BUYING AND SELLING STOCKS. Stocks are funds established by government, or individuals, in a corporate capacity; the value of which is fluctuating. The value of stock, at any rate per cent above or below par, is found by the following RULE. Multiply by the rate per cent, and divide by 100, or point off two decimal places to the right of the rate per cent, (it then becomes a ratio;) multiply the stock by such ratio, and the thing is done. EXAMPLES. 1. What is the amount of 3756 dollars national bank stock, at 130 per cent. 3756 X 1.30=4882.80 Ans. Second method. 2543756. 5=939 187.80 $4882.80 Ans. 2. What is the value of 6000 dollars worth of bank stock, at 93 per cent? Ans. $5580. 3. What amount of stock, at 871 per cent, can be purchased for 9000 dollars? Ans. $10285.71+ 4. What is the amount of 8750 dollars of 8 per Ans. $10062.50. cent stock, at 115 per cent? 5. What is the amount of 9000 dollars of 6 per cent stock, at 87 per cent? Ans. $7875. dollars 3 per cent Ans. $5343.75. [ These stocks are instituted for the support of government. Cubes cubed, 1 512 19683 262144 1953125 10077696 40353607 134217728 387420489 Sursolids squared, 1 1024 59049 1048576 9765625 60466176 282475249 1073741824 5486784401 INVOLUTION, OR THE METHOD OF RAISING POWERS. 1. The powers of any number, are the successive products arising from unity, continually multiplied by such number. 2. The first power of any number is, unity multiplied by such number. 3. Unity multiplied by any number, being equal the first power of such number, it follows, that the second, third, fourth, &c. powers of the same number, are produced by multiplying unity one, two, three, four, &c. times by it. EXAMPLES.. Let 2 be raised to all the successive powers, from the first to the fifth. 1x2= 2, 1st power of 2=21. 1×2×2= 4, 2d power of 2=22 its square. 1×2×2×2= 8, 5d power of 2=23 its cube. 1×2×2×2×2=16, 4th power of 2=24 its biquadrate 1×2×2×2×2×2=32, 5th power of 2-25 its sursolid. PRACTICAL EXAMPLES. 1. A square chamber is 36 feet each way; how many square feet of boards will floor the same? Ans. 1296. 2. In a plantation 400 perches square, how may square perches? Ans, 160000. 3. If a stone pier was 20 feet every way, how many cubic feet would it contain? Ans. 8000ft. 4. Required, the 4th power of 12. Ans. 20736. 5th power of 24. 6th power of 48. 7962624. 12230589464. From the above examples, we deem the doctrine of raising powers is clear. 179 EVOLUTION, OR THE EXTRACTION OF ROOTS. To extract the square root, 1. Prepare the number for extraction, by pointing it off from units' place, into periods of two figures each. 2. Find, in the table of powers, a square nearest to the first, or left hand period, subtract, bring down the next period, and call this the first dividend. 3. Double the quotient figure for a divisor, and try how often it is contained in all the figures of the dividend, except the one on its right. 4. Place this in the quotient for the second figure of the root, as well as to the right of the divisor. 5. Multiply by this quotient figure, as in division;. the product subtract as before, and to the difference bring down the third period. 6. Proceed in like manner, still doubling the quotient figures for a new divisor, and bringing down another period each time for a new dividend, until the whole be brought down, and the thing is done. EXAMPLES. 1. What is the square root of 10342656? 10'34'26'56(3216 9 62)134 124 641)1026 641 Here, the number consisted of 4 periods; in the table of powers, I found a square nearest to the first period, 10, and set the root, 3, in the quotient; I now doubled 3 for a divisor, and said 6 into 13, the first dividend, all but its right hand figure, and found it was contained in 13 twice; I now placed 2 for the second figure of the root and also beside 6, the divisor, and multiplied 62 by 2, which gave 124; this I subtracted from 134. So I proceeded until the work was finished. 6426)38556 38556 The use of the Square Root is very great; but I shall content myself with giving a few examples only, in this place. 1. If the General of an army desired to scale the walls of a city, which were 15 feet high, and surrounded by an inaccessible mote, of 20 feet wide, he could, by help of the Square Root, ascertain the length of a ladder which would reach from the outside of the mote to the top of the wall. Thus: √20×20+15 x 15*25 feet, the length required. 2. If the length of a building be 80 feet, and its breadth 60, what distance should it measure from corner to corner diagonally? Ans. 100 feet. 3. If a person desired to lay out the foundation of a building by lines, so that it be exactly square, measure 6 feet on one line from the corner, and eight upon the other, (crossing the first at said corner;) if these two points be just 10 feet asunder, the lines cross at right angles and are squared with each other; for 6x6+8×8=10. 4. The length of one side of a garden was 400 feet, and its breadth, or the length of the other side, 300, and it measured diagonally 500 feet; was it square, or in other words, right-angled? (400 x 400+300 x 300)=500; which proves that the garden was right-angled. By the 47th proposition of the 1st book of Euclid's Elements of Geometry, it is proved, that the square root of the sum of the squares of any two numbers or lines, is equal to the root of a number whose square would be equal to the sum of the squares of both the former numbers, or a line equal the side of a square as large as both the squares made upon the given lines. |