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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 41
by David Munn - 1873
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

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...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

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...
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Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1859 - 624 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....
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

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 —...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 438 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 —...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

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. <33. Theorem...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...circumferences of two circles are to each other as their radii, or as their diameters, and their areas are to each other as the squares of their radii, or as the squares of their diameters. Cor. 2. Because similar sectors and similar segments are like parts of the circles to which...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...Circumferences of circles are to each other as their radii, or as their diameters ; and the circles as the squares of their radii, or as the squares of their diameters. For circles are regular polygons of an infinite number of sides (44) ; and if the circumferences...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 pages
...their circumferences or of their diameters. For circles are similar figures. (2) Either the lateral or the total surfaces of similar cylinders are to each other as the squares ot tlieir radii or of their heights. Similar cylinders have their heights proportional to their radii....
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The Southern Review, Volumes 10-11

Albert Taylor Bledsoe, Sophia M'Ilvaine Bledsoe Herrick - Reconstruction (U.S. history, 1865-1877) - 1872 - 496 pages
...2' + 31 + 4' + . . . . + n' = 2n' + 3n'+n. "ireU known form, etc. 1. -. O. But these elements are to each other as the squares of their radii, or as the squares of their distances from the vertex of the cone. If, then, B denote the base of the cone, H its height, b any...
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