2. C. owes D. 100 dollars on demand; 100 dollars in one year; 100 dollars in two years; 100 dollast in there years; what is the equated time to pay all at once? Ans. 11. year. ALIGATION MEDIAL. DEFINITION.-Aligation medial is a rule made use of, to find the price of a compound of several things mixed together: the prices of the ingredients and quantities being known. RULE. As the sum of all the quantities, is to the total value of all the quantities, so is any part of the mixture to the price of that part. Examples. 1. A farmer mixes 4 bu. of blighted corn at 42 cents per bu.; 6 bu. of oats at 33 cents; 5 bu. of barley at 96 cents; and 15 bu. of potatoes at 20 cents per bu.; what is one bu. of the mixture worth? 2. A trader mixes 60 gal. of rum at 90 'cts. with 62 gal. at 80 cts.; 40 gal. at 45 cts.; and 10 gal. of water what is 10 gal. worth?' Ans: $7.06 cts. 3. A trader mixes 1 cwt. of sugar at 10 dollars per cwt. with 3 cwt. at 12 dollars, and adds 40 lbs. of sand to the mixture; what is the value of 1 cwt. of the mixture? Ans. 810-55t ALIGATION ALTERNATE. DEFINITION.-Aligation alternate is a rule made use of to find the quantity of any number of simples, whose prices are given, that will make a mixture worth a certain price, therefore it is the reverse of aligation medial, and may be proved thereby. CASE I. RULE. Write down the prices of the several simples in a column, one above the other, beginning with the least, &c. on the left of the column draw a perpendicular line; and on the left of the line, write down the price of the mixed quantity; then connect with a curved line each of the simples which is less, with one that is greater than the mixed quantity; and set the difference between the least simple (and price of the mixed quantity) against the simple that is largest ; and the difference of the larger against that which is less, &c. after having connected each simple that is less with one that is greater, and found the differences; the figures standing against each simple will express the quantity that must be taken of that price, to form a mixture of the price intended. Examples. 1. A farmer would make a mixture, of corn at 50 cents; oats at 25 cents; barley at 90 cents; and potatoes at 20 cents, per bush.: I demand the quantity of each that must be taken, that the mixture may be orth 30 cents per bushel. NOTE.-Questions in this rule adinit of a great variety of answers, according to the manner of their being linked together; and yet the value of the mixture will be the same. Proof by aligation medial. Bushels 20x20 cts.=$4.00 10x 50 cts. 5:00 5x 90 cts. 4.50 2. A seller of wines would mix wine at 90 cts. 80 cts; 70 cts. 60 cts. and .50 cts. per gallon ; and take such a quantity of each, that the mixture may be worth 85 cts. per gallon: I demand the quantity of each that may be taken. The price of A This question admits of a variety of linkings the Mixture. cts. gal. 5 at 60 Ans. 5 at 70 5 at 80 35+25+15+5= 80 at 90 CASE II. When the mixture is limited to a certain quantity. RULE. Find a quantity that will compose a mixture by case first: then say as the sum of the quantities thus found, is to the limited quantity, so is each particular quantity found, to the part of that quantity. Examples. 1. A seller of liquors would make a cask of cherry of 80 gallons: and would compose it of rum at •50 cts. and 90 cts. per gallon, and of water: I demand the quantity that must be taken, allowing the mixture to be worth 60 cts. per gallon." NOTE,This question admits of but one linking. 00- 30 ets. 30 .60 30 gallons of water. 60+1070 gallons of W. 1. rum. Galis galls. galls. - 130 sum of all the quantities. 60 As 130: 80:: 30: 18 of water 130: 80:: 30: 18 of N.E. rum 60 130 130: 80:: 70: 4313% of W.I. rum CASE III. Ans When one of the simples is limited to a certain quantity. RULE. Find the quantities that will make a mixture by case first, (the simple that is limited must be linked) then say, as the quantity that stands against the price of the limited quantity, is to the other quantities taken separately, so is the limited quantity to the quantity of each. Examples. 1. A grocer has 40lbs. of tea worth 30 cts. per lb. which he would mix with other teas at 90, .80, and 70 cts. per lb.: what quantity of each must be tar ken, that the mixture may be worth 60 cts. per lb.? EXTRACTION OF THE SQUARE root. DEFINITION.-Extracting the square root, is the finding of a number, which being multiplied into itself will produce the given number, or is finding the root of a square number.* 8, 9. Roots 1, 2, 3, 4, 5, 6, 7, RULE-Point the given number into periods of two figures each beginning at the place of units, thus 134567: If the point happen to fall upon the last figure, it must be considered as a full period, thus, 12345; secondly, having pointed the number into periods of two figures each: begin at the left hand, and find the greatest square that can be had in that period; place the root thereof in the quotient, and its square under the first period, subtract it therefrom, and to the remainder bring down the next period, and call it the resolvend: double the (*A number is squared when it is multiplied into itself. |