Thus, 3a added to 5a, makes Sa. And-2ab added to-7ab, makes-9ab. And 5a+76 added to 7a + 36, makes 12a + 106. CASE II When the Quantities are Like, but have Unlike Signs ADD the affirmative co-efficients into one sum, and all the negative ones into another, when there are several of a kind. Then subtract the less sum, or the less co-efficient, from the greater and to the remainder prefix the sign of the greater, and subjoin the common quantity or letters. So + 5a and- 3a, united, make + 2a. 2a. CASE III. When the Quantities are Unlikej HAVING collected together all the like quantities, as in the two foregoing cases, set down those that are unlike, one after another, with their proper signs. Add a + b and 3a-56 together. Add 5a 8x and 3a-4x together. Add 6x-56 + a + 8 to −5a-4x + 4b-3. Add a +26—3c-10 to 3b-4a + 5c + 10 and 56 —c. Add 3a + 6-10 to c-d-a and -4c+2a-36—7. Add 3a2 + b2 -c to 2ab-3a2 + bc-b. Add a3 + b2c—b2 to ab2 —abc + b2. Add 9a-86 + 10x—§d −7c + 50 to 2x - Sa−5c + 46 + 6d-10. SUBTRAC SUBTRACTION. SET down in one line the first quantities from which the subtraction is to be made; and underneath them place all the other quantities composing the subtrahend: ranging the like quantities under each other as in Addition. Then change all the signs (+ and -) of the lower line, or conceive them to be changed; after which, collect all the terms together as in the cases of Addition*. This rule is founded on the consideration, that addition and subtraction are opposite to each other in their nature and operation, as are the signs + and -, by which they are expressed and represented. So that, since to unite a negative quantity with a positive one of the same kind, has the effect of diminishing it, or subducting an equal positive one from it, therefore to subtract a positive (which is the opposite of uniting or adding) is to add the equal negative quantity. In like manner, to subtract a negative quantity, is the same in effect as to add or unite an equal positive one. So that, by changing the sign of a quantity from + to or from to, changes its nature from a subductive quantity to an additive one; and any quantity is in effect subtracted, by barely changing its sign. From 3a+b+c 56 + a + 6x. 10, take c+2a d-10, take b d. 19+ 3a. b, take 3a2-c+ b2. From a33b2c + ab2 — abc, take b2 + ab2 From 12x + 6a 4640, take 46 3a +4x+6ď– 10. From 2r-3a + 4b + 6c - 50, take 9a + x + 6b −6c-40. From 6a-46-12c + 12x, take 2x-8a+ 46 — 5c. MULTIPLICATION. This consists of several cases, according as the factors are simple or compound quantities. CASE 1. When both the Factors are Simple Quantities: FIRST multiply the co-efficients of the two terms together, then to the product annex all the letters in those terms, which will give the whole product required. Note*. Like signs, in the factors, produce + and unlike signs, in the products. EXAMPLES *That this rule for the signs is true, may be thus shown. 1. When a is to be multiplied by + c; the meaning is, that is to be taken as many times as there are units in c; and since the sum of any number of positive terms is positive, it follows that + a x+cmakes+ac. 2. When |