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Books Books 71 - 80 of 156 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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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 440 pages
...apothems. 351. (6) The areas of two regular polygons of the same number of sides are in the same ratio as the squares of their radii, or as the squares of their apothems. 352. (7) The area of a regular polygon is equal to half the product of its perimeter and...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 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

George Albert Wentworth - Geometry, Solid - 1902 - 218 pages
...the area of the surface of a sphere. 823 825. COR. 2. The areas of the surfaces of two spheres are as the squares of their radii, or as the squares of their diameters. Let R and R' denote the radii, D and I)' the diameters, and S and S" the areas of the surfaces of...
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Solid Geometry

George Albert Wentworth - Geometry, Solid - 1902 - 218 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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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 384 pages
...circumference of a great circle of the sphere. 1187. COROLLARY III. The surfaces of spheres are to each other as the squares of their radii, or as the squares of their diameters. QED SOLID GEOMETRY 1189. EXERCISE. Find the radius of a sphere if the area of its trirectangular triangle...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 372 pages
...quantities by the method of Exhaustions. By the use of these he obtained such theorems as that the areas of two circles are to each other as the squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 B. 0.) we first find the formula for the...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 206 pages
...quantities by the method of Exhaustions. By the use of these he obtained such theorems as that the areas of two circles are to each other as the squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the...
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PLANE AND SOLID GEOMETRY

FLETCHER DURELL. PH.D. - 1911
...quantities by the method of Exhaustions. By the nse of these he obtained such theorems as that the areas of two circles are to each other as the squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 473 pages
...COR. 2. The area of a circle is equal to TT times the square of its radius. 464. COR. 3. The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R' the radii, 465. COR. 4. Similar arcs are to each other...
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School Science and Mathematics, Volume 12

Science - 1912
...revolution. Proposition 15. The lateral areas, or total areas, of similar cylinders of revolution are to each other as the squares of their radii, or as the squares of their altitudes. Definition. Pyramidal surface. Pyramidal space. Edges. Faces. Vertex. Transverse section....
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