18 What must be paid for 73 yds. of broad cloth, at ♬ dollars per yard? answer 40,5625D. or 40D. 551cts. 19 How does broad cloth sell per yard, when 7 yards cost 40D. 564cents? answer 5,5 D. 20 The French foot is just 1,068ft. English; how tall then would a 6ft. Philadelphian be at Paris! answer but 5,618ft. INVERSE PROPORTION. EXAMPLES. How many men can do as much work in 14 month, as 16 could in a month and a half? mo. men. mo. men. As 1,5 : 1 6 ::,4 : 60 answer. of a 2 If, when wheat flour is as high as 61. per C.wt the half penny cake weighs 1,13330%. what should be the weight of it, when flour is only 1,81251. per C.wt.? answer 16ft. answer 3,750z.=30%, 12dr. 3 If a board be 75 foot broad, what length will it require to measure 12 square feet? 4 How much Persian ,75yd. wide, will line 25,5 yards of five quarter cloth? answer 42,5 yds. 5 A had 40,7 yards of linen, for which B gave him 25,6 ells of Holland, valued at 4,5s. per ell; how was A's linen rated per yard? answer 2s 9d. 3,8qr. 6 How many dollars of 7,5s. each, should be given in exchange for 100 French guineas, at 34,5s? answer 460 7 What sum has A at interest, when it yields as much in 7 months, as B's 450l. do in 15? answer gool. THE DOUBLE RULE OF THREE IN DECIMALS. Questions in this rule are wrought as in whole numbers, placing the points agreeably to the preceding directions. EXAMPLES. If 3 men receive 8,97. for 19,5 days labour; how much must 20 men have for 100,25 days? If 3M. M. answer £.305 0 8,2 2 If 2 persons receive 4,625s. for day's labour, how much should 4 persons have for the work of 10,5 days? answer 4l 17s id 3 If 16s 4d. be the porterage of 5,25 hundred weight for 20 miles; what must be paid for carrying 17,75 hundred weight 7,5 miles? answer il os 8d. 4 How many men should reap 417,6 acres in 12 days, when 5 persons cut down of that quantity in half the time? answer 20 men, 5 Suppose the interest of 76,941. for 9,5 months to be 15,257. what principal will gain 67. in 12,75 months? answer 221 11s id 6 When 12 oxen graze down 15,25 acres; in 20 days; how much, of like pasture, would suffice 24 such cattle for Icò days? answer 162,5 acres. 7 What money, at 3 per cent. per annum, will clear 38/ 10s. in a year and a quarter? answer 8801. 8 A cellar which is 22,5ft. long. 17,3 wide, and 10,25 deep, being dug in 24 days, by six men, working 12,3 hours a day; how many days, of 8,2 hours, should to excavate one which measures 45, by 34,6 by 12,3 feet? men take answer 12 days. 9 INVOLUTION; OR THE RAISING A OF POWERS. POWER is the product arising from multiplying any given number into itself continually a certain number of times; thus, 2 X 2 4 is the second power, or square of 2. 2 X2 X2 8 the third power, or cube of 2. 2X2 X2 X2=16 the fourth power of 2, &c. The number denoting the power is called the index, or the exponent of that power.. If two or more powers are multiplied together, their product is that power whose index is the sum of the exponents of the factors; thus, 2X24 the square of 2; 4X4=16=4th power of 2; and 16X16=256=8th power of 2, &c. N TABLE 4096 16384 65536 262144 Cubes 4th power Roots Squares 416 64 256 1024 525 125 625 3125 15625 78125 390525 1953125 6362161296 7776| 46656 279936 1679616| 10077696 749343240116807|117649 823543 5764801| 40353607 8645124096 32768 262144|2097152 16777216|134217728 981729656159049|531441|4782969|43046721 387420489 7×7×7×7×7=16807=fifth power. 2 What is the third power or cube of 35? HE root of any number, or ber, as, being multiplied into of times, will produce that power. power, is such a num itself a certain number Thus 2 is the square root of 4, because 2 x 24; and 4 is the cube root of 04: because 4X4 X4-64, and so on. THE SQUARE ROOT. HE square of a number is the product arising from that number multiplied into itself. TH Extraction of the square root is the finding of such a number, as, being multiplied by itself, will produce the number proposed. RULE. 1. Distinguish the given number into periods of two figures each, beginning at the units place, or decimal point; and when the decimal does not consist of an even number of figures, annex a cipher; and equal to the periods of whole numbers and decimals respectively, will be the places of each in the root. 2. Deduct from the first period the greatest square it contains, setting the root thereof as a quotient figure, and doubling it for a divisor; and bring down the second period to the remainder, for a dividual 3. Try how often the said divisor, with the resulting figure of this trial, thereto annexed, are contained in the dividual, and set this resulting figure to both divisor and root; then multiply and subtract as in division, and bring down the next period. 4. Double the ascertained root for a new divisor, and re peat the process to the end. PROOF. Square the root, adding in the remainder (if any) which will equal the number given. EXAMPLES. 1 What is the square root of 30138,696025 ? 30138,696025(173,605 answer. 1 27)201 189 343)1238 1029 3466 20969 347205)1736025 1736025 Note. When one more than half the figures of the root are found, the reft may be obtained by working as in contracted divifion of decimals. 2 Required the square-root of 14876,2357? 14876,2357 (121,968175 I 22)48 44 241)475 241 2420)23523 24386)166257 24392) 19941(8175 427 183 33 I ? facit 2345 answer 8647 607,34092+ 3 Required the square root of 5499025? 57,19+ 1,50701+ 3,162277+ ,01809 facit 12,649+per. 11 A certain number of men gave 30s id. for a charit able purpose; each man giving as many pence as there were men; query the number? answer 19 men. 12 If a circular pipe. of 1,5 inches diameter, fill a cistern in 5 hours; in what time would it be filled by one of 3,5 inches diameter ? answer 55min.6sec. 13 If |