 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...a cone of revolution, and R is the radius of the base, 674. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, or of their radii ; and their volumes are to each other as the cubes of their altitudes, or of their radii.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...similar right triangles about homologous sides. 959. COR. III. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii of their... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Therelore H. QE 966. COR. I. If the base of the cone is a circle of radius /?, 967. COR. II. The volumes of two similar cones of revolution are to each other as the cubes of their altitudes, or as tlic cubes of the radii of their bases. If int. — The method of proof... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...850. COR. III. The lateral areas, or the total areas, of two similar cylinders of revolution arc to each other as the squares of their altitudes, or as the squares of their radii. S 2wKff KHHH in A" OUTLINE PROOF: -= - ~ = ~x , =T x T = TT =-T' s 2irrA rhhh &• r1... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...the radius of the base. PROPOSITION X. THEOREM. 630. The lateral areas, and also the entire areas, of two similar cones of revolution are to each other as the squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii of their... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...V=$B x HQED 966, COR. I. If the base of the cone is a circle of radius R, 967. COR. II. The volumes of two similar cones of revolution are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. Hint. — The method of proof... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...proposition. Can you make an arithmetical formula for this proposition ? EXERCISES. 498. The lateral areas of two similar cones of revolution are to each other as the squares of their slant height, or the squares of their altitudes, or the squares of the radii of their bases.... | |
 | William James Milne - Geometry - 1899 - 396 pages
...their bases? Theorem. The lateral areas, or the total areas, of similar cones of recolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. Data : Any two similar cones of revolution, whose altitudes are H and H', slant heights L and L', and... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...III. THEOREM. 646. The lateral or total areas of two similar cylinders of revolution (§ 550) are to each other as the squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii... | |
 | Webster Wells - Geometry - 1899 - 196 pages
...III. THEOREM. 646. The lateral or total areas of two similar cylinders of revolution (§ 550) are to each other as the squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii... | |
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The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes... 
