A Course of Mathematics; Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying - Adapted to the Method of Instructi (Paperback)

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. 1853 edition. Excerpt: ...plane. This method may serve to verify the calculations which are made by the rules in arts. 50 and 51. Ex. If one end of the frustum CDGL (Fig. 17.) be 90 feet square, the other end 60 feet square, and the height RN 36 feet; what is the height of the whole pyramid VCD: and what are the solidity and lateral surface of the frustum DP=DN--GR=45--30=15. And, GP=RN-36. Then, 15: 36:: 45: 108=VN, the height of the whole pyramid. And, 108--36=72=VR, the height of the part VLG. The solidity of the large pyramid is 291600 (Art. 48.) of the small pyramid 86400 of the frustum CDGL 2(15200 The lateral surface of the large pyramid is 21060 (Art. 49.) of the small pyramid 9360 of the frustum 11700 PROBLEM VII. To find the Solidity of a Wedge. 54. Add The Length Of The Edge To Twice The Length Of The Base, And Multiply The Sum Bv J Of The Product Of The Height Of The Wedge And The Breadth Of The Base. Let L=AB the length of the base. (Fig. 20.) /=GH the length of the edge. 6= BC the breadth of the base. A=PG the height of the wedge. Then, L--l=AB--GH=AM. If the length of the base and the edge be equal, as BM and GH, (Fig. 20.) the wedge MBHG is half a parallelopiped of the same base and height. And the solidity (Art. 43.) is equal to half the product of the height, into the length and breadth of the base; that is to I bhl. If the length of the base be greater than that of the edge, as ABGH; let a section be made by the plane GMN, parallel to HBC. This will divide the whole wedge into two parts MBHG and AMG. The latter is a pyramid, whose solidity (Art. 48.) is iMx(L--I) The solidity of the parts together, is, therefore, i bhl+l bh x(L--/)-bh3l+6A2L--bh 2l=ibhx(2L+l) If the length of the base be less than that of the edge, it is evident that the pyramid..