To find an Ordinate of a Parabola, . To find an Abscissa of a Parabola,. To find the Area of a Hyperbola, DEFINITIONS OF THE SIGNS USED IN THE FOLLOWING WORK. = 1 lb. 20. Equal to. The sign of equality; as 16 oz. - 3. = 96. 8, or 8 12, shows that the less number is to be subtracted from the greater, and the difference, or remainder, only, is to be used; so, too, heights breadth, shows that the difference between the height. and breadth is to be taken. ::: Proportion; as 2: 4 :: 3:6; that is, as 2 is to 4, so is 3 to 6. Sign of the square root; prefixed to any number indicates that the square root of that number is to be taken, or employed; as No64 = 8. Sign of the cube root; and indicates that the cube root of the number to which it is prefixed is to be employed, instead of the number itself; as 3/64: = 4. 2 To be squared, or the square of; shows that the square of the number to which it is affixed is the quantity to be employed; as 122 ÷ 6 = = 24; that is, that the square of 12, or 1446 = 24. 3 Indicates that the cube of the number to which it is subjoined is to to be used; as 43 = 64. 42 2 Decimal point, or separatrix. See DECIMAL FRACTIONS. Vinculum. Signifies that the two or more quantities over which it is drawn, are to be taken collectively, or as forming one quantity; thus, 4+6 X 4 = 40; whereas, without the vinculum, 4+6 X 4 = 28; also, 12 − 2 × 3 +4=2; and 52-32 4. So, also, ✔ (52 — 32 ) = 4, and (4+6) × 4 = 40. half of 42 or half of the square of 4 2 (*)*(the square of half the square of 4) = 64. 162 or (b)2 (half the square of b.) (36)2 (the square of half b.) (26)2 (the square of twice b.) SECTION I. MONEYS, WEIGHTS AND MEASURES. THOSE OF THE UNITED STATES AND OF OTHER GOVERNTHEIR DENOMINATIONS, VALUES, COMPARATIVE MENTS VALUES, MAGNITUDES, &C. MONEYS OF ACCOUNT OF THE UNITED STATES. These are the mill, the cent, the dime, and the dollar. = = 1 dime, 10 dimes 10 mills = 1 cent, 10 cents 1 1 dollar. The dollar is the unit or ultimate money of account of the United States, or of what is sometimes called Federal money. In practice, the dime, as a denomination of value, is rejected. Thus, = 1 dollar. 10 mills 1 cent, and 100 cents This mark, $, is equivalent to the word dollar, or dollars, in this money. COINS OF THE UNITED STATES. Until June, 1834, the government of the United States estimated gold in comparison with silver as 15 to 1, and in comparison with copper as 850 to 1. From June, 1834, until February, 1853, the same government estimated gold in comparison with silver as 16 to 1, and in comparison with copper as 720 to 1. For all time since February, 1853, this government has estimated gold in comparison with silver as 143 to Ï, and in comparison with copper as 720 to 1. The standard for mint gold with this government until 1834, was 11 parts pure gold and 1 part alloy, the alloy to consist of silver and copper mixed, not exceeding one half copper. The gold coins, therefore, struck at the United States mint prior to 1834, are 22 carats fine. |