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Books Books 91 - 100 of 155 on The areas of two circles are to each other as the squares of their radii ; or, as....  
" The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary When the radius is unity, the area is expressed by ;r. 503. Theorem The area of a sector is measured by half the product... "
Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ... - Page 92
by Charles Davies, William Guy Peck - 1865 - 592 pages
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Secondary-school Mathematics, Book 2

Robert Louis Short, William Harris Elson - Mathematics - 1911
...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 and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 488 pages
...The area of a circle is equal to ir if. HINT. A'=JC. .R = %.2irB.R = irR2. 563. Cor. II. The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. 564. Cor. HI. The area of a sector whose angle is a is #. (See 551.) Ex. 1008. Find the area of...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 332 pages
...The area of a circle is equal to TT times the square of the radius. 495. COROLLARY 2. The areas of two circles are to each other as the squares of their radii or of their diameters. Discussion. Why is the circumscribed polygon used in the above theorem, while the...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 332 pages
...The area of a circle is equal to 'rr times the square of the radius. 495. COROLLARY 2. The areas of two circles are to each other as the squares of their radii or of their diameters. Discussion. Why is the circumscribed polygon used in the above theorem, while the...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 376 pages
...bisector extended to the opposite side an isosceles triangle is formed. 433. THEOREM. The areas of two circles are to each other as the squares of their radii. (412) Prove this theorem in a manner like that of 432. 434. A second proof of 432. SUG. 1....
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 321 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 of two circles...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 457 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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Schultze and Sevenoak's Plane and solid geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 457 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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Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 107 pages
...circle is equal to it times the square of its radius, that is, A = irr2. 217. Corollary 2. The areas of two circles are to each other as the squares of their radii. 220. Problem 1. Given the side and radius of a regular inscribed polygon, to find the side of a regular...
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Plane and Solid Geometry

George Wentworth, George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 470 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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