is only great or fmall in a relative sense; here we would be understood to speak of whole and broken numbers or fractions vulgar and decimal, when wẹ alledge that number has neither maximum or minimum. Whence we conclude that time flows evenly, and periods thereof are measured by real or apparent motions; as years by the fun's apparent annual courfe; days by the apparent diurnal motion of the fun; and the fmaller portions of time by pendulum and spring machines. Space is every where, and all objects, terreftrial and celeftial, are in space; but to fpeak of their magnitudes, distances, motions, rotations, and other affections, opens too large a field for our prefent purpofe; only it may be observed that numbers are fo blended and intermixed with all knowledge, that very little can be known without them.

Therefore fetting afide time and fpace that we may confider number, weight, and measure more diftinctly.

Number defines how many, weight how much, meafure how long; and if weights or measures are equally or unequally repeated, the affiftance of numbers is called in of neceffity to define how often, and without doubt, neceffity, as the parent of invention, originally brought men to an acquaintance with numbers.

;

In the first age while mankind where in one family under one head or governor, there was no need of much acquaintance with numbers, arithmetic or geometry; but when the firft family divided, and began to fettle, under diftinct, heads or rulers, in tribes or claffes, this would introduce a divifion of property or stock, and the aid of numbers would be requifite to afcertain how many, or how much each tribe or division had and altho' it cannot be supposed they divided the ground of surface of the earth by the modern method of acres, roods and perches, yet might not each clafs or tribe have a right alloted them of fo many hills and valleys; or a right to fo many fprings or lakes for the tuftenance of their live stock. And as every individual began to dif tinguish his property, it became neceffary for men to betake themselves to different branches of business,

whence

whence the origin of trades; and confequently, as the number of people increased, which would be quick, confidering their longevity, neceffity would point them out various employments, in conjunction with their feveral capacities and inclinations; fo that when the earth did not produce a fufficiency, for its needy inhabitants without culture; husbandry or agriculture was introduced, in order to improve the foil; and when this became too heavy and operofe for men to effect by manual operation: Cattle, as horfes, mules, affes, and oxen, were by art and industry, made fubfervient to the promotion of agriculture; this introduced various machines for that purpofe, as Ploughs, Harrows, Sledges, Carts, &c. which gave birth to variety of mechanics, artificers in brass and iron; add to this, the diverfity of feafons and climate, begat Architecture which required a long lift of neceffary tools, for cutting, fplitting, dividing of wood, and framing binding and faftning together their houses, or habitations, which probably confifted originally of timber either totally or in great

part.

Thus in procefs of time it became neceffary for men to Barter or give in exchange one commodity or article for another, this required the affiftance of numbers, to adjuft the quantity by weight, or measure. When filver, gold, or other metal was to be bartered or exchanged, for the other neceffaries of life, then to affign quantity, weight and numbers took place, and the quantities of liquids as wine or oil were determined by measure, and how often repeated by numbers.

When many families or tribes fettled either defignedly or accidentally under one head, or king, and luxury got footing, many things were wanted, that could not be got at home, fo that it became neceffary to travel in queft of those things, by land on foot, and with beafts of burden, as horfes, affes, camels and dromedaries, alfo by water in fhips or veffels on the feas, to procure either the real or imaginary articles that the cuftom of the times required.

This introduced trade and commerce, so that the ufe of numbers became more neceffary and confpicuous in all branches of buying, felling, and bartering. The fame parent viz. neceffity, that introduced numbers alfo produced Geometry, and Menfuration; for, as mankind for conveniency fettled on the borders of rivers fubject to annual inundations or overflowings, which swept away all land marks; the property of individuals could only be ascertained by Geometry, and its fifter science Trigonometry with Menfuration, or Surveying.

The art or fcience of computing by numbers or Arithmetic was without doubt among the early inventions ; yet hiftory gives us little intelligence either in regard to the author or time: Some have attributed it to SETH, others to NOAH, and the Turks to ENOCH whom they call EDRIS; but the most approved conjecture is, that it had its rife from the introduction of commerce and in confequence thereof fix its Epocha with that of the Tyreans who flourished about a thousand years after the flood. JOSEPHUS tells us that ABRAHAM taught the Egyptians Arithmetic, during the interval of his fojournment in that country; but whether ABRAHAM learnt it of NOAH, or of fome other, or he was the inventor, he doth not fay. PLINY and STRABO alledge that the inundations of the Nile gave occafion to the origin of both Arithmetic and Geometry, however the Egyptians greatly venerated both, and commited the care of thofe arts to their priests, who founded their Theology on them.

The Greeks borrowed their knowledge of Arithmetic, from the Egyptians, and PYTHAGORAS built his Philofophical Syftem upon numbers, affirming that the nature of numbers extends through the whole universe and that the knowledge of the deity was closely connected with the knowledge of numbers.

Howbeit the antient Arithmetic we believe fell far fhort of the modern ; their notations must have been imperfect, their operations abftrufe and tedious as they wanted the cypher, or a character, that, of it felf figni

fies nothing, to fill up a place and change the value of their numbers locally in a decuple progreffion, their feries extending only to nine.

It is generally believed that we owe our present notation to the genius of the eastern nations, and received it from the Arabians, who learned it from the Indians. But when or by whom it was first invented cannot certainly be known.

It appeared in Europe before Annum Chrifti 1000, and in Britain before 150. The oldest treatise extant on the theory of Arithmetic, is the 7th. 8th. and 9th. books of EUCLID'S Elements, where he has delivered the doctrine of proportion, and that of prime and compofite numbers. EUCLID lived about 330 years before CHRIST. The next of whom we know any thing is NICHOMACHUS the PYTHAGOREAN, who wrote a treatise on the theory of Arithmetic confifting chiefly of certain kinds and claffes of numbers, as plain, folid, triangular, quadrangular, and other fpecies of figu rate numbers.

BOETIUS the Philofopher, cotemporary with ERASMUS and COPERNICUS, is the next remarkable writer on this fubject. After the Arabian notation was known in Europe many wrote on the theory and practice of Arithmetic, efpecially in the 15th, century, after the invention of Printing; fo that as learning advanced in Europe, fo did the knowledge of numbers, which by degrees received great improvement. Since the year 1600 in Italy, France, Germany and Britain, writers have been numerous and yet the fubject is not exhausted nor arrived at perfection. Geometry, faid to be the most excellent science in the world, as being the bafis or foundation of all foreign trade, and on which all arts depend, is faid to be invented by JABEL the fon of LAMECH and ADAH, that he and TUBAL-CAIN and NAAMAH together wrote on two columns the arts of Geometry, Mufic, Working in brafs and Weaving, which being found after the flood of NOAH, by HER MARINES afterwards called HERMES the father of wisdom, who taught thofe fciences to

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"others.

others. The mighty NIMROD king of Babylon underftood both Geometry, and Mafonry.

ABRAHAM was alfo a Geometer, and taught it the Egyptians when he was drove thither by a famine about 1926 years before CHRIST. HIRAM the chief inspector over the workmen of SOLOMON's temple was an excellent Geometer, fo was GRECUS his cetcmporary a curious mason, and a workman at the temple.

England was little accquainted with this noble fcience until the time of St. ALBAN; and Geometry made no great progress until the time that ATHELSTON king of England about the year 924 re-established it; he was a great admirer of Geometry, and is faid to have read lectures on that fubject to others. Some alledge this fcience had its origin among the Egyptians, who were of neceffity led to the invention thereof, as a remedy for the confufion that happened in their lands occafioned by the inundations of the river Nile, which carried away all boundaries and effaced all landmarks, or limits of their poffeffions.

Geometry in procefs of time paffed out of Egypt into Greece, where it received additional improvements, in the time of THALES MILESIUS, about 600 years antecedent to the Chriftian Era, alfo EUCLID about 300 years after greatly enriched that fcience, and compiled his Elements of Geometry,; that are fo extensively ufeful and so univerfally admired, as to be tranflated into moft of the modern Languages.

The extenfive utility of numbers is confpicuously evident in every branch of bufinefs; their aid is called upon by every tradefman, and every mechanic borrows affiftance from them. So that the utility of numbers more loudly proclaims their dignity and worth, then doth their antiquity. Arithmetic is the grand regulator of all the various complex and intricate modes of traffic, commerce, and merchandize; all duties cuftoms, excifes, dues, tolls and impofts, upon all exports and imports, both coaft ways and over feas, to our own plantations, or to foreign ports, with all draw backs, debentures, bounties, premiums &c. etablished by the legislature,