« ΠροηγούμενηΣυνέχεια »
4. These Notes or Characters are either significant Figures, or a Cypher.
5. The significant Figures are the first nine, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9, usually called Digits. The first of these is more particularly called an Unit or Unity, and the rest are said to be composed of Units : So 2 is composed 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 several Articles of this Treatise 'may serve for an Example of the natural rank or series of Numbers, so increasing by the continual addition of 1. These Characters were first used in England, about the
Note also, That in the natural series of Numbers, 1, 2, 3, 4, 5, 6, 7, 8, &c. the first, third, fifth, &c. Numbers, viz. 1, 3, 5, 7, 9, II, &c. are called odd Numbers; and the second, 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 signifies nothing, yet, being annexed after any of the rest, it increases their value ; as will appear in the following Rules.
7. Arithmetic has two Parts, Notation and Numeration.
8. Notation teaches how to express, read, or declare the fignification or value of any number written ; and also to write down any number proposed, with proper characters, in their due places.
9. A Number is faid to have so 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 distinction interposed; all those characters make but one number, which consists of so many places as there are characters fo placed together ; fo this number 205 consists of 3 places, and this 30,600 of 5 places, &c.
10. Notation consists 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 Itands in the first place, 6 in the second, and 4 in the third; likewise in this number 7560, a cypher stands 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 outermost towards the Right-hand is called the place of Units; in which place any figure signifies its own simple value: So in
this number 465, the figure 5 ftanding in the first place signifies five units, or five.
13. The second place of a number is called the place of Tens, in which place any figure signifies so many tens as the figure contains units : So in this number 465, the figure 5 in the first place fignifies simply 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 signifies so many hundreds as there are units contained in the figure : So in this number 465, the figure 4 in the third place expresses 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 aforesaid rules, to pronounce it thus, four hundred fixty-five; likewise 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 signifies nothing, yet being placed on the right-hand of a figure it increases the value of it, by advancing such figure to an higher place, than that wherein it would be seated, if the cypher were absent.
The true reading or pronouncing the value of any number written, as also the writing down any number proposed, depends principally upon a right understanding of the three first places before-mentioned, and therefore the learner should 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 Thousands; 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 colleEted to read or express the value of a number propounded, viz. Let it be required to read or pronounce this number, 521426341, First, distinguish by a comma, or point, every three places, beginning at the right-hand, and proceeding towards the lett, so will the aforesaid number be distinguish'd into parts, which may. be called periods, and stands thus, 521,426,341. Where you may note the first period towards the right-hand to consist of
these figures, 341, the second of these 426, and the third of these 521. Secondly, read or pronounce the figures in every period, as if they stood apart from the rest; 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 first towards the right-hand, a peculiar denomination or surname is to be applied, viz. the furname of the second 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 surname, the said 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 seventh, trillions ; the eighth, thousands of trillions; the ninth, quadrillions, &c.
Note, When a number is distinguished into periods, as before, the highest period will not always compleatly consist of three places, but sometimes of one place, and sometimes of two; nevertheless after fuch period is pronounced as if it stood apart, the due surname 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, seventeen thousand two hundred thirteen.
18. The aforesaid 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 Order of Places. The Value of Places. &c.
Tenth Place 1 Thousands of Millions.
Ninth Place 9 Hundreds of Millions.
Tens of Thousands.
The TABLE of NOTATION,
300CCC. 12 XII,
40oCCCC. 18 XVIII. or thus XnIX. 500 D. or thus 15. 19/XVIIII. or thuş XIX. 600 DC. or thus 1°C. 201XX,
17oolDCC. or thus loCC. 1000 CIÒ. or thus M. 2000 CIO. CIO. or MM. 3000 CIO. CIO. CO. or MMM. 500010 10,000 CCIO.
100,000 CECI. or thus CM.
1750.CII, 13CC,L, or MDCCL.
“C H A P.