Mr. Wm. James Donohue, 1 piece Irish Linen, 25 yds. at Baltimore, June 10, 1840. $1.12 FARMERS' ACCOUNTS. Dr. William Wallace, Jr. To 11 bbls. cider "14 lbs. butter dried beef $35.45 To Norman Nash, $3.00 33 10 EIT "52 แ 83 cheese 4 bushels of apples 25 3 firkins of butter, each 115lbs. at 17 $109.94 LECTURE IV. ON SUBTRACTION. (Sign) It is a fact well known to Mathematicians, that the principles of ARITHMETIC and ALGEBRA, admit of INCREASE, DECREASE, and EQUALITY. Increase consists of ADDITION and MULTIPLICATION; decrease, of SUBTRACTION and DIVISION. Equality, (being the result or answer agreeably to the data of the question, under different names,) is represented by a statement or equation, reduced by increase or decrease, to the lowest term or answer. Hence, to facilitate increase or decrease, nothing remains but to simplify expressions or statements. After having learned to compose a number by the addition and multiplication of several others, agreeably to the laws of increase, the first question that presents itself is, how to take one number from another that is greater; or, in other words, to separate the greater number into two parts, one of which shall be the given number. This is called the doctrine of decrease, and may be illustrated thus: Suppose we wish to take $3 from $10, by so doing we separate $10 into two parts, one of which shall be $3 the given number; then we begin with 10, the greater number in question, and descend as many places from 10 as there are units in the lesser number, and we shall come to the number required, which is $7. Hence, we find that 7 is the excess of 10 above 3, or we might say, that is the difference or remainder between 10 and 3. Consequently, the words excess, difference, and remainder, are synonymous, each answering to the separation of $10 into the parts, $3 and $7, which is always designated by the name SUBTRACTION. DEFINITION-TO SUBTRACT IS TO MAKE LESS. (Sign -) Q. What is the upper line denoting the greater number called? A. The MINuend. Q. What is the lower line denoting the lesser number called? A. The SUBTRAHEND. The difference of both is called the remainder. RULE. 1. Place the lesser number under the greater, so that units may appear under units, tens under tens, and hundreds under hundreds, &c. and draw a line underneath. 2. Begin at the right hand, and take each figure in the lower line from the figure above it, and set down the remainder. 3. If the lower figure is greater than that above it, add 10 to the upper number, from which number, so increased, take the lower, and set down the remainder, carrying ONE to the next lower number, with which proceed as before, and so on, till the whole is finished. PROOF. Add the remainder to the lesser number, and if the sum be equal to the greater, the work is right. |