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 367 A R I T H M E T I C K. 6. An odd number is that which 2 does not meafure, T A B L E.^ or which cannot be divided by 2, without a remainder II 3d Period. 2d Period. ifl: Period. « 7. 3»A prime f. 7» 9*number > !3is that which unity, or itfelf, . onBillions. Millions. Units. ly meafures; as 3, 5, 7, 11, 13, 17, 19. 8. A compojite number is that which is meafured by fome other number than itfelf, or unity; as 12, which is meafured by 2, 3, 4, or 6. 9. Numbers are called prime to one another, when unity only meafures them. Thus 13 and 36 are prime to one another; for no number, except unity, meafures both. Numbers are called compojiie to one another, 8 1 3,700.2 3 7,8 94 .678,040. when10. fome number, befides unity, meafures them. Thus compofite to one another ; for 3 or 6 meaThe table may be exprefled in a more concife fornv 12furesandboth18 are of them. thus, 11. A number which meafures another is called an 3. 1.APer. A2. aliquot part of that other. Thus 6-is an aliquot part of ^ >, 18, and 3 of 12, and 5 of 20. Billions. ( Millions. ( Units. 12. The number meafured, or which.contains the ali813,700:237,894:678,040. part a certain number of times, is called a multiple From the table it is obvious, that though a cipher fig- quot of aliquot part. Thus 18 is a multiple of 6, and nify nothing of itfelf, yet it ferves to fupply vacant pla- 12 that of 3. ces, and raifes the value of fignificant figures on its left 13. A number is called an aliquant part of another, hand, by throwing them into higher places. Thus, in when it does divide that other without a- remainder. the firft period, by a cipher’s filling the place of units, Thus 7 is an not part of 24. the figure 4 is thrown into the place of tens, and figni- 14. Two, aliquant three, or more numbers, which, multiplied; fies forty. But a cipher does not change the value of a together, produce another are called the.comfignificant figure on its right-hand. Thus, 07, or 007, ponent parts of the numbernumber, produced. Thus 3 and 4, is the fame as-7. 2 and 6, are the component parts of 12; and 2, 3, and 4, are the component parts of 24. II. Numeraiitm. I j. The product of a number multiplied into itfelf is thefquare, or fecondpower, of that number; and Notation and numeration are fo nearly allied, that called number itfelf is in this cafe called the root. And if he who underftands the one cannot fail foon to acquire the the fquare be multipled into the root, the product is the other. The method of reading numbers, exprefled the cube, or third power, of that number. And if by figures, may be eafily learned, from the table of the called the cube be multiplied into the root, the product thence figural notation ; in which obferve the following Rule. Beginning at the left hand, and reading to- arifing is called the biquadrate, ox fourth power. See. ward the right; to the Ample value of every figure join the name of its place, and conclude each period by exiChap. II. Addition, prefling its title, every where omitting the ciphers.. is the collecting of two or more numbers HI. Defcriptions of the kinds or fpecies of numbers i intoAddition one fum or totaL 1. An integer, or whole number, is an unit; or any multitude of units ; as i, 7, 48, 100, 125. I. Addition of Integers; 2. A frailion, ox broken number, is any part or parts of an unit; and is exprefled by two numbers, which are Rule I. Set figures of like places under other, viz. ■ feparated from one another by a line drawn betwixt units under units, tens under tens, <bc. them; the under number being c^Jled the denominator, II. Beginning at the lowed place, fet down the rightand the upper one the numerator, of the fraction ; as hand figures of the fum of every column, and carry the as fo many units to the next luperior place. t» 3. A-rs'mixt number is an integer with a fraction joined ' redExamp. I. Becaule fimilar or like things only can be added, place the numbers as directed in Rule I. viz. to it; as 4-3-, 7^, 48^ 4. A number is faid to meafure another number, units under units, tens under tens, eSrc. as in the when it is contained in that other number a certain num- margin. Then beginning at the lowed place, 453 ber of times, or when it divides that other number with- viz, that of units ; fay, 4 units and 3 units make 234 out any remainder. Thus, 3 meafures 6, 9, or 12. 7 units, which fet below in the place of units ; 5. An even number is that which is meafured by 2, then 3 tens-and 5 tens make 8 tens, which fet be- 687 or which 2 divides without any remainder; as 2, 4, 6, 8, low in the place of tens; then 2 hundreds and 4 10, 12. hundreds make 6 hundreds, which fet below in the place