EXPLANATION OF THE CHARACTERS + or 6)30(5 875 25 * ::: : USED IN THIS TREATISE. 12 pence I THE fign of equality: as, fhilling, fignifies that 12 pence are equal to one fhilling; and, in general, that whatever precedes it is equal to what follows. The fign of Addition: as, 5+5=10, that is, 5 added to 5 is equal to 10. Read 5 plus .5, or 5 more 5 equal to 10. The fign of Subtraction: as, 12-4-8, that is, 12 leffened by 4 is equal to 8,0 or 4 from 2 and 8 remains. Read 12 minus 4, or 12 lefs 4 equal to 8. The fign of Multiplication: as, 6×5=379 that is, 6 multiplied by 5 is equal to 30. Read 6 into 5 equal to 30. { The fign of Divifion: as, 30÷5=6, that is, 30 divided by 5 is equal to 6. Read 30 by equal to 6. Numbers placed fraction-wife do alfo denote divifion, the numerator, or upper number being the dividend, and the denominator or lower number, the divifor; thus, the fame as 875÷25=35. 875 25 The fign of proportion, thus, 2 : 4 8 16, that is, as 2 is to 4 fo is 8 to 16. Signifies Geometrical Progreffion. Shews that the difference between, 2 and 9 added to 6 is equal to 13. 9-2+6=13nus 2 plus 6 equal to 13 Reid miAnd that the line atop (called a Vinculum) connects all the numbers over which it is drawn. S Signifies that the fum of 3 and 5 taken 12-3+5=4 from 12 leaves or is equal to 4. Signifies the fecond power, or Square: Prefixed to any number or quantity, fignifies that the fquare root of that number is required. It likewife (as alfo the character for any other root) ftands for the expreffion of the root of that number or quantity to which it is prefixed. As √36-6, and √108+36=12, or 36|2=6, &c. Prefixed to any number, fignifies that the cube root of that number is required or ex 3 3 preffed. As/216=6, and 513+216 = 9, &c.—or 2166, &ê. ARITHMETICK. A RITHMETICK is the Art or Science of compute ing by numbers, and is comprifed under five prin.. cipal or fundamental Rules, viz. Notation, or Numerations. Addition, Subtraction, Multiplication, and Divifion. NUMERATION Teaches the different value of figures by their different. places, and to read or write any fum or number by these ten characters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. o is called a cypher, and all the reft are called figures or digits./ 2. Befides the fimple value of figures as above noted, they have each a local value, according to the following law; viz. In a combination of figures, reckoning from. right to left, the figure, in the first place, reprefents its primitive fimple value; that in the fecond place, ten. times its fimple value, and fo on; the value of the figure, in each fucceeding place, being ten times the value of it, in that immediately preceding it. 3. The values of the places are estimated according to their order the first is denominated the place of units; the fecond, tens; the third, hundreds; and fo on, as in the Table. Thus, in the number 3467: 7, in the first place, fignifies only feven; 6, in the fecond place, fignifies 6 tens, or fixty; 4, in the third place, four hundred; 3, in the fourth place, three thoufand; and the whole, taken together, is read thus; three thoufand four hundred and fixty feven. 4 A cypher, though of no fignification itself, yet pof feffes a place, and, when fet on the right hand of figures, in whole numbers, increases their value in he fame tenfold proportion; thus, 9 fignifies only nine; but, if a cypher be placed on its right hand, thus, 90, it then becomes ninety. To enumerate any parcel of figures, obferve the fol lowing RULE. First Commit the words at the head of the Table, viz. units, tens, hundreds, &c. to memory; then, to the fimple value of each figure, join the name of its place, beginning at the left hand and reading towards the right. More particularly- Place a dot under the right hand figure of the 20, 4th, 6th, 8th, &c half periods, and the figure over fuch dot will, univerfally, have the name of thoufands.-2. Place the figures 1, 2, 3, 4, &c. as indi. ces, over the 2d, 3d, 4th, &c. period: Thefe indices will then fhow the number of times the millions are involved the figure under 1 bearing the name of millions, that under 2, the name of billions, (or millions of millions) that under 3, trillions, (or millions of millions of mill ions.) EXAMPLE. Sextill. Quintill. Quatrill. Trillions. Billions. Millions. Units. 5 4 3 2 th, un, c.x t.c.x.t. I 913,208;000,341;620,057; 219,35 6; 8$ 9, 379; 1 20,406;129,763, NOTE I. Billions is fubftituted for millions of mill. ions; Trillions, for millions of millions of millions Quatrillions for millions of millions of millions of mill. ions. Quintillions, Sextillions, Septillions, Oftillions, Nonillions, Decillions, Undecillions, Duodecillions, &c. answer to millions fo often involved as their indices refpectively denote. NOTE 2. The right hand figure of each half period has the place of units, of that half period; the middle one,. that of tens, and the left hand one, that of hundreds. |