| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two **circles are to each other as their radii, and their...areas are to each other as the squares of their radii.** Corollary I. The circumferences of circles are to each other as their diameters, and their areas are... | |
| James Morton - Mathematics - 1887 - 236 pages
...GB is 16 yards, and the square of BF is 9 yards, and the sum of their squares is 25 yards. GEOMETRY. **The circumferences of circles are to each other as their radii, and** the areas are to each other as the squares of their radii. The circumferences of circles are to each... | |
| Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...two lines, and the point of intersection of the perpendiculars will be the center of the circle. 26. **The circumferences of circles are to each other as their radii, and their areas are to each other** aa the squares of their radii. EXAMPLES. If the circumference of a circle is 62-83 in. and its radius... | |
| Yale University - 1892 - 200 pages
...given straight line to construct a polygon similar to a given polygon ? 6. The circumferences of two **circles are to each other as their radii, and their...areas are to each other as the squares of their radii.** II. — SOLID AND SPHERICAL GEOMETRY. 7. If a straight line and a plane are parallel, the intersection... | |
| William Chauvenet - 1893 - 340 pages
...the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two **circles are to each other as their radii, and their...areas are to each other as the squares of their radii.** Corollary I. The circumferences of circles are to each other as their diameters, and their areas are... | |
| Mathematics - 1898 - 228 pages
...following: — 6. Two triangles are similar when they are mutually equiangular. 7. The circumferences of two **circles are to each other as their radii and their areas are** as the squares of their radii.] JUNE 1887. (The candidate may omit any two propositions.) 1. To inscribe... | |
| Yale University - 1898 - 212 pages
...following: — 6. Two triangles are similar when they are mutually equiangular. 7. The circumferences of two **circles are to each other as their radii and their areas are** as the squares of their radii.] JUNE 1887. (The candidate may omit any two propositions.) 1. To inscribe... | |
| William Robert Martin - Nautical astronomy - 1899 - 474 pages
...of latitude. 1 Described in Norwood's Seaman's Practice, 1637. Then since by a property of geometry **the circumferences of circles are to each other as their radii, and** the same is true of equivalent arcs of those circles, it follows that — u V : AB :: ou : CA : : o... | |
| Edward Brooks - Geometry, Modern - 1901 - 278 pages
...by the hypothetical introduction of the infinite into the statement." PROPOSITION VII. — THEOREM. **The circumferences of circles are to each other as...areas are to each other as the squares of their radii.** To Prove. — Then we are to prove that Circ. OA : Circ. ffM ::R:R, Circle OA : Circle ffM : : I? :... | |
| William Chauvenet - 1905 - 336 pages
...the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two **circles are to each other as their radii, and their...areas are to each other as the squares of their radii.** Corollary I. The circumferences of circles are to each other as their diameters, and their areas are... | |
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