The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their... Plane and Solid Geometry - Page 312by Arthur Schultze, Frank Louis Sevenoak - 1901 - 370 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 - 592 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 - 592 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, Plane - 1864 - 276 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 - 420 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 - 368 pages
...12) H h R_H+ R r therefore, 8 t h + r ' R H_IP r ' h ~ h* T t R) 2w(A + R r H+R h + r IT h* That is, **the lateral areas, or the total areas, of similar...cylinders of revolution are to each other as the squares** of their altitudes, or as the squares of the radii of their bases. PROPOSITION III.— PROBLEM. 12.... | |
| William Chauvenet - Geometry - 1872 - 368 pages
...(III. 12) R). H h therefore, S I T t ~ R) r ~h+r' RH=H^ r ' h ~ A2 : ^R H+R ~ rh + r R IP A' That is, **the lateral areas, or the total areas, of similar...cylinders of revolution are to each other as the squares** of their altitudes, or as the squares of the radii of their bases. PROPOSITION III.— PROBLEM. 12.... | |
| Edward Olney - Geometry - 1872 - 239 pages
...truth of the theorem is demonstrated. FIG. 382. PROPOSITION XT. 498. Theorem, — The convex surfaces **of similar cylinders of revolution are to each other as the squares** of their altitudes, and as the squares of the radii of their bases. DEM.— Let H and h be the altitudes,... | |
| Edward Olney - Geometry - 1872
...truth of the theorem is demonstrated. FIQ. 80Z. PROPOSITION XV. 498. Theorem. — The convex surfaces **of similar cylinders of revolution are to each other as the squares** of their altitudes, and as the squares of the radii of their bases. DEM. — Let H and h be the altitudes,... | |
| David Munn - 1873
...It follows, therefore, that the lateral surfaces, or the total surfaces of similar cylinders, are to **each other as the squares of their radii, or as the squares of their** heights. Cor. 2. — If h = r, that is, if the height be equal to the radius of the base, the lateral... | |
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