less than half of the entire figure, the following geometrical method is given to supply the defect. Let the curve, of which the length is required to be found, be A B C. k B Produce the height line, B d, to meet the centre of the curve, in g. Draw the right line, A g, and from the centre, g, with the distance, g B, describe an arc, Bh, meeting Ag in h. Bisect A h in ¿, and from the centre, g, with the radius, g i, describe the arc ik, meeting d B, produced to k; then ik is half the arc A B C. 6* The following TABLES of Areas and Solidities will be found considerably to diminish the labour of calculation. The numbers in the first column after the names represent the areas or solidities, when the length of the side or edge is 1, or unity; and the numbers in the other columns are multiples of those in the first, by the unit over each. To find, therefore, the area of a Polygon, take the square of the length of the side, and seek in the proper columns the multipliers, which are to be ranged under each other as in common multiplication. The sum of these will be the area required. EXAMPLE. To find the area of a Pentagon, whose side is 18 inches, the multiplier being the square of 18= 324. The same RULE is applicable to Table X., of the Solidities of Regular Bodies, using the cube instead of the square. |