| Robert Louis Short - 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... | |
| Clara Avis Hart, Daniel D. Feldman - Mathematics - 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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