 | Rutgers University. College of Agriculture - 1893 - 680 pages
...any two homologous sides. 5. The area of a circle is equal to r. times the square on its radius. 6. Similar segments are to each other as the squares of their radii. (103) ALGEBRA. (Time, two hours.) TV .. 14x' — lx , 2z — 1 1. Divide — -= --- „ by „ - .... | |
 | John Macnie - Geometry - 1895 - 390 pages
...circle is twice that of another. What is the ratio of their radii ? 211 PROPOSITION XI. THEOREM. 405. Similar segments are to each other as the squares of their radii. o' Given : OA = R, O'A' = R', radii of similar segments B, B' ; To Prove : B : B' = R* : R'\ Since... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...of their respective circles, are to each other as the squares of their radii. 428. The areas of two similar segments are to each other as the squares of their radii. PROBLEMS OF CONSTRUCTION. 429. To inscribe a square in a given circle. 430. Cor. By bisecting the arcs... | |
 | Joe Garner Estill - 1896 - 214 pages
...A parallelogram is divided by its diagonals into four triangles of equal area. 7. The areas of two similar segments are to each other as the squares of their radii. 8. The diameter of a circle is 5 feet ; find the side of the inscribed square. 9. Find a side of the... | |
 | Joe Garner Estill - 1896 - 186 pages
...A parallelogram is divided by its diagonals into four triangles of equal area. 7. The areas of two similar segments are to each other as the squares of their radii. 8. The diameter of a circle is 5 feet ; find the side of the inscribed square. 9. Find a side of the... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...sectors are to each other as the squares of their radii. PROPOSITION XII. THEOREM. 466. The areas of two similar segments are to each other as the squares of their radii. Let AC and A'C' be the radii of the two similar sectors ACB and A'C'B', and let ABP and A'B'P' be the... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...whose ratio to a given circle shall equal the ratio of two given lines. Proposition 216. Theorem. 253. Similar segments are to each other as the squares of their radii. Consult Prop. 215, Cor., Prop. 177, and §§95 and 98. Ex. 655. The area of a circumscribed square... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...sectors are to each other as the squares of their radii. PROPOSITION XII. THEOREM. 466. The areas of two similar segments are to each other as the squares of their radii. Let AC and A'C' be the radii of the two similar sectors ACB and A'C'B', and let ABP and AfBT?' be the... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...Similar sectors are to each other as the squares of their radii. [§§ 776 and 788.] 790. COROLLARY V. Similar segments are to each other as the squares of their radii. 791. EXERCISE. The circumferences of two circles are 942.48 ft. and 157.08 ft. respectively. The diameter... | |
 | Arthur Schultze - 1901 - 260 pages
...diameter is the perpendicular CD, D being in the largest semicircle. A PROPOSITION XVII. THEOREM 426. Similar segments are to each other as the squares of their radii. Hyp. S and S' are two similar segments, having the radii R and R' respectively. To prove S:S' = R 2... | |
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Theorem. Similar sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'&B ' (ng. 136) are, by the same reasoning as in § 97, the same parts of their respective circles, which the angle O= O... 
