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A R I T H M E T I C K. quently.be of Tyrian invention. From Afia it paffed the method of notation by them, were originally inventby fome of the eaftern nations, probably the Indians; into Egypt, where it was greatly cultivated. From edafterwards improved by the Arabians; and at laft brought thence it was tranfmitted to the Greeks, who conveyed over to Europe, particularly into Britain, betwixt the it to the Romans with additiortal improvements. But, from feme treatifes of the ancients remaining on this fub- tenth and twelfth century. From the ten fingers of the jett, it appears that their arhhmetick was much inferior hands, on which it hath been ufual to compute numbers, figures were called digiti. Their form, order, to that of the moderns. and value, are as follows : Number, which is the objeft of arithmetick, is that 1 One, an unit, or unity, 2lvtwo, 3 three, 4 four, which anfwers dire&ly to the queftion. How many ? and j five, 6 fix, 7 feven, 8 eight, 9 nine, o cipher, nought, is either an unit, or fome part or pans of an unit, or a null, or nothing. Of theft, the firft nine, in contradiftinCtion to the cipher, are caed. Jignificant figures. multitude of units. To a perfon having the idea of number in his mind, The value of the figures now affigned is called their the following queftions naturally occur, viz. i. How is Jimple value, as being that which they have in themfuch a number to be exprefled or written ? Hence we ftlves, or when they ftand alone. But when two or more have Notation. 2. What is the fum of two or more figures are joined as in a line, the figures then receive numbers? Hence Addition. 3. What is the difference alfo a local value from the place in which they ftand, of two given numbers ? Hence Subtraction. 4. What reckoning the order of places from the right-hand towards will be the refult or produCt of a given number repeated the left, thus, or taken a certain number of times ? Hence Multiplication. 5. How often is one given number contained in another? Hence Divifion. Thefe five, viz. Notation, Addition, Subtraction, Multiplication, and Divifion, are the chief parts, or rather the whole of arithmetic; as every arithmetical operation requires the ufe of fome of them, and nothing but 777777777777 a proper mixture of them is neceffary in any operation whatever.; and, by an Arabic term, thefe are called the A figure {landing in the firft place has only its fimple value ; but a figure in the fecond place has ten times the algorithm. value it would have in the firft place; and a figure in the third place has ten times the value it would have in the fecond place; and univerfally a figure in any fuperior Chap. I. Notation. place has ten times the value it would have in the next place. Notation is that part of arithmetic which explains inferior Hence it is plain, that a figure in the firft place limply the method of writing down, by characters or fymbols, fignifies fo many units as the figure exprefles; but the any number expreffed in words; as alfo the way of fame figure to the fecond place will fignify fo reading or expreffing, in words, any number given in many tens; advanced third place, it will fignjfy fo many characters- or fymbols, But the firft of thefe is proper- hundreds; inin thethe fourth fo many thoufands; in ly notation, and the laft is more ufually called numera- the fifth place, fo many tenplace, thoufands; in the fixth place, tion. hundred thoufands; and in the feventh place, The things then proper to be comprifed in this chap- fofo many many millions, e5rc. Thus, 7 in the firft place, will ter are, 1. The figural notation. 2. Numeration, or denote units; in the fecond place, ftven tens, or the way of reading numbers. 3. Defcriptions of the feventy;feven in the third place, feven hundred; in the fourth kinds- or ■ fpecies of numbers. place,, ftven thoufand, <bc. Every three places, reckoning from the right-hand, I. Figural Notation. make a half period; and the right-hand figures of thefe are termed units and thoufands by turns; A w unit, or unity, is that number by which any thing half-periods middle figure is always tens, and the left-hand fiis called one of its kind. It is the firft number; and if the hundreds. to it be added another unit, we fttall have another num- gureTwoalways or fix places, make a full period *, ber called two; and if to this laft another unit be add- and the half-periods, reckoning from the right-hand towards ed, we {hall have another number called three ; and the left, periods, are titled as follows, viz. the firft is the period thus, by the continual addition of an unit, therewill arife an infinite increafe of numbers. On the otherhand, of units ', the fecond, that of millions; the third is titled if from unity any part be fubtraCled, and again from bimilliomr or bilfions; the fourth, trimillions, or trilthat part another part be taken away, and this Be done lions ; the fifth, quadrillions; the fixth, quintillions; feptillions; the ninth, continually, we {hall have an infinite decreafe of num- the ftventh fextillions; the the tenth, nonillions, &c. bers. But though number, with-relpeCl: to increafe-and * oftillions; decreafe, be infinite, and knows no limits ; yet ten fi- Half-periods are ufually diftinguilhed from one angures, varioufly combined or repeated, are found fuffi- other by a comma, and full periods by a point or colon; dent to exp refs any number, whatfoever. Theft,, with as in the following TABLE.