Mensuration and Practical Geometry: Containing Tables of Weights and Measures, Vulgar and Decimal Fractions, Mensuration of Areas, Lines, Surfaces, and Solids ... to Which Is Appended a Treatise on the Carpenter's Slide-Rule and Gauging
Mensuration and Practical Geometry: Containing Tables of Weights and Measures, Vulgar and Decimal Fractions, Mensuration of Areas, Lines, Surfaces, and Solids ... to Which Is Appended a Treatise on the Carpenter's Slide-Rule and Gauging
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. 1863 Excerpt: ...646.3842 inches. Centre of Gravity. It is at a distance from the base of (R]r)2+2R2 the smaller end=i height X-z--T=--=-; K and r radii of (R+r)2--Kr J the greater and less ends. Pyramid. Definition. A figure, the base of which has three or more sides, and the sides of which are plane triangles. Note.--The volume of a ...
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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. 1863 Excerpt: ...646.3842 inches. Centre of Gravity. It is at a distance from the base of (R]r)2+2R2 the smaller end=i height X-z--T=--=-; K and r radii of (R+r)2--Kr J the greater and less ends. Pyramid. Definition. A figure, the base of which has three or more sides, and the sides of which are plane triangles. Note.--The volume of a pyramid is equal to one third of that of a prism having equal bases and altitude. To ascertain the Contents of a Pyramid, Fig. 90. Rule.--Multiply the area of the base by the perpendicular height, and one third of the product will be the contents required. Or, = L Example.--What are the contents of a hexagonal pyramid, a b c, Fig. 90, a side, a b, being 40 feet, and its height, c e, 60 feet? 40-x2.5981 (tabular multiplier, p. 60)=4156.96=areo of base. 4156.96X60, ., ., -=83139.2=one tiard of the area of the oasexthe height= the contents required. Ex. 2. The height of a quadrangular pyramid is 67 feet, and the width of its base is 16.5 feet; what are its contents in cubic feet? Ans. 6080.25. Ex. 3. What are the contents of a pentagonal pyramid, its height being 12 feet, and each of its sides 2 feet? Ans. 27.528 feet. Centre of Gravity. It is at a distance from the base of the line joining the vertex and centre of gravity of the base. To ascertain the Contents of the Frustrum of a Pyramid, Fig. 91. Rule.--Add together the squares of the sides of the greater and less ends and the product of these two sides; multiply the sum by the tabular multiplier for areas in Table, p. 60, and this product by the height; then, divide the last product by three, and the quotient will give the contents required. Or, (s2+s'2+sxS')xiab. mult. X =S, s and s' representing o the lengths of the...
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