 | William Chauvenet - Geometry - 1871 - 380 pages
...Also the similar sectors AOB and A'O'B' are like parts of the circles to which they belong. Therefore, similar arcs are to each other as their radii, and...sectors are to each other as the squares of their radii. 40. Corollary III. The ratio of the circumference of a circle to its diameter is constant ; that is,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...the similar sectors AOB and A' O'B' are like parts of the circles to which they belong. Therefore, similar arcs are to each other as their radii, and similar sectors are to each otiier as the squares of their radii. 40. Corollary III. The ratio of the circumference of a circle... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...the polygons become equal to the ureas of the circles, and we shall have A : a : : R" : r\ Cor. 1. Similar arcs are to each other as their radii ; and similar sectors are as the squares of their radii. For since the arcs AB, ab are . timilar, the angle C is equal to the... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...Also the similar sectors AOB and A'O'B' are like parts of the circles to which they belong. Therefore, similar arcs are to each other as their radii, and...sectors are to each other as the squares of their radii. 40. Corollary III. The ratio of the circumference of a circle to its diameter is constant ; that is,... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...second ratio of the second proportion by 4, or 2 squared, we have A : A' ::4jR2 THEOREM XXXI. 241. Similar arcs are to each other as their radii; and...sectors are to each other as the squares of their radii. Let AB, DE be similar arcs ; ACB, DOE, similar sectors ; and denote the radii CA and OD by R and r... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...of the circumferences to which they belong, and similar sectors, as A GH and I? OE, are like parts of the circles to which they belong : hence, similar...proposed to make the number of sides of the polygons infinite, by the method indicated in the scholium of Proposition X., it is simply meant to express... | |
 | Charles Davies - 1874 - 464 pages
...sectors, as ACB and DOE, are like parts of the circles to which they belong : hence, similar arc« are to each other as their radii, and similar sectors...as the squares of their radii. Scholium. The term inf1nite, used in the proposition, is to be understood in its technical sense. When it is proposed... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...ratio of the second proportion by 4, or 2 squared, we have A : A : : 4 R 2 : 4 r 2 . THEOREM XXXI. 241. Similar arcs are to each other as their radii; and...sectors are to each other as the squares of their radii. Let AB, DE be similar arcs; ACB, DOE, similar sectors; and denote the radii CA and OD by R and ;•;... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...sectors AOB and A'O'B' are like parts of the circles to which they belong. Therefore, similar ares are to each other as their radii, and similar sectors are to each other as the squares of their radii. 40. Corollary III. The ratio of the circumference of a circle to its diameter is constant ; that is,... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...circumferences. Similar sectors, as ABC, DEF, are also like parts of their respective circles. Therefore similar arcs are to each other as their radii, and similar sectors as the squares of their radii. THEOREM XVI. 40. The area of a circle is equal to half the product of... | |
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DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as... 
