 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 - Σελίδα 312των Arthur Schultze, Frank Louis Sevenoak - 1901 - 370 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Charles Davies, William Guy Peck - 1855 - 592 σελίδες
...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 - 1855 - 628 σελίδες
...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 - 1859 - 622 σελίδες
...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 - 1864 - 288 σελίδες
...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 - 1868 - 444 σελίδες
...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 - 1871 - 380 σελίδες
...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 - 1872 - 382 σελίδες
...(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.... | |
 | Eli Todd Tappan - 1873 - 288 σελίδες
...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 - 1872 - 472 σελίδες
...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 - 1872 - 562 σελίδες
...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,... | |
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