Annuities, or Pensions in Arrears, at Compound Interest Present Worth of Annuities at Compound Interest Annuities in Reversion at Compound Interest B Table of the Measure of Length of the principal places in Europe compared Table directing how to buy and sell by the Hundred Weight Comparison of the American Foot with the Feet of other Countries Table to cast up Wages or expenses for a yr. at so much per day, week, or mo. 405 Table to find Wages, or Expenses for a mo. week or day, at so much per yr. 405 Tables reducing Troy Weight to Avoirdupois, and the contrary 3. To calculate the Moon's Age on any given Day 9. To find the Times of the New and Full Moon, and first and last Qrs. 431 Article 17. Having the Dimensions of any of the parts of a Circle, to find the Side of a Square, equal to the Circle 20. Having the Side of a Square, to find the Diameter of a Circle, which shall be equal to the Square whose side is given 21. Having the Side of a Square, to find the Circumference of a Cir- 22. Having the Diam. of a Circle, to find the Area of a Semicircle 456 23. Having the segment of a circle, to find the length of the Arch Line 456 24. Having the Chord and Versed Sine of a Segment, to find the Di- OF THE CHARACTERS MADE USE OF IN. THIS TREATISE. THE sign of equality: as 12 pence = 1 shilling, signifies that 12 pence arc 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, 12-4-8, 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. X The sign of Multiplication: as 6×5—30, that is, 6 multiplied by 5 is equal to 30. Read 6 into 5 equal to 30. or 5)30( The sign of Division: as 30÷5-6, that is, 30 divided by 5 is equal to 6. Read 30 by 5 equal to 6. 875 25 Numbers placed fractionwise, do likewise denote division, the numerator or upper number being the dividend, and the denominator or lower number, the divisor; thus, is the same as 875-25-35. 875 :::: The sign of proportion, thus, 2: 48: 16, that is, as 2 is to 4 so is 8 to 16. Signifies Geometrical Progression. 9-26 13 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 above (called a Vinculum) connects all the numbers over which it is drawn. 12—3+4=5 Signifies that the sum of 3 and 4 taken from 12 leaves or is equat to 5. Signifies the second power, or Square. Signifies the third power, or Cube. Signifies any power in general, as 63=square of 6; and 50]=cube of 50, &c. thus m signifies either the square or cube, or any other power. √, or Prefixed to any number or quantity, signifies that the square root of that number is required. It likewise (as also the character for any other Toot) stands for the expression of the root of that number or quantity to which it is prefixed. As √36=6, and √✓108+36=12, and 36]=6, &c. 3 3 3 , or 13 Prefixed to any number, signifies that the cube root of that number is required, or expressed. As 216=6, and √513+216=9, &c. or 216 6, &e. Signifies any root in general. As 36 square root, 2163-cube n root, &c. Thus, signifies either the square root, cube root, or any oth foot whatever. m abed When several letters are set together, they are supposed to be multi plied into each other; as those in the margin are the same as axbxcxd, and represent the continual product of quantities or numbers. If a be the root, then a×a=aa or a2 is the square of a, and axaxaαaz or a3 is the cube of a, &c. Note The figure above is called the index of the power. It is usual to write shillings at the left hand of a stroke, and pence at the ight; thus, 13/4 is thirteen shillings and four pence. Note. The use of these characters must be perfectly understood by the pu pil, as he may have occasion for them. A NEW AND COMPLETE SYSTEM OF ARITHMETICK. A RITHMETICK is the Art or Science of computing by numbers, 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 1. 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; &+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. The value of figures when alone, is called their simple value, and is invariable. Besides the simple value, they have a local value, that is, a value which varies according to the place they stand Thefe frures or digits were obtained from the Arabians, and were introduced into Europe in the ninth century. The Arabs probably derived the decimal notation from India. The fexagefimal division had previously been in general ufe in Europe. This mode of divifion is yet retained in a few cafes, as in the divifion of time, where fixty minutes make an hour, fixty seconds a minute, &c. The figures are doubtless called digits from digitus, a finger, because counting fed to be performed on the fingers. ( ་ |