and thickness; but duration is but as is were the lengthfo one ftraight line, extended in infinitum, not capable of multiplicity, variation, or figure; but is one common meafure of all existence whatfoever, wherein all things, whilst they exist, equally partake. For this prefent moment is common to all things that are now in being, and equally comprehends that part of their existence, as much as if they were all but one fingle being; and we may truly fay, they all exift in the fame moment of time. Whether angels and fpirits have any analogy to this, in respect of expanfion, is beyond my comprehenfion and perhaps for us, who have understandings and comprehenfions fuited to our own prefervation, and the ends of our own being, but not to the reality and extent of all other beings, it is near as hard to conceive any existence, or to have an idea of any real being, with a perfect negation of all manner of expanfion, as it is to have the idea of any real existence, with a perfect negation of all manner of duration and therefore what spirits have to do with fpace, or how they communicate in it, we know not. All that we know, is, that bodies do each fingly poffefs its proper portion of it, according to the extent of folid parts; and thereby exclude all other bodies from having any share in that particular portion of space, whilft it remains there.

§ 12. Duration has never two Parts together, Expansion all together.

DURATION, and time which is a part of it, is the idea we have of perishing distance, of which no two parts exift together, but follow each other in fucceffion; as expansion is the idea of lafting distance, all whofe parts exift together, and are not capable of fucceffion. And therefore though we cannot conceive any duration without fucceffion, nor can put it together in our thoughts, that any being does now exift to-morrow, or poffefs at once more than the present moment of duration; yet we can conceive the eternal duration of the Almighty far different from that of man, or any other finite being. Because man comprehends not in his knowledge or power, all paft and future things: his thoughts are but of yesterday, and he knows not what to-morrow will

L

bring forth. What is once paft, he can never recal, and - what is yet to come, he cannot make. prefent. What "I fay of man, I fay of all finite beings: who, though they may far exceed man in knowledge and power, yet are no more than the meaneft creature, in comparilon with God himfelf. Finite of any magnitude, holds not any proportion to infinite. God's infinite duration being accompanied with infinite knowledge and infinite power, he fees all things paft and to come; and they are no more diftant from his knowledge, no farther removed from his fight than the prefent: they all lie under the fame view; and there is nothing which he cannot make exist each moment he pleases. For the exist-ence of all things depending upon his good pleafure, all things exift every moment that he thinks fit to have them "exiít. To conclude, expansion and duration do mutually embrace and comprehend each other; every part of Space being in every part of duration, and every part of duration in every part of expanfion. Such a combination of two diftinct ideas, is I fuppofe, fcarce to `be found in all that great variety we do or can conceive, and may afford matter to farther fpeculation.

CHAP. XVI.

OF NUMBER.

1. Number the fimplest and most univerfal Idea. AMONGST all the ideas we have, as there is none Tuggefted to the mind by more ways, fo there is none more fimple than that of unity, or one. It has no fhadow of variety or compofition in it; every object our fenfes are employed about, every idea in our underftandings, every thought of our minds, brings this idea along with it. And therefore it is the moft intimate to our thoughts, as well as it is, in its agreement to all other things, the most univerfal idea we have. For number applies itself to men, angels, actions, thoughts, every thing that either doth exift, or can be imagined. § 2. Its Modes made by Addition.

By repeating this idea in our minds, and adding the rep→

etitions together, we come by the complex ideas of the modes of it. Thus by adding one to one, we have the complex idea of a couple; by putting twelve units together, we have the complex idea of a dozen; and fo of. a fcore, or a million, or any other number.

§ 3. Each Mcde diftinct.

THE fimple modes of number a e of all other the moft diftinct, every the leaft variation, which is an unit, making each combination as clearly different from that which ap-..proacheth neareft to it, as the most remote: two being as diftinct from one, as two hundered; and the idea of two. as diftinct from the idea of three, as the magnitude of the whole earth is from that of a mite. This is not fo in other fimple modes, in which it is not fo eafy, nor perhaps poffible for us to diftinguish betwixt two approaching ideas, which yet are really different. For who will undertake to find a difference between the white of this paper, and that of the next degree to it; or can form. diftinct ideas of every the leaft excefs in extenfion ?

§ 4. Therefore Demonstrations in Numbers the most precife, THE clearness and diftinctness of each mode of number from all others, even thofe that approach neareft, makes. me apt to think that demonstrations in numbers, if they are not more evident and exact than in extenfion, yet they are more general in their ufe, and more determinate in their application. Because the ideas of numbers are more precife and distinguishable than in extenfion, where every equality and excefs are not fo eafy to be.. obferved or measured; because our thoughts cannot in space arrive at any determined fmallness, beyond which it cannot go, as an unit; and therefore the quantity or proportion of any the leaft excefs cannot be difcovered: which is clear otherwise in number, where, as has been faid, 91 is as diftinguishable from 90, as from 9000, though 91 be the next immediate excefs to 90. But it is not fo in extenfion, where whatsoever is more than just a foot or an inch, is not, diftinguishable from the standard of a foot or an inch; and in lines which appear of an equal length, one may be longer than the other. by innumerable parts; nor can any one affign an angle... which fhall be the next biggest to a right one.

§ 5. Names necessary to Numbers.

By the repeating, as has been faid, of the idea of an unit, and joining it to another unit, we make hereof one collective idea, marked by the name two. And whofoever can do this, and proceed on, ftill adding one more to the last collective idea which he had of any number, and give a name to it, may count, or have ideas for feveral collections of units, diftinguished one from another, as far as he hath a series of names for following numbers, and a memory to retain that feries, with their several names: all numeration being but still the adding of one unit more, and giving to the whole together, as comprehended in one idea, a new or dif tinct name or fign, whereby to know it from thofe be fore and after, and distinguish it from every smaller or greater multitude of units. So that he that can add one to one, and fo two, and fo go on with his tale, taking still with him the diftinct names belonging to every progreffion; and fo again, by fubtracting an unit from each collection, retreat and leffen them, is capable of all the ideas of numbers within the compass of his language, or for which he hath names, though not perhaps of more. For the feveral fimple modes of numbers, being in our minds but fo many combinations of units, which have no variety, nor are capable of any other difference, but more or lefs, names or marks for each diftinct combination, feem more neceffary than in any other fort of ideas. For without fuch names or marks we can hardly well make ufe of numbers in reckoning, especially where the combination is made up of any great multitude of units: which put together without a name or mark, to distinguish that precife collection, will hardly be kept from being a heap in confufion.

§ 6. Names neceffary to Numbers.

THIS I think to be the reason, why fome Americans I have spoken with (who were otherwife of quick and rational parts enough) could not, as we do, by any means count to 1000; nor had any distinct idea of that number, though they could reckon very well to 20. Because their language being fcanty, and accommodated

only to the few neceffaries of a needy fimple life, unacquainted either with trade or mathematics, had no words in it to ftand for 1000; fo that when they were difcourfed with of thofe greater numbers, they would fhow the hairs of their head, to exprefs a great multitude which they could not number: which inability, I fuppofe, proceeded from their want of names. *The

Tououpinambos had no names for numbers above 5; any number beyond that, they made out by fhowing their fingers, and the fingers of others, who were pref

ent.

And I doubt not but we ourfelves might diftinctly number in words a great deal farther than we ufually do, would we find out but fome fit denominations to fignify them by; whereas, in the way we take now to name them by millions of millions of millions, &c., it is hard to go beyond eighteen, or at most four and twenty decimal progreffions, without confufion. But to fhow how much diftinct names conduce to our well reckoning, or having ufeful ideas of numbers, let us fet all thefe following figures in one continued line, as the marks of one number; v. g.

Nonilions. Octilions. Septilions. Sextilions. Quintilions. 857324. 162486. 345896. Quartilions. Trilions. Bilions. 248106. 235421. 261734. 368149. 623137.

437916. 423147. Millions. Units.

The ordinary way of naming this number in English, will be the often repeating of millions, of millions, of millions, of millions, of millions, of millions, of millions, of millions (which is the denomination of the fecond fix figures.) In which way, it will be very hard to have any diftinguishing notions of this number: but whether, by giving every fix figures a new and orderly denomination, thefe, and perhaps a great many more figures in progreffion, might not eafily be counted diftinctly, and ideas of them both got more easily to our

* Hiftorie d'un voyage fait en la tene du Brafil par Jean de Lery, c. 20. 207-282.

VOL. I.

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