wide, how many solid inches is it said to contain ? A. 1 solid or cubic inch. Q. How many solid feel does a block, that is 1 foot long, 1 foot thick, and 1 foot wide, contain ? A. 1 solid or cubic foot. Q. If a block 1 foot thick, 1 foot wide, and 1 foot long, contains 1 solid foot, how many solid feet does such a block that is 2 feet long contain ? 3 feet long? 5 feet long? 10 feet long? 20 feet long? 30 feet long? Q. How many solid feet does lock 2 feet long, 2 feet thick, and I fool wide, contain ? 2 feet wide? 3 feet wide ? Q. How many solid inches does a block 3 inches long, 2 inches wide, and I inch ihick, contain ? 2 inches thick ? 4 inches thick ? 10 waches thuck ? |