| William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...to each other as the squares of their radii. M' M 499. COK. 6. The areas of similar segments are to **each other as the squares of their radii or as the squares of their** chords. For let S and S' denote the areas of the similar As AOB and A'O'B', and K and K' the areas... | |
| Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...O'A' O'F' (§ 435). 539. Cor. The areas of two regular polygons of the same number of sides are to **each other as the squares of their radii or as the squares of their** apothems. Ex. 998. Two regular hexagons are inscribed in circles whose radii are 7 inches and 8 inches,... | |
| Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...From step 2, § oon BC R Then, K R2 K' Or, the areas of two similar polygons are in the same ratio **as the squares of their radii, or as the squares of their** apothems. THEOREM LXXVIII 284. The area of a regular polygon is equal to one half the product of its... | |
| William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...product of its circumference and its radius. That is, But C = 466. The areas of two circles are to **each other as the squares of their radii, or as the squares of their** diameters. S TrR2 R* If1' = ~R^ = "cT* = -D'*' 467. A sector of a circle is the figure formed by two... | |
| William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...product of its circumference and its radius. C = 2 7TR. That is, But 466. The areas of two circles are to **each other as the squares of their radii, or as the squares of their** diameters. v' TrP ''* /? '^ 7}^ For 467. A sector of a circle is the figure formed by two radii and... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...to the base, or 683. COR. 2. Sections made by planes parallel to the bases of a circular cone are to **each other as the squares of their radii, or as the squares of their** distances from the vertex of the cone. PROPOSITION XXX. THEOREM 684. The lateral area of a cone of... | |
| Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...7rr2 is the area of a great circle. 380. Corollary 3. The areas of the surfaces of two spheres are to **each other as the squares of their radii; or, as the squares of their** diameters. 381. Zones. A zone is a portion of the surface of a sphere bounded by the circumferences... | |
| Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...irr2 is the area of a great circle. 380. Corollary 3. The areas of the surfaces of two spheres are to **each other as the squares of their radii; or, as the squares of their** diameters. 381. Zones. A zone is a portion of the surface of a sphere bounded by the circumferences... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...total areas, of two similar cones of revolution are to each other as the squares of their altitudes, **as the squares of their radii, or as the squares of their** slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of... | |
| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...total areas, of two similar cones of revolution are to each other as the squares of their altitudes, **as the squares of their radii, or as the squares of their** slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of... | |
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