Again, the square of _a_ + _b_ + _c_ + _d_ or (_a_ + _b_ + _c_ + _d_)(_a_ + _b_ + _c_ + _d_) will be found to be _aa_ + 2_ab_ + 2_ac_ + 2_ad_ + _bb_ + 2_bc_ + 2_bd_ + _cc_ + 2_cd_ + _dd_; or the rule for squaring such a quantity is: Square the first term, and multiply all that come _after_ by twice that term; do the same with the second, and so on to the end. SECTION IV. DIVISION. 69. Suppose I ask whether 156 can be divided into a number of parts each of which is 13, or how many thirteens 156 contains; I propose a question, the solution of which is called DIVISION. In this case, 156 is called the _dividend_, 13 the _divisor_, and the number of parts required is the _quotient_; and when I find the quotient, I am said to divide 156 by 13. 70. The simplest method of doing this is to subtract 13 from 156, and then to subtract 13 from the remainder, and so on; or, in common language, to _tell off_ 156 by thirteens. A similar process has already occurred in the exercises on subtraction, Art. (46). Do this, and mark one for every subtraction that is made, to remind you that each subtraction takes 13 once from 156, which operations will stand as follows: 156 13 1 ------ 143 13 1 ------ 130 13 1 ------ 117 13 1 ------ 104 13 1 ------ 91 13 1 ------ 78 13 1 ------ 65 13 1 ------ 52 13 1 ------ 39 13 1 ------ 26 13 1 ------ 13 13 1 ------ 0 Begin by subtracting 13 from 156, which leaves 143. Subtract 13 from 143, which leaves 130; and so on. At last 13 only remains, from which when 13 is subtracted, there remains nothing. Upon counting the number of times which you have subtracted 13, you find that this number is 12; or 156 contains twelve thirteens, or contains 13 twelve times. This method is the most simple possible, and might be done with pebbles. Of these you would first count 156. You would then take 13 from the heap, and put them into one heap by themselves. You would then take another 13 from the heap, and place them in another heap by themselves; and so on until there were none left. You would then count the number of heaps, which you would find to be 12. 71. Division is the opposite of multiplication. In multiplication you have a number of heaps, with the same number of pebbles in each, and you want to know how many _pebbles_ there are in all. In division you know how many there are in all, and how many there are to be in each heap, and you want to know how many _heaps_ there are.