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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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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...to the base, or 661. Con. 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 XXXI. THEOREM 662. The lateral area of a cone of...
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Plane Geometry: A Complete Course in the Elements of the Science

Edward Brooks - Geometry, Modern - 1901 - 278 pages
...it. We have S=jr.R2 Th. 10. Whence, S = n ( JD) 2 = kn D 2. COR. 2. — The arena of circles are to each other as the squares of their radii or as the squares of their diameters. Let S and R and .S" and R' denote respectively the areas and radii of two circles. Then,...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...to the base, or 661. 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 XXXI. THEOREM 662. The lateral area of a cone of...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 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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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 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 - 1901 - 392 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, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 248 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 - 392 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...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...Or K=nlP. Ax. 8. Again R=% 1> :. K= — —• Ax. 8. 4 452. COR. 2. The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. K _^__^_ £ _ ' "' ~'~~"~* als° '' = 453. The area of a sector is equal to one-half the...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...THEOREM 700* The lateral areas, or the total areas, of tic o similar cylinders of revolution are to each other as the squares of their radii, or as the squares of their altitudes; and their volumes are to each other as the cubes of their radii, or as the cubes of their...
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