The particular extension, whether under the name of inch, foot, yard, metre, league, &c., tt ith which other exten sions are compared, or by which they are measured, is estab lished only by the common consent or a:PTeement of persons of a certain nation, or profession, and used as standard mea sure by them only. Hence, the measures of ditliPrent nations, though sometimes they have the same name, differ consider ably from each other. Great endeavou• have been made by divers ingenious persons, at different times. for the purpose of determining an unalterable universal standard of measures; those endeavours, and the results with which they have been attended, will be found described under the article STANDARD of Measures.
Extension is usually described as consisting in the situation of parts beyond parts ; but to this definition some authors object, maintaining, that we can conceive absolute extension without any relation to parts.
If a man consider the distance between two bodies abstractedly, and without any regard to bodies which may fill that interval, it is called ;pace; and when he considers the distance between the extremes of a solid body, it is called extension.
Extension is frequently confounded with ppiantity and magnitude; and, for what we can perceive. without much harm, the thing signified by them all appearing to he the same; unless we admit a distinction made by 14,111e authors, that the extension of a body is something more absolute, and its ipiantity and magnitude more respective. or implying a nearer relation to much and little. The infinite divisibility of extension has been a famous question in all ages. It is not easy to reconcile the doctrine of mathematicians on this head with the tenets of some philosophers. Those who hold that all extension and magnitude are compounded of certain minima sensibilia ; and that a line, for instance, cannot inerease or decrease, but by certain invisible increments or decrements only, must, consistently with themselves, affirm, that all lines are commensurable to each other. But this is contrary to the tenth book of Euclid, who demonstrates that the diagonal of a square is incommensurable to its side. And further, if all lines were composed of certain indivisible elements, it is plain one of those elements must be the com mon measure of the diagonal and the side.
Bishop Berkeley observes, that the infinite divisibility of finite extension, though it is not expressly laid down, either as an axiom or theorem in the elements of geometry, is yet throughout the same everywhere supposed. and thought to
have so inseparable and essential a connection with the prin ciples and demonstrations in geometry, that mathematicians never admit it into doubt. ur make the least question of it. And as this notion is the source from whence do spring all those amusing geometrical paradoxes, which have such a direct repugnancy to the plain common sense of mankind ; so it is the principal occasion a all that nice and extreme subtilty which renders the study of mathematics so difficult and tedious. Renee, says he, if we can make it appear. that no finite extension contains innumerable parts, or is infinitely divisible, it follows, that we shall at once clear the science of geometry from a great number of difficulties and contradic tions which have ever been esteemed a reproach to human reaspet, and withal, make the attainment thereof a business of much less time and pains than it hitherto bath been.
Every particular finite extension. which may possibly be the object of our thought. is an idea existing only in the mind, and consequently each part thereof must be perceived. 11' therefore, says this author. I cannot perceive innumerable parts in any finite extension that I consider, it is certain they are not contained in it ; but it is evident, that 1 cannot distinguish innumerable parts in any particular line, surface, or solid, which 1 either perceive by sense, or figure to myself in my mind ; wherefore, I conclude they are not contained in it. Nothing can he plainer to me than that the extensions I have in view are no other than nv own ideas ; and it is no less plain, that I cannot resolve any one of my ideas into an infinite number of other ideas; that is, that they arc not infinitely divisible. If by an infinite extension be meant something distinct from a finite idea, I declare 1 do not know what that is, and so cannot affirm or deny anything of it. But if the terms extension, parts, and the like, are taken in any sense conceivable ; that is, for ideas; then to say a finite quantity or extension consists of parts infinite in number, is so manifest a contradiction, that every one at first sight acknowledges it to be so.