being viewed in different Lights. Now as this is by far the moft comprehensive Branch of our Ideas, and includes those that moft frequently occur in the Search and Purfuit of Knowledge, I shall endeavour to treat of thein in the exactest Order and Method, and for that purpose range them under several Heads, according to the different Acts of the Mind exerted in framing and putting them together.

H. THESE Acts may in the general be all reduced to three. 1. Composition, when we join many fimple Ideas together, and confider them as one Picture or Reprefentation. Such are our Ideas of Beauty, Gratitude, a Furlong, &c. And here let it be obferved, that the Mind fometimes

Three Several
Afts exerted

in fraving iss arbitrary

by the Mind Idea, viz. Composition. confines itself to the various Confideration of the same Idea, and by enlarging it in different Degrees, exhibits it under a Diversity of Forms. Thus by adding Units together, in diftinct feparate Collections, we come by all the several Combinations of Numbers, as a Dozen, a Score, a Million. At other times, we unite Perceptions of different Kinds, in which cafe the Compofition is more manifeft, and the Idea itself becomes of course more complicated. Harmony for inftance is a compound Idea, made up of many different Sounds united; all which the Musician must have, and put together in his Mind, before the Ear can be entertained with the actual Performance. Now although the Act of the Mind, is in fome Measure exerted in the framing of all our complex Notions, yet as many of them include certain limited and particular Confiderations, arifing from other Operations of the Mind employed about them, it is neceffary to take account of these Acts alfo, if we would conceive clearly the Manner, | in which the several Species of our compound Ideas are formed,

1

Abstraction.

III. 2. THE next Operation therefore of the Mind, about its Ideas, is Abstrastion; when we feparate from any of our Conceptions, all those Circumstances that render it particular, or the Representative of a fingle determinate Object; by which means, instead of standing for an Individual, it is made to denote a whole Rank or Class of Things. Thus upon seeing, for instance, a Square, or Circle, we leave out the Confideration of their Bulk and every thing elfe peculiar to them, as they immediately affect our Sight, retain only the Notion of their Figure and Shape. In this manner we get our general Ideas; for such naked Apsarances, feparated from the Circumstances of Time, Place, Sr. ferve the Mind as Standards, by which to rank and denominate particular Objects. When therefore we meet with a Figure, answering to the Shape and Form we have laid up in our Understandings, it is immediately referred by the Mind to this Pattern, and called by its Name, which by this means becomes proper to the whole Species. Thus a Square, or Circle, are univerfal Terms, common to all Figures of that particular Shape, anu alike applicable to them where-ever they exist; in like manner as the Ideas themselves are general, and Reprefentatives of all of the Kind.

And Comparifon.

IV. 3. THE third and last Act of the Mind about its Ideas, is the comparing them one with another; when we carry our Confideration of Things beyond the Objects themselves, and examine their Respects and Correspondencies, in reference to other Things which the Mind brings into a View at the same time. It is thus we get all our Idea of Relations, as of Greater, Lefs, Older, Younger, Father, Son, and innumerable others. This threefold View of our Ideas, as either compounded of many others put together, or made universal by the Abstraction of the Mind, or as representing the various Relations and Habitudes of Things, will give us an Opportunity of observing, whatever is moft curious and useful in this fundamental Branch of Knowledge, and of explaining the Manner and Procedure of the Understanding, in enlarging its Views, and multiplying the Objects of Perception. That we may therefore conceive of this Matter with the greater Order and Clearness, we shall make each of these several Divisions, the Subject of a diftinct Section.

1.

Corpound Ideas corfider

ad bore mari'y

as Combinar

I.

SECT. I.

Of Compound Ideas.

E begin therefore with those Ideas W which may be properly termed compound, as being derived from that Power the Mind has of uniting many Conceptions into one. Though this Class comprehends, in fome fort, all our complex Notions; yet they are at prefent confidered, merely as they are Combinations of the Understanding,

s of the

derstanding.

ftanding, and with a view to those particular Ideas, out of which they are framed. Here, as, was already observed, the Mind fometimes proceeds, by enlarging and diverfifying the fame Idea: at other times it brings together Ideas of different Kinds, and in both ways finds infinite Scope and Variety. But that we may follow the natural Procedure of the Intellect, and trace it in its Advances from simple to more complicated Acts, we shall first take a View of it as employed about one and the fame Idea, where perhaps we may meet with such Instances of Address, Management, and Contrivance, as will appear perfectly aftonishing to one, who never fet himself seriously to consider the Manner and Conduct of his

own Mind.

Unity the 0riginal and

Foundation of

all our Ideas of Number.

II. THE most obvious and fimple Idea we have, is that of Unity or One. By adding it to itself continually, and retaining the several Collections in our Minds, we come by all the different Combinations of Numbers, in which we readily perceive an endless Diversity. All these Ideas are nevertheless evidently diftinct among themselves, the Addition of a single Unit, constituting a Number as clearly different from that immediately before it, as any two the most remote Ideas, are one from another. But that the Understanding may not lose itself, in the Confideration of those infinite Combinations, of which Unity is capable, it proceeds by regular Steps, and beginning with the original Idea itself, pursues it through all its Varieties, as they are formed by the repeated continual Addition of Unit after Unit. Thus Numbers are made to follow one another in an orderly Progreffion, and the several successive Collections are diftinguished by particular Names.

The artful

Compofition of Numbers a great Help to our Conceptions.

III. AND here we may take notice of a wonderful Artifice, made use of by the Mind, to facilitate and help it forward in its Conceptions. For as the Advance from Number to Number is endless, where they all to be diftinguished by different Denominations, that had no Connection or Dependence one upon another, the Multitude of them muft foon overcharge the Memory, and render it impoffible for us to go any great Way in the Progress of Numbering. For this Reafon, it is so contrived, that the Change of Names is reftrained to a few of the first Combinations, all the rest that follow, being marked by a Repetition of the

1

:

:

fame Terms, variously compounded and linked together. Thus thirteen is ten and three, fourteen ten and four, and fo on to twenty, or two tens, when we begin again with one, two, &c. until we advance to thirty, or three tens. In this Manner the Progression continues, and when we arrive at ten tens, to prevent Confusion, by a too frequent Repetition of the fame Word, that Sum is diftinguished by the Name of a Hundred. Again ten hundred is called a Thousand; at which Period the Computation begins anew, running through all the former Combinations, as ten thousand, a hundred thousand, ten hundred thousand; which last Collection, for the Reasons mentioned above, has the Name of a Million appropriated to it. With this Million we can begin as before, until it is repeated a million of times, when if we change the Denomination to Billions, and advance in the fame manner through Trillions, Quartillions, the Series may be carried on without Confufion, to any Length we please..

diflintt.

IV. THIS artful Combination of Names, to And one of mark the gradual Increase of Numbers, is perhaps the principal one of the greatest Refinements of the human UnReasons that cor Ideas of derstanding, and particularly deserves our AdmiNumbers are ration, for the Manner of the Compofition; the (ovemarkably feveral Denominations being so contrived, as to dittinguish exactly the Stages of the Progreffion, and point out their Distance from the Beginning of the Series. By this means it happens, that our Ideas of Numbers are of all others the most accurate and distinct, nor does the Multitude of Units affembled together, in the least puzzle or confound the Understanding. It is indeed amazing, that the Mind of Man, so limited and narrow in its Views, should yet here seem to shake off its natural Weakness, and discover a Capacity of managing with Eafe the most bulky and formidable Collections. It we enquire particularly into the Reasons of this, we shall find it wholly owing to the Address of the Mind, in thus diftinguishing Numbers by different Names, according to the natural Order of Progreffion. For as those Names are made to grow one out of another, they may be aptly compared to a Chain, all whose Parts are linked together, by an obvious and viibie Connection. Hence comes it to pass, that when we fix our Thoughts upon any Number, however great and teemingly unmanageable, yet if it is once determined to a particular Name, we find it easy to run back through all the Stages of the Progreffion, even till we arrive

1

at_

at Unity itself. By this means we fee, with a fingle Glance of our Minds, not only the two Extremes of the Number under Confidearation, but also the several intermediate Parts, as they are united to make up the whole.

As they belp Perception of theinterjucent

us to a clear

Parts.

V. Now it is to this clear and accurate View of the interjacent Ideas, that we owe our fo diftinct Perception of the various Combinations of Numbers. And indeed we may observe in the general, that all our Ideas of Quantity, efpecially when they grow to be very large, are no otherwife afcertained, than by that Perception we have of the intervening Parts, lying, if I may so say, between the Extremes. When we look at any Object confiderably diftant from us, if we have a clear View of the interjacent Lands and Houses, we are able to determine pretty nearly of its Remoteness; but if without such a Knowledge of the intervening Spaces, we should pretend to judge of the Distance of Objects, as when we fee the Spire of a Steeple, behind a Wall, or beyond a Mountain, every one's Experience is a Proof, how liable we are in these Cafes to be deceived. Just so it is in judging of Duration. When we carry back our Thoughts to any past Period of our Lives, without Confideration of the Number of Years, or Months; we find, that our Idea of the Time elapfed grows more distinct, in proportion as we become sensible of the intermediate Parts of our Exiftence. At first, we are apt to judge the Distance extremely short, but when we fet ourselves to consider our several fucceffive Thoughts and Actions, the Idea of the Duration grows upon us, and continues to increase, as the Attention of the Mind brings new Periods of Life into view.

Without

Names que

cannot make any Progrefs in Numbering.

VI. Hence it will be easy to conceive, how much the Mind is helped forwards in its Perception of Number, by that ready Comprehenfion of all the feveral Stages in a Progression, which peculiarly belongs to Ideas of this Class. But this, as I have before intimated, we derive from the orderly Series and Connection of Names, infomuch that where they cease, the Computation of Numbers also ceafes with them. We can have no Idea of any Sum, without a Knowledge of all the Terins that go before, according to the natural Order, in which they follow one another; fo that he who cannot, in a regular way, count to ninety-nine, will never, while that Incapacity continues, be able to form

the