4. Thefe Notes or Characters are either fignificant Figures, or a Cypher.

5. The fignificant Figures are the firft nine, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9, ufually called Digits. The first of these is more particularly called an Unit or Unity, and the reft are faid to be compofed of Units: So 2 is compofed of two Units, 3 of three Unitis, &c. that is, I more I is equal to 2; 2 more I is equal to 3, &c.

Note, The Characters prefixed to the feveral Articles of this Treatife may ferve for an Example of the natural rank or feries of Numbers, fo increafing by the continual addition of 1.

These Characters were firft ufed in England, about the year 1130.

Note alfo, That in the natural feries of Numbers, 1, 2, 3, 4, 5, 6, 7, 8, &c. the first, third, fifth, &c. Numbers, viz. 1, 3, 5, 7, 9, 11, &c. are called odd Numbers; and the fecond, fourth, fixth, &c. Numbers, viz. 2, 4, 6, 8, 10, 12, &c, are called even Numbers.

6. The Cypher is the last, which tho' of itself it fignifies nothing, yet, being annexed after any of the reft, it increases their value; as will appear in the following Rules.

7. Arithmetic has two Parts, Notation and Numeration.

8. Notation teaches how to exprefs, read, or declare the fignification or value of any number written; and alfo to write down any number propofed, with proper characters, in their due places.

9. A Number is faid to have fo many places, as there are characters in the number, viz. when divers figures, whether they be intermixed with a cypher or cyphers or not, are placed together, like letters in a word, without any point, comma, line, or other note of diftinction interpofed; all those characters make but one number, which confifts of fo many places as there are characters fo placed together; fo this number 205 confifts of 3 places, and this 30,600 of 5 places, &c.

10. Notation confifts in the knowledge of two things, viz. the order of places, and their values.

11. The order of the places is from the right-hand towards the left: So in this number 465, the figure 5 ftands in the first place, 6 in the fecond, and 4 in the third; likewife in this number 7560, a cypher ftands in the first place, 6 in the second, 5 in the third, and 7 in the fourth.

12. The first place of a number, which, as before, is the outermoft towards the Right-hand is called the place of Units; in which place any figure fignifies its own fimple value: So in

this number 465, the figure 5 ftanding in the first place fignifies five units, or five.

13. The fecond place of a number is called the place of Tens, in which place any figure fignifies fo many tens as the figure contains units: So in this number 465, the figure 5 in the first place fignifies fimply 5, but the figure 6 in the fecond place denotes fix tens, or fixty.

14. The third place of a number is called the place of Hundreds; in which place any figure fignifies fo many hundreds as there are units contained in the figure: So in this number 465, the figure 4 in the third place expreffes four hundreds: Wherefore if it be required to read or pronounce this number 465, you are to begin on the left-hand; and, according to the aforefaid rules, to pronounce it thus, four hundred fixty-five; likewife this number 315, is to be pronounced thus, three hundred and fifteen; and this number 205, two hundred and five; also this number 500, five hundred. Whence it is manifeft, that although a cypher of itself fignifies nothing, yet being placed on the right-hand of a figure it increases the value of it, by advancing fuch figure to an higher place, than that wherein it would be feated, if the cypher were abfent.

The true reading or pronouncing the value of any number written, as also the writing down any number propofed, depends principally upon a right understanding of the three firft places before-mentioned, and therefore the learner fhould be well exercised therein, before he proceeds to the following Rules.

15. The fourth place of a number is called the place of Thousands (that is, any number of thousands under ten thousand;) the fifth place Tens of Thoufands; the fixth place Hundreds of Thousands; the seventh place Millions; (a million being ten, hundred thousand;) the eighth place Tens of Millions; the ninth place Hundreds of Millions; the tenth place Thousands of Millions; the eleventh place Tens of Thousands of Millions; the twelfth place Hundreds of Thousands of Millions: And, in that order, you may conceive places to be continued infinitely from the right-hand towards the left, each following place being ten times the value of the next preceding.

16. From the Rules aforegoing, an easy way may be collected to read or express the value of a number propounded, viz. Let it be required to read or pronounce this number, 521426341. Firft, diftinguifh by a comma, or point, every three places, beginning at the right-hand, and proceeding towards the left, fo will the aforefaid number be diftinguish'd into parts, which may be called periods, and ftands thus, 521,426,341. Where you may note the first period towards the right-hand to confift of

B 2

thefe

thefe figures, 341, the fecond of these 426, and the third of thefe 521. Secondly, read or pronounce the figures in every period, as if they stood apart from the reft; fo will the first period be pronounced three hundred forty-one, the second four hundred twenty-fix, and the third five hundred twenty-one. Thirdly, to every period, except the firft towards the right-hand, a peculiar denomination or furname is to be applied, viz. the furname of the fecond period, is thousands; of the third, millions; of the fourth, thousands of millions, &c. Therefore beginning to pronounce at the highest period, which in this example is the third, and giving every period its due furname, the faid number will be pronounced thus, five hundred twentyone millions, four hundred twenty-fix thousand, three hundred and forty-one.

17. And, when 'tis required to write down or read more places than twelve, let the fifth period be called billions; the fixth, thousands of billions; the feventh, trillions; the eighth, thousands of trillions; the ninth, quadrillions, &c.

Note, When a number is diftinguished into periods, as before, the highest period will not always compleatly confift of three places, but fometimes of one place, and fometimes of two; nevertheless after fuch period is pronounced as if it stood apart, the due furname is to be annexed; fo this number 3204689, after it is divided into periods will stand thus, 3,204,689, and is to be pronounced thus, three millions, two hundred and four thousand, fix hundred eighty-nine; and this number 17,213, is to be read, feventeen thousand two hundred

thirteen.

18. The aforefaid Rules for the right pronouncing or reading of a number which is written down, being well understood, will fufficiently inform the reader how to write down any number propounded to be written.

The

The TABLE of NOTATION.

&c.

Twelfth Place 3 Hundreds of Thousands of Millions.
Fourth Period Eleventh Place 2 Tens of Thousands of Millions.

Tenth Place

1Thousands of Millions.

9 Hundreds of Millions.
8 Tens of Millions.
Millions.

6 Hundreds of Thousands.
5 Tens of Thousands.
Thoufands.
Hundreds.
2 Tens.

Fourth Place

3

Third Place

Second Place

First Place

32

Units.

400 CCCC.

18 XVIII. or thus XIIX.500 D. or thus I.

19 XVIIII. or thus XIX. 600 DC. or thus IOC.

20 XX,

yoolDCC. or thus IOCC.

1000 CIO. or thus M.

2000 CIO. CIO. or MM.

3000 CIO. CIO. CIO. or MMM.

5000 100.

10,000 CO.

50,000 0.

100,000 CCCIOƆO. or thus CM.

500,000,000.

x,၀၀၀,၀၀၀ CCCCID၁၁.

1750. CID, IƆCC,L, or MDCCL.

CHAP.