 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...greater nor less than the rectangle P, it must necessarily be equivalent to it. PROPOSITION XII. THEOREM. Circles are to each other as the squares of their radii. Let the circles ABCD, abed, be compared, we shall have the proportion AO" : ao* :: circ. ABCD : circ. abed.... | |
 | Timothy Walker - Geometry - 1829 - 138 pages
...-^T«jo similar polygons are to each other as the squares of their homologous sides — . r 2. — Two circles are to each other as the squares of their radii or diameters — . <t 3. — The surfaces of two spheres are to each other as the squares of their... | |
 | Charles Davies - Geometrical drawing - 1840 - 264 pages
...ABD. 33. The areas of circles are to each other as the squares described on their diameters : that is, the areas of two circles are to each other as the squares described on the diametres AB and CD. 39. If from any point of the circumference of a circle, a line... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...will also be equal to the two other similar figures formed upon the other sides. 962. PROP. LXXXIII. Circles are to each other as the squares of their radii. Let two circles DCB, deb (fig. 317.) be drawn. The surface contained within the circumference DCB is to... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...nor less than the rectangle P, it must necessarily be equivalent to it. PHOPOS1TION XIII. THEOREM. Circles are to each other as the squares of their radii. .Let the circles ABCD, abed, be compared : we shall have the proportion AO" : ao' : : circle ABCD : circle... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...greater nor less than the rectangle P, it must necessarily be equivalent toil. PROPOSITION XII. THEOREM. Circles are to each other as the squares of their radii. Let the circles ABCD, abed, be compared : we shall have the proportion AO' : ao' : : circle ABCD : circle... | |
 | James Elliot - 1852 - 106 pages
...whole circle of which EGF forms a part, and c, that of the circle forming the base of the cone. Since the circumferences of two circles are to each other as their radii, C:c::CB:ED, and £ C:1<;::CB:AB. But C: arc EGF :: 360° : Z ECF (Euc. vi, 33). .-. £ C-:£arcEGF::90°:ZECG.... | |
 | George Salmon - Conic sections - 1855 - 376 pages
...indefinitely near lines of equal length are at right angles to the line joining their extremities. Ex. 2. The circumferences of two circles are to each other as their radii. If polygons of the same number of sides be inscribed in the circles, it is evident, by similar triangles,... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...or as their radii. 3. The area of a circle is IT multiplied by 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... | |
 | James Stewart Eaton - Arithmetic - 1857 - 376 pages
...conversely, if the area is divided by .785398, the quotient will be the square of the diameter. 5. The areas of two circles are to each other as the squares of their radii, diameters or circumferences. FIG. 12. 6. The square described on the hypothenuse of a right-angled... | |
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The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R 
