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" 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. "
Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ... - Σελίδα 274
των Eli Todd Tappan - 1868 - 420 σελίδες
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 138 σελίδες
...the same, they are as their bases. If the bases are the same, they are as their altitudes. 164. — The surfaces of two spheres are to each other as the squares of their radii, and the solidities are as the cubes of thtir radii — . 1. Let S be the surface of...

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

Charles Davies, William Guy Peck - 1855 - 628 σελίδες
...the following formulas for the are 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...

The discovered laws of the sizes and rotations of the sun and planets

Robert Linton - 1858 - 54 σελίδες
...Define then the laws of the sphere, and their application to distance. Definition 1st. The surfaces of spheres are to each other as the squares of their diameters, and therefore their diameters are to each other as the square root of their surfaces. Definition 2nd. The...

Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1864 - 288 σελίδες
...the same ratios as in other similar solids. These principles may be demonstrated as follows : 806. Theorem The areas of the surfaces of two spheres are...For the superficial area of any sphere is equal to i: times the diameter multiplied by the diameter (786) ; that is ~D2. But TT is a certain or constant...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 380 σελίδες
...Corollary II. Let S and S' be the surfaces of two spheres whose radii are R and R ' ; then, R2 hence, the surfaces of two spheres are to each other as the squares of their diameters, or as the squares of their radii. ./v PROPOSITION XII.— LEMMA. 44. If a triangle revolves about an...

Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - 1873 - 288 σελίδες
...the same ratios as in other similar solids. These principles may be demonstrated as follows : SO6. Theorem The areas of the surfaces of two spheres are to each of her as the squares of their diameters ; and their volumes arc as the cubes of their diameters, or...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1875 - 390 σελίδες
...surfaces of two spheres whose radii are R and R ' ; then, S ^ 4xR' _ (2.R)2 _IP_t ~ ~ ~ R"' hence, the surfaces of two spheres are to each other as the squares of their diameters, or as the squares of their radii. PROPOSITION XII— LEMMA. 44. If a triangle revolves about an axis...

Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - 1878 - 236 σελίδες
...equal to four times the area of one of its great circles. BOOK VIII.] MEASUREMENT OF SOLIDS. COR. 3. The surfaces of two spheres are to each other as the squares of their radii. COR. 4. If a right cylinder be circumscribed about a sphere whose radius is R, then...

Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 σελίδες
...the sphere is equal to^ the area of the circle whose radius is the diameter of the sphere. COR. 3. The surfaces of two spheres are to each other as the squares of their radii or the squares of their diameters, or as the squares of the circumferences of their...

The Heavens Above: A Popular Handbook of Astronomy

Joseph Anthony Gillet - 1882 - 496 σελίδες
...distance through its centre. The radius of a sphere is the distance from the surface to the centre. The surfaces of two spheres are to each other as the squares of their radii or diameters ; and the volumes of two spheres are to each other as the cubes of their...




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