To find the perpendicular height of that pyramid of which any given frustum is the part, To find the area of the front of a circular arch To find the solidity of the segment of a sphere, 179 To find the convex surface of any segment or 12. To find the solidity of a spheroid, To find the solidity of the segment of a sphe- To find the solidity of the frustum of a parabo- 14. To find the solidity of a parabolic spindle, CHAPTER IN. The Mensuration of Board and Timber. 1. To find multipliers, divisors, and gauge-points, 250. 2. To find the area in gallons, of any rectilineal 3. To find the area of a circle in ale gallons, &c. 4. To find the area of an ellipsis in ale gallons, &c. 5. To find the content of any prism in ale gallons, 6. To find the content of any vessel whose ends are squares, or rectangles of any dimensions, Of the weight and dimensions of Balls and shells. xii EXPLANATION OF THE CHARACTERS MADE USE OF IN THE FOLLOWING WORK. Charact. Names. + :: : Plus, or more Minus, multipli- by equal to Propor tion, m2, m3, signifies the Significations. the sign of addition, as 2+4 signifies that 2 and 4 are to be added together. the sign of subtraction, as 8-3 signifies that 3 is to be subtracted from 8. the sign of multiplication, as 7×5 signifies that 7 is to be multiplied into or by 5. the sign of division, as 9-3 signifies that 9.is to be divided by 3; and or 3-9, signifies, the same. the sign of equality, as 9-9 signifies that 9 is equal to 9. or 5+42=7 signifies that 5 increased by 4 and diminished by 2 is equal to 7 as 2:4:8: 16 signifies that 2 18 to 4 as 8 is to 16. square or cube of the letter m. To signifies the square of the line TS. ✔ɑA signifies the square root of aA, THE COMPLETE MEASURER. PART I. CHAPTER I. NOTATION of DECIMALS. A DECIMAL fraction is an artificial way of setting down and expressing natural, or vulgar fractions, as whole numbers. A decimal fraction has always for its denominator an unit, with a cypher or cyphers annexed to it, and must therefore be either 10, 100, 1000, 10000, &c. and consequently in writing down a decimal fraction there is no necessity for writing down the denominator: as by bare inspection, it is certainly known, consisting of an unit with as many cyphers annexed to it as there are places (or figures) in the numerator. EXAMPLES. The decimal fraction 25 may be written thus, .25, its denominator being known to be an unit with two cyphers; because there are two figures in the numerator. In like manner, 125 may be thus written, .125 thus, .5575; 1 thus, .075; and thus, .0065. 65 3575 10000 B 75 1000 |