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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 312
by Arthur Schultze, Frank Louis Sevenoak - 1901 - 370 pages

## 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...

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

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...

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

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....

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

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 —...

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

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 —...

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

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....

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

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....

## A Treatise on Special, Or Elementary Geometry

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,...