A Complete System of Mensuration, with Additions by J. Trotter
General Books LLC, 2013 - 66 pages
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1851 edition. Excerpt: ...height CF of the hoof 120, and the height or versed sine of its base CE 10 inches. Required the content of the hoot B Ans. 10-i-50 =-200versine, of which the tabular area is-111823, then-111823 x 50-= 279-5575 circular segment, and (40 x 10) x 2 = 40thechord. Now (40J-=-12)--(279-5575 x (10--25) x 12 = 5333-33333--4193-3625 x 12 = 1139-97083 x 12 = 13679-65 cubic inches the content. 2. Suppose the versed sine of the base to be 40, the rest as before. Required the content. Here the chord is 40, the base 1683-9359. Ans. 917771875 cu. in. 3. Suppose the cutting plane to pass through the centre, the rest as before. Required the content. Ans. 50000 cubic inches. 4. Suppose the diameter of the cylinder 48, the versed sine of the hoof 30, and its height 36 inches. Required the content. Ans. 18604-98 cubic inches. 5. Suppose the diameter of the cylinder 36, the height of the hoof 42, and its versed sine 12 inches. Required the content. Ans. 5167-07117 cubic inches. Prob. III. To find the content of the hoof of the frustum of a cone. Case I. When the cutting plane passes through the extremities of the two bases. Rule. Take the square root of the product of the diameters at the base and the top of the hoof, and multiply it by the diameter at the top, then take the difference between this product and the square of the diameter of the base, and divide it by the difference of the diameters: the quotient, multiplied by the diameter of the base, by the height, and by-2618, will give the content. 1. Suppose the diameter of the base of the hoof to be 30, and the diameter of the frustum at the top of the hoof to be 19-2, and the height 18 inches. Required the content. Ans. /(19-2 x 30) x 19-2 = 24 x 19-2 =460-8, and 302--460-8-t(30--19-2) =...
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