Denoting the perpendicular by P, the base by b, and the diedral angle by A, we have Formula (3), Art. 37, Trig., Pb tan A; but is the apothem of one face; if, therefore, we denote the number of sides in that face by n, and the length of each side by 8, we shall have (Art. 101, Mens.), The volumes of all hence, the volume may be computed. the regular polyedrons have been computed on the supposition that their edges are each equal to 1, and the results are given in the following From the principles demonstrated in Book VII., we may write the following RULE. To find the volume of any regular polyedron, multiply the cube of its edge by the corresponding tabular volume; the product will be the volume required. EXAMPLES. 1. What is the volume of a tetraedron, whose edge is 15? Ans. 397.75. 2. What is the volume of a hexaedron, whose edge is 12? Ans. 1728. 8. What is the volume of a octaedron, whose edge is 20? Ans. 3771.236. 4. What is the volume of a dodecaedron, whose edge is 25 ? Ans. 119736.2328. 5. What is the volume of an icosaedron, whose edge is 20? Ans. 17453.56. REMARK. In the following table, in the nine right hand columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the U's, to catch the eye, and to indicate that from thence the two figures of the Logarithm to be taken from the second column, stand in the next line below. 132 120574 0903 1231 1560 1888 2216 2544 2871 3198 3525 328 133 3852 4178 8076 135130334 0655 0977 1298 3539 3858 7753 8399 8722 1619 4177 4496 4814 5133 137 6721 7037 138 9879194 7354 7671 7987 8303 4504 4830 5156 5481 5806 6131 6456 9045 9368 9690 12 323 1939 2260 2580 2900 3219 321 5451 5769 6086 6403 318 8934 9249 9564 315 ⚫508 •822 1136 1450 1763 2076 2389 2702 314 6781 325 8618 139 143015 3327 3639 3951| 4263| 4574 4885 5196 5507 5818 311 211 215 216 217 213 210 322219 2426 2633 2839 3046 3252 3458 3665 3871 8855 9054 9253 9451 98058 3649 3850 4051 5458 5658 5859 6059 7459 7659 7858 8058 8257 200 9650 9849 47 •246 199 1237 1435 1632 1830 2028 2225 198 |