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" 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'* "
Mensuration of lines, surfaces, and volumes - Page 40
by David Munn - 1873
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Elements of Plane Geometry

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...
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Plane Geometry

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,...
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Secondary-school Mathematics, Book 2

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...
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Plane Geometry

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...
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Plane Geometry

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...
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Schultze and Sevenoak's Plane and Solid Geometry

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...
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Solid Geometry

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...
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Plane and Solid Geometry

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...
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Schultze and Sevenoak's Plane and Solid Geometry

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...
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Plane and Solid Geometry

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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