 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'*  Solid Geometry - Page 383by Charles Austin Hobbs - 1921 - 192 pagesFull view - About this book
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...3. The area of a circle is - multiplied bv the square of the radius. Hence, any two circles are to each other as the squares of their radii, or as the squares of their diameters, or generally as the squares of any two homologous lines. 4. The area of a circle is less... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...again subdivided into varieties, &c. For ' surface, , - 4;rr3 = The surfaces of two spheres are to each other as the squares of their radii, or as the squares as spherical angle, spherical triangle, spherical polygon, &c. SPHERICAL ANGLE. An angle included of... | |
 | Charles Davies, William Guy Peck - Mathematics - 1859 - 622 pages
...spherical angle, spherical triangle, spheri- . The sur?jccs of two spheres are to each other ea' polygon, as the squares of their radii, or as the squares of their diamctcre ; or in general, as the squares of any two homologous lines that can be drawn in the sphere.... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...the ratio of the circumference to the diameter. 9O1. Corollary. — 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 a. 503. Theorem —... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...the ratio of the circumference to the diameter. 501. Corollary. — 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 —... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...nR(L + R). 25. Corollary II. Hence, by the same process as was employed in (11), we can prove that the lateral areas, or the total areas, of similar...cones of revolution are to each other as the squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii of their... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...-R(L + R). 25. Corollary II. Hence, by the same process as was employed in (11), we can prove that the lateral areas, or the total areas, of similar...cones of revolution are to each other as the squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii of their... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the ratio of the circumference to the diameter. 501. Corollary — 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 TT. <3©3. Theorem... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...px A' are the areas of the lateral surfaces. PROPOSITION X. 529. TJieorem. — The convex surfaces of similar cones of revolution are to each other as the squares of their slant heights, the radii of their bases, and their altitudes ; ie, as the squares of any two... | |
 | Edward Olney - 1872 - 270 pages
...$ p x h' are the areas of the lateral surfaces. PROPOSITION X. 520. Theorem.—The convex surfaces of similar cones of revolution are to each other as the squares of their slant heights, the radii of their bases, and their altitudes ; ie, as the squares of any two... | |
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