INFINITE

(Lat. inf in it us, boundle .) In Geometry, an infinite quantity is properly that which is greater than any a ignable magnitude; and as no such quantities exist in nature, it follows that an infinite quantity is merely an abstraction of the mind, formed by excluding the idea of limit or boundary. An infinitely small quantity is a quantity considered as le than any a ignable magnitude. There is, however, a peculiar signification attached to this expre ion in mathematical language, which has frequently been misunderstood. Infinitely small quantities are not absolutely zeros, or even quantities actually le than certain determinate magnitudes; they are merely quantities which the conditions of the proposed question permit to be regarded as variable until the calculation is entirely completed, and as diminishing continually until they become as small as we please, without its being nece ary to change the values of those quantities of which the relation is sought. It is in this circumstance only that the peculiar character of what are called infinitely small quantities consists, and not in the littlene which their denomination seems to imply, or in the absolute nullity which may be attributed to them. [s. 616]