Mensuration, Plane and Solid

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1857 Excerpt: ...9 yds. 6 ft. 12 in. 8. Isosceles A. Side 5 ft. 5 in.; base 8 ft. 8 in.; height 16f ft. Ana. 8 yds. 19 ft. 1548 in. 9. Scalene A. Sides 5 ft. 9 in., 7 ft. 8 in., 9 ft. 7 in.; height 15 yds. Ana. 38 yds. 20 ft. 1692 in. 10. Trapezium. Diagonal 13 yds.; 2 J.S 29$ and 36$ft.; height 23f yds. Ana. 3396 yds. 2 ft. 36 in. 11. Trapezium. Diagonal 2 c. 48 Iks.; 2 is 13 c. 70Iks. and 9 c. 60 Iks.; height 22 yds. Ana. 28 c. 892000 Iks. 12. Trapezoid. 2 //s 26J and 19J yds.,-J. 62 yds.; height 13Jp. Ana. 105880J yds. 13. Trapezoid. 2;/s 23 and 17 in.; 1 4 ft. 8 in.; height 13 ft. 6 in. Ana. 15 ft. 14. Diamond. 2 diagonals 11 and 9 ft.; height 3J p. Ana. 1052 yds. 15. Diamond. Diagonal 4 ft. 8 in.; side 2 ft. 11 in.; height 7J yds. Ana. 6 yds. 21ft. 1296 in. 16. Hexagon. Side 4 ft. 9 in.; height 8 yds. 1 ft. Ana. 54 yds. 7 ft. 810 in. 17. Hexagon. Bisecting diagonal 3 ft. 2 in.; height 5 ft. 5 in. Ana. 1 yd. 8 ft. 483$in. Case I. When the edge or thin end E F equals A B or c D, the depth of the back, the wedge is a triangular prism, dBF THE PYRAMID AND CONE. 1. The Pyramid may stand on a base of any figure. Its sides or walls taper off gradually until they meet in a point at the vertex or summit, and thus form a series of triangular faces, all equal when the base is a regular polygon. 2. The pyramid thus loses both length and breadth at the summit, i. e. 2 out of its 3 dimensions: and the student may hence keep in mind the fact that " the solidity of any pyra mid is just-.', that of a prism having the same base and altitude." (Euclid, xn. 7. 10.) 3. This is an important fact to remember, and may be thus practically illustrated: Take a cube or square prism of cork, clay, or other convenient substance. Draw a line joining the centres of two opposite edges of any...