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" Since the volume of a cylinder or a prism is equal to the product of the area of the base and the altitude, we conclude that The volume of a cone or a pyramid is equal to one third the product of the area of the base and the altitude. "
A History of Greek Mathematics: From Aristarchus to Diophantus - עמוד 332
מאת Sir Thomas Little Heath - 1921
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Mensuration for elementary and middle class schools

Henry Lewis (M.A.) - 1875 - 104 דפים
...however, it is used to denote an oblique cone (fig. II.), the volume of which is equal to one-third of the product of the area of the base, and the perpendicular height AB. It is evident that the convex surface of a right cone is in the form of a sector of a circle, the...
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Mensuration for beginners [With] Answers

William Dodds - 1883 - 198 דפים
...the prism on the rectangular base. The solidity of the rectangular prism is found by Art. D 142 to be equal to the product of the area of the base and the height. Hence the solidity of the triangular prism will be found by taking half this product. If the...
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An Intermediate Course of Practical Physics

Sir Arthur Schuster, Charles Herbert Lees - 1896 - 272 דפים
...calculated, since a circular area is equal to Trr-2, where r is the radius of the circle. The volume will be equal to the product of the area of the base and the length. Record as follows : Cylinder No. 9. Diameter = 1-59 cms. Area of base = 3-14 x -795 x .795...
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Exercises in Wentworth's Geometry: With Solutions

George Albert Wentworth - 1896 - 296 דפים
...described by the intersection of the diagonals equals tR. By I 650, we have V = *R'H = (RH) (*R). That is, the volume is equal to the product of the area of the generating rectangle by the length of the circumference generated by the point of intersection of its...
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Plane and Solid Geometry

George Albert Wentworth - 1900 - 344 דפים
...described by the intersection of the diagonals equals nR. § 458 V = irR?H = (RH) (*tR). § 700 That is, the volume is equal to the product of the area of the generating rectangle by the length of the circumference generated by the point of intersection of its...
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Ferrell and Sisk's Advanced Arithmetic

John Appley Ferrell, B. F Sisk - 1901 - 436 דפים
...divided by 2, plus the area of the base. RELATION XVIII. Abstractly, the volume of a right pyramid is equal to the product of the area of the base and the altitude, divided by 3. NOTE. — The development of this relation is too difficult to be given before...
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Elementary Algebra and Mensuration: Instruction Paper

American School (Lansing, Ill.) - 1902 - 80 דפים
...113.0976 Total area = 113.0976 + 301.502 = 414.6896 square inches. 276. Volume. The volume of a cone is equal to the product of the area of the base and one-third the altitude. Example. The altitude of a cone is 18 inches and the radius of the base is...
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An Elementary Text-book on the Differential and Integral Calculus

William Holding Echols - 1902 - 536 דפים
...torus generated by the circle (x - a)' + y* = r> (a ^ r) about Oy We hare dy = 2ittria. Observe that the volume is equal to the product of the area of the generating circle into the circumference described by its centre. 2. Show that the volume of the elliptic...
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Mathematics

American School (Chicago, Ill.) - 1903 - 426 דפים
...113.0976 Total area = 113.0976 + '301.592 — 414.6896 square inches. 276. Volume. The volume of a cone is equal to the product of the area of the base and one-third the altitude. Example. The altitude of a cone is 18 inches and the radius of the base is...
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Everyday Arithmetic: Book One-three, ספר 3

Franklin Sherman Hoyt, Harriet E. Peet - 1915 - 378 דפים
...third as much as a prism having the same base and altitude. Since the volume of a cylinder or a prism is equal to the product of the area of the base and the altitude, we conclude that The volume of a cone or a pyramid is equal to one third the product of the...
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