EXPLANATION OF THE PRINCIPAL MATHEMATICAL CHARACTERS. The sign or character = (called equality) denotes that the respective quantities between which it is placed are equal; as 4 poles 22 yards 100 links. 1 chain The sign + (called plus, or more) signifies that the numbers between which it is placed are to be added together; as 9 + 6 (read 9 plus 6) = 15. Geometrical lines are generally represented by capital letters; thus AB + CD signifies that the line CD is to be added to the line AB. The sign (called minus, or less) denotes that the quantity which it precedes is to be subtracted; as 15 6 (read 15 minus 6) = 9. In geometrical lines also, AB CD signifies that the line CD is to be subtracted from the line AB. The sign × denotes that the numbers between which it is placed are to be multiplied together; as 5 × 3 (read 5 multiplied by 3) 15. = The sign signifies division; as 15 ÷ 3 (read 15 divided by 3) 5. Numbers placed like a vulgar fraction also denote division; the upper number being the dividend, and the lower the divisor; as 15 = 5. :: The signs (called proportionals) denote proportionality; as 25 615, signifying that the number 2 bears the same proportion to 5, as 6 does to 15; or, in other words, as 2 is to 5, so is 6 to 15. The sign, placed above a quantity, represents the square of that quantity; as 5 + 32 = = The sign, placed above a quantity, denotes the cube of that quantity; as 9 + 3 82 8x8 = 64. 831 12 √ 36 = 6. = The sign √or, placed before a quantity, denotes the square root of that quantity; as √9 × 4 The sign, placed before a quantity, represents the cube root of that quantity; as 6 × 4 × 3 8 = 24 x 3 81 DIRECTIONS TO BOOKBINDER. Plans VIII., IX., X., XI., XIII., and Earthwork Tables at the end of the work, in the order thus given: Fold Plans VIII. and IX. to face each other when open. LAND-SURVEYING. PART I. DEFINITIONS, PROBLEMS, AND THEOREMS IN GEOMETRY. GEOMETRY originally signified the art of MEASURING the EARTH, or any distance or dimensions upon, or within it; but it is now used for the science of quantity, extension, or magnitude. GEOMETRICAL DEFINITIONS. 1. A point is considered as having neither length, breadth, nor thickness. 2. A line has length, but is considered as having A neither breadth nor thick ness; as AB. 3. Lines are either right, curved, or parallel. 4. A right or straight line lies wholly in the same direction between its extremities, and is the shortest distance between two points; as AB. 5. A curved line continually changes its direction between its extremities; as AB. 6. Parallel lines always remain at the same distance from each other, and, though continually produced, would never meet; as AB and CD. B B B B |