or 6)30( { 875 25 :::: 9—2+6=13 OF IN THIS TREATISE. THE sign of equality: as 12 pence = 1 shilling, signifies that 12 pence are equal to one shilling; and, in general, that whatever precedes it is equal to what follows. The sign 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 sign of Subtraction: as, 12-48, that is, 12 lessened by 4 is equal to 8, or 4 from 12 and 8 remains. Read 12 minus 4, or 12 less 4 equal to 8. The sign of Multiplication: As 6x5 = 30, that is, 6 multiplied by 5 is equal to 30. Read 6 into 5 equal to 30. The sign of Division: as, 30-56, that is, 30 divided by 5 is equal to 6. Read 30 by 5 equal to 6. Numbers placed fractionwise, do likewise denote division, the numerator or upper number being the dividend, and the denominator or lower number, the di875 visor; thus, {is, 12—3+5=4 { 25 is the same as 875÷25 = 35. The sign of proportion, thus, 2 : 48: 16, that as 2 is to 4 so is 8 to 16. Signifies Geometrical Progression. Shews that the difference between 2 and 9 added to 6 is equal to 13. Read 9 minus 2 plus 6 equal to 13. And that the line atop (called a Vinculum) connects all the numbers over which it is drawn. Signifies that the sum of 3 and 5 taken from 12 leaves or is equal to 4. Signifies the second power or Square. Signifies the third power, or Cube. Signifies any power in general, as 6] = square of 6; and 50 cube of 50, &c. thus m signifies either the square or cube, or any other power. = It Prefixed to any number or quantity, signifies that the square root of that number is required. likewise (as also the character for any other root) stands for the expression 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. 3 ✔, or Prefixed to any number, signifies that the cube root of that number is required, or expressed. 9, &c.-or 3 3 As √ 216 = 6, and 513+216 = Signifies any root in general. As 361⁄2 = square n , or root, 216 cube root, &c. Thus, — signifies either abcd = m the square root, cube root, or any other root whatever. When several letters are set together, they are supposed to be multiplied into each other; as those in the margin are the same as axbxcxd, and represent the _continual product of quantities or numbers. { Is the reciprocal of a, and is the reciprocal of -. If a be the root, then axa of a, and axaxa = aaa or a3 Note. The figure atop is power. - It is usual to write shillings at the left hand of a stroke, and pence at the right; thus, 13/4 is thirteen shillings and four pence. Note. The use of these characters must be perfectly understood by the pupil, as he may have occasion for them. A NEW AND COMPLETE SYSTEM OF ARITHMETICK. RITHMETICK is the Art or Science of computing by num bers, and consists both in Theory and Practice. The Theory considers the nature and quality of numbers, and demonstrates the reason of practical operations. The Practice is that, which shews the method of working by numbers, so as to be most useful and expeditious for business, and is comprised under five principal or fundamental Rules, viz. NOTATION OF NUMERATION, ADDITION, SUBTRACTION, MULTIPLICATION, and DIVISION; the knowledge of which is so necessary, that, scarcely any thing in life, and nothing in trade, can be done without it. NUMERATION TEACHES the different value of figures by their different places, and to read or write any sum or number by these ten characters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.-0 is called a cypher, and all the rest are called figures or digits. The names and significations of these characters, and the origin or generation of the numbers they stand for, are as follow; 0 nothing; 1 one, or a single thing called an unit; 1+1=2, two; 2+1=3, three; 3+1-4, four; 4+1=5, five; 5+1=6, six; 6+1=7, seven; 7+1=8, eight; 8+1=9, nine; 9+1=10, ten; which has no single character; and thus, by the continual addition of one, all numbers are generated. 2. Beside the simple 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 represents its primitive simple value; that in the second place, ten times its simple value, and so on; the value of the figure, in each succeeding place, being ten times the value of it, in that immediately preceding it. 3. The 3. The values of the places are estimated according to their order: The first is denominated the place of units; the second, tens; the third, hundreds; and so on, as in the table. Thus in the number5293467: 7, in the first place signifies only seven; 6, in the second place, signifies 6 tens, or sixty; 4, in the third place, four hundred ; 8, in the fourth place, three thousand; 9, in the fifth place, ninety thousand; 2, in the sixth place, two hundred thousand; 5, in the seventh place, is five millions; and the whole, taken together, is read thus; five millions, two hundred and ninety three thousand, four hundred and sixty seven. 4. A cypher, though it is of no signification, itself, yet, it possesses a place, and, when set on the right hand of figures, in whole numbers, increases their value in the same tenfold proportion; thus, 9 signifies only nine; but if a cypher is placed on its right hand, thus, 90, it then becomes ninety; and, if two cyphers be placed on its right, thus, 900, it is nine hundred; &c. To enumerate any parcel of figures, observe the following Rule. First, commit the words at the head of the table, viz. units, tens, hundreds, &c. to memory, then, to the simple value of each figure, join the name of its place, beginning at the left hand, and reading towards the right.-More particularly-1. Place a dot under the right hand figure of the 2d, 4th, 6th, Sth, &c. haif periods, and the figure over such dot will, universally, have the name of thousands.2. Place the figures, 1, 2, 3, 4, &c, as indices over the 2d, 3d, 4th, &c. period. These indices will then shew 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 millions.) EXAMPLE. Sextillions. Quintilli. Quatrill. Trillions. Billions. Millions. Units. 913,208;000,341;620,057;219,356;809,379;120,406;129,763 THE NOTE 1. Billions is substituted for millions of millions: Trillions, for millions of millions of millions: Quatrillions, for millions of millions of millions of millions. Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, &c. answer to millions so often involved as their indices respectively 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. Fifteen. THE APPLICATION. Write down, in proper figures, the following numbers. Two hundred and seventy nine. Three thousand four hundred and three. 15 279 3403 37567 Thirty seven thousand, five hundred and fixty-seven. Nine millions, seventy two thousand and two hundred. 8 Write down in words at length the following numbers. 401028 9072200 55309009 800044055 2543431702 7584397647 49163189186 500098400700 II. Two. III. Three. IV. Four. V. Five. VI. Six. VII. Seven. XI. Eleven. XII. Twelve. XVII. Seventeen. LX. Sixty. LXX. Seventy. XIII. Thirteen. XC. Ninety. XIV. Fourteen. C. Hundred. CC. Two hundred. A less literal number placed after a greater, always augments the value of the greater; if put before, it diminishes it. Thus, VI. is 6; IV. is 4; X1. is 11; IX. is 9, &c. ADDITION IS the putting together of two or more numbers, or sums, to make them one total, or whole sum. SIMPLE ADDITION Is the adding of several integers or whole numbers together, which are all of one kind, or sort; as 7 pounds, 12 pounds, and 20 pounds, being added together, their aggregate, or sum total, is 39 pounds. RULE. |