EXPLANATION OF CHARACTERS THERE are various characters or marks used in arithmetical computations, to denote several of the operations and propositions, the chief of which are as follows: Equal to. The sign of equality; as 100 cents=$1, signifies that 100 cents are equal to one dollar. Minus, or Less. The sign of subtraction; as 8—2=6; that is, 8, less 2, is equal to 6. + Plus, or More. The sign of addition; as 4+5=9; that is, 4, added to 5, is equal to 9. × Multiplied by. The sign of multiplication; as 6×6=36; that is, 6, multiplied by 6, is equal to 36. Divided by. The sign of division; as 12÷3=4; that is, 12, divided by 3, is equal to 4. : is to :: so is to } The signs of proportion; as 2:4:8:16; that is, as 2 is to 4, so is 8 to 16. 7-2+5=10. Shows that the difference between 7 and 2, added to 5, is equal to 10. 2 added to a number, signifies that the number is to be squared; thus: 62, means that 6 is to be multiplied by 6. * added to a number, signifies that the number is to be cubed; thus: 5=5x5x5=125. The index, or power, is the number of times a number is to be multiplied by itself, and is shown by a small figure placed at the right of the number to be raised, and a little elevated. The bar signifies that all the numbers under it are to be taken together; as 7+4-3=8; or, 5×6+4=50. The parenthesis () is sometimes used in place of the bar. A decimal point signifies, when prefixed to a number, that the number has a unit (1) for its denominator; as 1 is; 125 is 125, &c. A, A', A", A"", signifies A, A prime, A seconds, A thirds, &c. ✓ Prefixed to any number signifies that the square root of that number is required; as √9=3; or thus, √52—32=4, signifies that 3 squared, taken from 5 squared, and the square root extracted, =4. 3 ✓ Prefixed to any number signifies that the cube root of that num 3 ber is required; as √64=4. NOTE. The degree of temperature used in this treatise is Fahrenheit, which fixes upon 32° for the freezing point, and 212° for the boiling point. = 1 yard. 40 rods or 220 yds. = 1 furlong. 5 yards or 16 ft. = 1 rod or pole. | 60 geo. miles }=1 mile. = 1 degree. = 1 mile. = 1 geographical degree. NOTE. 69.121 miles 1 nautical mile 3 miles 20 leagues 360 degrees the earth's circumference. Bowditch gives 6120 feet in a sea mile, which, if taken as the length, will make the divisions 51 feet and 5 1-10 feet for the knot and fathom. NOTE. The Standard Yard of the State of New York is a brass rod, which bears to a pendulum beating seconds in vacuo, in Columbia College, the relation of 1.000.000 to 1.086.141, at a temperature of 32° Fahrenheit; that of the English is 629. EXPLANATION OF CHARACTERS Equal to. The sign of equality; as 100 cents=$1, signifies that 100 cents are equal to one dollar. Minus, or Less. The sign of subtraction; as 8-2-6; that is, 8, less 2, is equal to 6. + Plus, or More. The sign of addition; as 4+5=9; that is, 4, added to 5, is equal to 9. × Multiplied by. The sign of multiplication; as 6×6=36; that is, 6, multiplied by 6, is equal to 36. - Divided by. The sign of division; as 12÷3=4; that is, 12, divided by 3, is equal to 4. : is to :: so is to The signs of proportion; as 2:4::8:16; that is, as 2 is to 4, so is 8 to 16. 7-2+5=10. Shows that the difference between 7 and 2, added to 5, is equal to 10. 2 added to a number, signifies that the number is to be squared; thus: 62, means that 6 is to be multiplied by 6. added to a number, signifies that the number is to be cubed; thus: 5=5×5×5=125. The index, or power, is the number of times a number is to be multiplied by itself, and is shown by a small figure placed at the right of the number to be raised, and a little elevated. The bar signifies that all the numbers under it are to be taken together; as 7+4-3=8; or, 5×6+4=50. The parenthesis () is sometimes used in place of the bar. A decimal point signifies, when prefixed to a number, that the number has a unit (1) for its denominator; as 1 is; 125 10001 &c. is 125 10 A, A', A", A", signifies A, A prime, A seconds, A thirds, &c. ✓ Prefixed to any number signifies that the square root of that num 3 ber is required; as √9=3; or thus, √52-32=4, signifies that 3 squared, taken from 5 squared, and the square root extracted, =4. ✓ Prefixed to any number signifies that the cube root of that num 3 ber is required; as √64=4. |