On the other hand, it is observed by an eminent mathema tician, that geometricians are under no necessity of supposing that a finite quantity of extension consists of parts infinite in number, or that there are any more parts in a given mag nitude than they can conceive or express : it is sufficient that be conceived to be divided into a number of parts equal to any given or proposed number ; and this is all that is supposed in strict geometry concerning the divisibility of magnitude. It is true, that the number of parts into which a given magnitude may be conceived to be divided, is not to be fixed or limited because no given number is so great, but a greater than it may be conceived and assigned : but there is not therefore any necessity tier supposing that number infinite ; and if some may have drawn very abstruse conse quences from such suppositions they are not to be imputed to geometry. Geometricians are under no necessity of sup posing a given magnitude to be divided into an infinite num be• of parts, or to be made up ofinfinitesimals ; nevertheless they cannot so well avoid supposing it to be divided into a greater number of parts than may be distinguished in it by sense in any particular determinate circumstance. But they find no difficulty in conceiving this : and such a supposition does not appear to be repugnant to the corn mon sense of man kind, but, on the contrary, to be most agreeable to it, and to be illustrated by common observation. It would seem very unaccountable not to allow them to conceive a given line. of an inch in length for example, viewed at the distance of 10 feet, to be divided into more parts than are discerned in it at that distance : since by bringing it nearer, a greater number of parts is actually perceived in it. Nor is it easy to limit the number of parts that may be perceived in it when it is brought near to the eye, and is seen through a little hole in a thin plate ; or, when by any other contrivance it is rendered distinct at small distances from the eye. If we conceive a
given line, that is the object of sight. to be divided into more parts than we perceive in it, it would seem that no good rea son can be assigned why we may not conceive tangible mag nitude to be divided into more parts than are perceived in it by the touch; or a line of any kind to be divided into any given number of parts, whether so many parts be actually distinguished by sense or not. In applying the reasonings and demonstrations of geometricians on this subject, it ought to be remembered, that a surfiwe is not considered by as a body of the least sensible magnitude, but as the termi nation or boundary of a body ; a line is nut considered as a surthce of the least sensible breadth, but as the termination or limit of a surthce ; nor is a point considered as the least sensible line, or a moment as the least perceptible time ; but a point as a termination of a line, and a moment as a termi nation of a limit of time. In this sense they conceive clearly what a surface, line, point, and a moment of time, is; and the postulate of Euclid being allowed and applied in this sense, the proofs by which it is shown, that a given magnitude may be conceived to be divided into any given number of parts. appear satisfactory ; and if we avoid supposing the parts of a given magnitude to be small, or to be infinite in number, this seems to be all that the most scrupulous can require.
Dr. Reid, in his " Inquiry into the Human Mind, on the Principles of Common Sense," considers that it is absurd to deduce from sensation the first origin of our notions of exter nal existence, of space, motion, and extension, and the primary qualities of bodies ; they have, he says, no resem blance to any sensation, or to any operation of our minds, and therefore they cannot be ideas either of sensation or reflection ; nor can he conceive how extension, or any image of extension, can be in an unextended and indivisible subject like the human mind.