 | Ignace Gaston Pardies - Geometry - 1734 - 192 pages
...been faid of Circles in the fourth Book. Wherefore all fimilar Figures, &c. COROLLARY I. •• I. Circles are to each other as the Squares of their Radii or Diameters .- forfuppofe a Circle whbfe Radius is r, and then another Circle greater/ or"'lfefs;' than... | |
 | William Hawney - Geometry - 1820 - 336 pages
...SA*xAB; ---- x -- = -- xAB, 3 5 )5 the sum of all the series of squares, ma", nc*, py2, Sfe. But as circles are to each other as the squares of their radii or diameters ; it evidently follows that -^ SA1 x.7854xAB will he the solidity of one-fourth of the spindle... | |
 | 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 radii... | |
 | James Stewart Eaton - Arithmetic - 1857 - 376 pages
...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... | |
 | Horatio Nelson Robinson - Arithmetic - 1859 - 348 pages
...a right-angled triangle is equal to the sum of the squares of the other two sides. 2d. The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. 1. The two sides of a right-angled triangle are 3 and 4 feet ; what is... | |
 | John Daniel Runkle - Mathematics - 1860 - 460 pages
...radius CK, describe a circle ; then, as is easily seen, (1) CA* : CK* =2:1. But since the areas of two circles are to each other as the squares of their radii, it follows from (1) that the area of the circle CK is half the circle C A. In precisely the same way... | |
 | Horatio Nelson Robinson - Arithmetic - 1860 - 444 pages
...this class relating to circles, may be solved by means of the following property : — The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. NOTE. — This property of the circle is only a particular case of a... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...radius multiplied by 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 — The area... | |
 | James Stewart Eaton - Arithmetic - 1868 - 356 pages
...if the area is divided by .785398, the quotient will be the square of the diameter. 10. The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. 376. Of an equilateral triangle? Of the perpendicular drawn from the... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...radius multiplied by 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 — The area... | |
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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 — The area of a sector is measured by half the product... 
