nexed in their distinct orders, and the dependence of so long a train of numeral progressions, and their relation one to another, are not able all their life-time to reckon or regularly go over any moderate series of numbers. For he that will count twenty, or have any idea of that number, must know that nineteen went before, with the distinct name or sign of every one of them, as they stand marked in their order; for wherever this fails, a gap is made, the chain breaks, and the progress in numbering can go no farther. So that to reckon right, it is required, 1. That the mind distinguish carefully two ideas, which are different one from another only by the addition or subtraction of one unit. 2. That it retain in memory the names or marks of the several combinations, from an unit to that number; and that not confusedly, and at random, but in that exact order that the numbers follow one another: in either of which, if it trips, the whole business of numbering will be disturbed, and there will remain only the confused idea of multitude, but the ideas necessary to distinct numeration will not be attained to.
Number measures all measurables.§ 8. This farther is observable in numbers, that it is that which the mind makes use of in measuring all things that by us are measurable, which principally are expansion and duration ; and our idea of infinity, even when applied to those, seems to be nothing but the infinity of number. For what else are our ideas of eternity and immensity, but the repeated additions of certain ideas of imagined parts of duration and expansion, with the infinity of number, in which we can come to no end of addition? For such an inexhaustible stock, number (of all other our ideas), most clearly furnishes us with, as is obvious to every one. For let a man collect into one sum as great a number as he pleases, this multitude, how great soever, lessens not one jot the power of adding to it, or brings him any nearer the end of the inexhaustible stock of num-
