RULE, RULER. In a mechanical sense these words are both used for a straight piece of wood, brass, or ivory, from which a straight line is drawn on paper by guiding a pen or pencil along the edge. These rules or rulers are convenient for the laying down of scales, on which point see SCALE ; SECTOR ; SLIDING-RULE.
The word rule, in its more common sense, means a set of directions for the attainment of any required object, and various rules will be found in this work, scattered under many heads. The word rule is generally dropped ; thus we do not speak of the rule of addition, or the rule of subtraction, but simply of addition or subtraction. In some isolated cases the word rule is most usually retained, as in the rule of three [Time, RULE or] and the rule of false. (lass I'osrr:or.] A rule differs from an algebraical formula only in the languago employed ; both the former and the latter indicate processes to the mind. The rule describes its data at length, and requires many more signs than the formula, which however is much more intelligible than the rule, so soon as its symbols are well understood. For example, when it is known that a, b, c are the units in the sides of a right angled triangle, the formula for determining c is-- c = s/ + the rule is—To find the hypothenuso of a right-angled triangle, multiply the number of units in each side by Itself, add the products, and extract the square root of the sum : this square root is the number of units in the hypothenuse required. It might perhaps be thought that the preceding rule might have been expressed more briefly, but the practice of abbreviating the language of rules is almost sure to destroy the sort of advantage which, in one point of view, they possess over a formula. A rule should embody a description of the object
to be gained, and the process by which it is to be gained; it should also point out the step at which it is gained, and everything necessary to describe the result. It should even specify the case in which the rule is to be used, or that in which it becomes necessary rather than any other ; and should be tio complete in itself, that any reader of that class to whom the book is addressed might learn all it teaches (tbat everything but the demonstration) by reading only what conies between the word RULE and the full stop at the end of it. Thus, though we have described the preceding rule in words which some persona may think too many, we should say that they are not too many for the student who is somewhat of a mathematician, and too few for the beginner. For the latter we should state as follows :—To find the bypotheouse of • right-angled triangle of which the two sides are given, reduce the two sides to the same denomination if necessary (feet and decimals of a foot, inches and decimals of an inch, &e., as most convenient), multiply the units in each side by itself, add the results, and extract the square root of the sum ; this square root is the number of such units in the hypothenuse as were used in the expression of the sides.
if however many rules are to be learned, it would in all probability be found more easy to learn the symbols of alegbra, that is, to learn to read an algebraic expression and to use formula', than to recur frequently to rules. •