Limits, THEORY

OF. Group of principles used in pa ing from measurements of rectilinear to those of curvilinear figures or from plane to curved solids; and as basis for the discu ions and rules of the Calculus. The chief propositions are: The difference between a variable and its limit is a variable whose limit is zero. If two variables are continually equal and each approaches a limit, their limits are equal. If one of two continually equal variables approaches a limit, the other has the same limit. The limit of the variable sum of a finite number of variables is the sum of their limits. The limit of the variable product of two or more variables is the product of their limits. The limit of the variable quotient of two variables is the quotient of their limits, except when the limit of the divisor is zero. The limit of the product of a variable and a constant is the product of the constant by the limit of the variable. The product quotient or sum of two or more variables being equal to a constant, the product quotient or sum of their limits will equal the same constant.