NEGATIVE siva, the sign of subtraction, or that which denotes something in de fect. The use of the negative sign in algebra is attended with several conse quences that at first sight are admitted with some difficulty, and has sometimes given occasion to notions that seem to have no real foundation. This sign im plies, that the real value of the quantity represented by the letter to which it is prefixed is to be subtracted ; and it serves; with the positive sign, to keep in view what elements or parts enter into the composition of quantities, and in what manner, whether as increments or decrements, that is, whether by addition or subtraction, which is of the greatest use in this art. Hence it serves to ex press a quantity of an opposite quality to a positive, such as a line in a contrary position, a motion with opposite direc tion, or a centrifugal force in opposition to gravity ; and thus it often saves the trouble of distinguishing, and demon strating separately, the various cases of proportions; and preserves their analogy in view. But as the proportions of lines
depend on their magnitude only, with out regard to their position; and motions and forces are said to be equal or une qual, in any given ratio, without regard to their directions; and in general the proportion of quantities relates to their magnitude only, without determining whether they are to be considered as in crements or decrements ; so there is no ground to imagine any other proportion of + a and — 6, than that of the real magnitude of the quantities represent ed by a and 6, whether these quantities are, in any particular case, to be added or subtracted.