distance, with or without solid matter possessing it.
4. Immensity.
Each different distance is a different modification of space; and each idea of any different distance, or space, is a SIMPLE MODE of this idea. Men having, by accustoming themselves to stated lengths of space, which they use for measuring other distances—as a foot, a yard or a fathom, a league, or diameter of the earth—made those ideas familiar to their thoughts, can, in their minds, repeat them as often as they will, without mixing or joining to them the idea of body, or anything else; and frame to themselves the ideas of long, square, or cubic feet, yards or fathoms, here amongst the bodies of the universe, or else beyond the utmost bounds of all bodies; and, by adding these still one to another, enlarge their ideas of space as much as they please. The power of repeating or doubling any idea we have of any distance, and adding it to the former as often as we will, without being ever able to come to any stop or stint, let us enlarge it as much as we will, is that which gives us the idea of IMMENSITY.
5. Figure.
There is another modification of this idea, which is nothing but the relation which the parts of the termination of extension, or circumscribed space, have amongst themselves. This the touch discovers in sensible bodies, whose extremities come within our reach; and the eye takes both from bodies and colours, whose boundaries are within its view: where, observing how the extremities terminate—either in straight lines which meet at discernible angles, or in crooked lines wherein no angles can be perceived; by considering these as they relate to one another, in all parts of the extremities of any body or space, it has that idea we call FIGURE, which affords to the mind infinite variety. For, besides the vast number of different figures that do really exist in the coherent masses of matter, the stock that the mind has in its power, by varying the idea of space, and thereby making still new compositions, by repeating its own ideas, and joining them as it pleases, is perfectly inexhaustible. And so it can multiply figures IN INFINITUM.
6. Endless variety of figures.
For the mind having a power to repeat the idea of any length directly stretched out, and join it to another in the same direction, which is to double the length of that straight line; or else join another with what inclination it thinks fit, and so make what sort of angle it pleases: and being able also to shorten any line it imagines, by taking from it one half, one fourth, or what part it pleases, without being able to come to an end of any such divisions, it can make an angle of any bigness. So also the lines that are its sides, of what length it pleases, which joining again to other lines, of different lengths, and at different angles, till it has wholly enclosed any space, it is evident that it can multiply figures, both in their shape and capacity, IN INFINITUM; all which are but so many different simple modes of space.
The same that it can do with straight lines, it can also do with crooked, or crooked and straight together; and the same it can do in lines, it can also in superficies; by which we may be led into farther thoughts of the endless variety of figures that the mind has a power to make, and thereby to multiply the simple modes of space.
7. Place.
Another idea coming under this head, and belonging to this tribe, is that we call PLACE. As in simple space, we consider the relation of distance between any two bodies or points; so in our idea of place, we consider the relation of distance betwixt anything, and any two or more points, which are considered as keeping the same distance one with another, and so considered as at rest. For when we find anything at the same distance now which it was yesterday, from any two or more points, which have not since changed their distance one with another, and with which we then compared it, we say it hath kept the same place: but if it hath sensibly altered its distance with either of those points, we say it hath changed its place: though, vulgarly speaking, in the common notion of place, we do not always exactly observe the distance from these precise points, but from larger portions of sensible objects, to which we consider the thing placed to bear relation, and its distance from which we have some reason to observe.
8. Place relative to particular bodies.
Thus, a company of chess-men, standing on the same squares of the chess-board where we left them, we say they are all in the SAME place, or unmoved, though perhaps the chessboard hath been in the mean time carried out of one room into another; because we compared them only to the parts of the chess-board, which keep the same distance one with another. The chess-board, we also say, is in the same place it was, if it remain in the same part of the cabin, though perhaps the ship which it is in sails all the while. And the ship is said to be in the same place, supposing it kept the same distance with the parts of the neighbouring land; though perhaps the earth hath turned round, and so both chess-men, and board, and ship, have every one changed place, in respect of remoter bodies, which have kept the same distance one with another. But yet the distance from certain parts of the board being that which determines the place of the chess-men; and the distance from the fixed parts of the cabin (with which we made the comparison) being that which determined the place of the chess-board; and the fixed parts of the earth that by which we determined the place of the ship—these things may be said to be in the same place in those respects: though their distance from some other things, which in this matter we did not consider, being varied, they have undoubtedly changed place in that respect; and we ourselves shall think so, when we have occasion to compare them with those other.
9. Place relative to a present purpose.
But this modification of distance we call place, being made by men for their common use, that by it they might be able to design the particular position of things, where they had occasion for such designation; men consider and determine of this place by reference to those adjacent things which best served to their present purpose, without considering other things which, to another purpose, would better determine the place of the same thing. Thus in the chess-board, the use of the designation of the place of each chess-man being determined only within that chequered piece of wood, it would cross that purpose to measure it by anything else; but when these very chess-men are put up in a bag, if any one should ask where the black king is, it would be proper to determine the place by the part of the room it was in, and not by the chessboard; there being another use of designing the place it is now in, than when in play it was on the chessboard, and so must be determined by other bodies. So if any one should ask, in what place are the verses which report the story of Nisus and Euryalus, it would be very improper to determine this place, by saying, they were in such a part of the earth, or in Bodley’s library: but the right designation of the place would be by the parts of Virgil’s works; and the proper answer would be, that these verses were about the middle of the ninth book of his AEneids, and that they have been always constantly in the same place ever since Virgil was printed: which is true, though the book itself hath moved a thousand times, the use of the idea of place here being, to know in what part of the book that story is, that so, upon occasion, we may know where to find it, and have recourse to it for use.
10. Place of the universe.
That our idea of place is nothing else but such a relative position of anything as I have before mentioned, I think is plain, and will be easily admitted, when we consider that we can have no idea of the place of the universe, though we can of all the parts of it; because beyond that we have not the idea of any fixed, distinct, particular beings, in reference to which we can imagine it to have any relation of distance; but all beyond it is one uniform space or expansion, wherein the mind finds no variety, no marks. For to say that the world is somewhere, means no more than that it does exist; this, though a phrase borrowed from place, signifying only its existence, not location: and when one can find out, and frame in his mind, clearly and distinctly the place of the universe, he will be able to tell us whether it moves or stands still in the undistinguishable inane of infinite space: though it be true that the word place has sometimes a more confused sense, and stands for that space which anybody takes up; and so the universe is in a place. The idea, therefore, of place we have by the same means that we get the idea of space, (whereof this is but a particular limited consideration,) viz. by our sight and touch; by either of which we receive into our minds the ideas of extension or distance.
11. Extension and Body not the same.
There are some that would persuade us, that body and extension are the