mixt; and confequently as it conforts with air, water, and earth, it must become airy, watry and carthy, as by Prop. 1, 2 and 3, Fire was proved to be in air, water, and earth.

COROLLARY 1.

From hence it follows, that all elementary bodies of this our globe, contain fomething of the other elements in them, and they are diftinguished by the different names of elements only upon account of the greater abundance of a particular elemental matter in one than another. Water is called fo, because it contains a much greater quantity of true elemental water than of air, earth and fire, which it also contains in fome proportion. Mix earth with water fo as to give it that confiftence, which is called clamminefs, and it lofes its former denomination and takes that of flime; drie that clammy earth by means of the fun or a culinary fire, and increase the fire till the earth is capable of continuing to burn by itself, then it lofes its former name, and is called fire; for the name is always attributed to the greater abundance of any elemental matter. Air may be fo impregnated with water, as to be called water; and water may be fo divided and expanded by air, as to be called air. Earth may be fo diluted with water, as to be called water: And water may be fo thickened with earth, as to be called earth: Fire may be fo intangled with other matter, as to take the names of other matter, as phofphorus &c. And that it is capable of being fixt, that is, in the vulgar fense of things (For in truth all matter is in abfolute, and

D

not

That these four forts of matter are never found by human experiments totally separated from each other, but in fome degree mixt; and that each of them in thefe mixt ftates, have certain peculiar qualities, and that an infinite variety of phænomena may arise from an infinite number of mixtures+, which these sorts of matter are fufceptive of, from their ca. pacity to admit of divifion to infinite minuteness. Inftead of a quinta effentia, we may allow the immediate ACTIVITY of the author of matter, and this will do as well, fince human experiments can never reach that quinta cffentia (if there be fuch a thing) to discover its properties.

+Those who have written de arte combinatoriâ reckon no fewer than one hundred feventy nine millions one thousand and fixty forts of earth. See Evelyn his treatife on earth. Kirchers his mundus fubterraneus.

merely relative motion) the impregnating mercury with the rays of the fun, fo as thereby to increafe the weight and make gold, is a proof; for which fee the writings of Homberg, and Sir Kenelm Digby (e).

COROLLARY 2.

All bodies of this our carth are mixtures of thefe four elements, and all diverfity of them arifes from mixtures in divers proportions; and although the diverfity may appear to be infinite, an infinite number of proportions in which the elements may be mixt, may fufficiently account for a variety of productions, although they are infinite. For if any two elements are to be mixt in all the variety of proportions possible, it may be conceived firft, as 2 to 1. or 2, 3, 4, 5, 6, 7 to 1, and fo on to infinity, or as th to 1. or 01.001.0001.0001. to 1, that is, by an infinite increafe of one towards the other, or an infinite decrease of one towards the other. For it is well known to the geometrician, that the fmalleft portion of matter is capable of infinite divifion (which fhall be next demonftrated) and thereby of holding infinite proportions to any other portion of matter, which is itself alfo capable of infinite divifion. But if this be the cafe between any two elements, the variety of all proportions poffible between four, muft become infinitely greater, and confequently the variety of bodies arifing from thefe mixtures can not be limited or conceived by the human mind. By this is not meant a mechanical account of the order of things, which never can be given accurately. Because HE, who made matter, is the Being who still acts, and continues in every phænomenon the laws of motion. No more therefore is meant by this, than whereas that Being is pleased to create matter, and use its paffive inftrumentality in producing various phænoraena; the four fpecics of clementary matter may be fo combined, according to the laws, which the author of matter has given them, as to exhibit an infinite variety of appearances.

PRO

(e) I remember a rare experiment, that a nobleman of much fincerity and a fingular friend of mine, told me that he had feen, which was that by means of glaffes made in a particular manner, and artificially placed, one by another, he had feen the fun beams gathered. together, and precipitated down into a brownish or purplish red powder. There could be no fallacy in this operation when the glaffes were placed and difpofed for this intent, and it must be in the hot time of the year, elfe the effect would not follow; and of this magiftery he would gather fometimes near two ounces in a day.

Kenelm Digby, of bodies. page. 63.

Homberg has exceeded this.

Since the infinite divifibility of matter has been mentioned, as a neceffary part of what preceded, and may be of great use in refpect to what follows, it will be proper here to give a demonftration of it. In this, and all other demonftrations applied in these lectures as little of mathematics fhall be ufed, as is poffible: And this particular property of matter having been largely demonftrated by Keil, in his introduction to natural Philofophy, a fhort demonftration of it fhall fuffice in this place; there is no defign oftentatiously to exhibit mathematical literature, but only in a brief, and perhaps a new manner, to demonftrate fome propofitions neceffary to the main part of our reafoning.

Suppofe BC, DE, FG, HI in fig. 1. to be ftrait lines parallel and equal to each other, and K a point which is the center of the circle BRCL, and of the exterior circles. It is plain that ftraight lines may be drawn from B and C to K, and alfo from D and E, F and G, H and I, and from all poffible lines parallel and equal to BC, and drawn beyond HI; that is, from an infinite number of lines: But it is alfo plain, that the lines which are drawn from DE fall between thofe from B and C, and cut the line BC at M and N, and those which are drawn from F and G fall between M and N and cut the line in points which are ftill nearer, and fo on to infinity; because an infinite number of lincs may be drawn, all parallel and equal to the first BC; that is, the line BC is capable of being divided into an infinite number of points.

The lines in the figure are drawn wide afunder for diftinction, but they may be conceived to be drawn extreamly clofe, and inftead of straight lines, you may conceive BRC a small portion of a circleBRCL, and BKN an angle at the center, and DSE a small portion of a circle DSP, and FTG a fmall portion of a circle FTQ, and the demonftration will be the fame as before, and the fuperficial angle BKC will hereby be demonstrated capable of infinite divifion. Then fuppofe folid globes or

D 2

spheres

fpheres (or folid bodies bounded by fingular and angular furfaces) inftead of thefe circles, and BRCK, DSEK &c. to denote folid portions or fectors of thofe fpheres, or folid bodies bounded by fimilar angular furfaces; and BKC a folid angle at the center, or a folid cone; and the demonstration is ftill fimilar; because there may be lines drawn to the center from the angular points, and all the points of the furfaces, removed at pleasure to infinity and parallel, which will in like manner infinitely divide BKC the folid angle, or the folid cone &c. Matter therefore is capable of divifion to infinity. Q. E. D.

Since the infinite divifibility of matter has been demonstrated, it will alfo be proper to demonftrate the increase of the furfaces of all bodies, upon divifion; for upon the truth of this depends the folution of many phænomena, concerning bodies, which may be made to fwim in fluids fpecifically lighter. Hence it is that not only water and earth floats in air, but also metals. As there may be frequent use made of this propofition in what follows, and a demonstration of it has not any where yet occurred, it will be proper here to give a full demonftration of it. For the propofition already demonftrated by mathematicians, will not intirely anfwer our purpofe, to wit, by divifion of regular folids, matter and gravity decreafes in a triplicate ratio of the diameters; but the furface decreafes only in a duplicate ratio of the diameters. Our defign is to demonftrate, that every irregular section of a regular body, and the fections of all bodies regular or irregular occafion a great inercafe of the quantity of furface.

And first of the increase of furface in the divifion of a cube or die to demonstrate which, the following lemma will be neceffary.

LE M M A.

Let ABC fig. 2. be a die or cube bounded by fix equal furfaces. Cut it through in lines equally diftant from any two fides in the fame plain, so as to divide it into halves: It is evident that each half of the die has over and above the half of all the furfaces of the whole die, the additional furface, markt by the prickt line GHIK, which is equal to one furface of the whole die, or part of the entire furface. Divide the half

dice

dice as before equally, cutting them parallel to the smallest surfaces, and each half, that is, each fourth part of the whole die will have an additional furface RPQS, over and above the whole furface of the entire body of which it is an half, that is, ith part of the furface of the whole die, which is equal to one fmall furface, or half a large furface of the half die: Divide the four parts as in fig. 3. by cutting them equally distant from the fmallest surfaces, and each half thereof will have the additional furface markt FGH, over and above the half of the whole furface of that intire body, of which it is half, that is, th part of the furface of the whole die. Therefore each eighth part of the large die, will become a fmall die, having fix furfaces all equal. By continuing to divide the fmall dice or cubes, the fame proportions of the increase of furface will be continued infinitely; that is, the aditional furfaces confidered collectively, as parts of the furface of the large die, and belonging to all the bodies in the divifion are 1, 3, 3, 4, &c. infinitely. For every fection paffing through the intire thicknefs of the die, and being parallel to one of the furfaces, occafions an addition of two furfaces, each equal to one of the fix furfaces of the large die, that is, th part of all the furface, and the two make

1 I I

I

I

12 127 48

2

But if the bodies are taken fingly, and their furfaces confidered as parts of the intire surface of the large die, belonging to each separately in the divifion, the additional proportions of them may be expreft by the following fractions, 12 • 12 7 247 24• 242 489 4, &c. infinitely, i. e. Upon the firft fection of the die, each half acquires an increase of th part of the whole furface, over and above half the whole furface; upon the divifion: of the half dice again, each quarter acquires th part of the intire furface of the whole die, over and above of the intire furface of the half die. Let therefore the first column A denote the matter of the cube: or die, and its parts by divifion, and the column C fhall denote the increase of furface over and above that which is proportional to the mat-ter, in the column B.