 The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.  Elements of Geometry - Σελίδα 76των Adrien Marie Legendre - 1819 - 208 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | William James Milne - 1899 - 258 σελίδες
...regular polygon is equal to one half the product of its perimeter by its apothem. 390. Cor. II. Regular polygons of the same number of sides are to each other as the squares upon their radii and also as the squares upon their apothems. §§ 386, 345 Ex. 645. The... | |
 | George Albert Wentworth - 1900 - 344 σελίδες
...equivalent to the sum of the three given octagons. Let x be the side of the regular octagon required. Two regular polygons of the same number of sides are to each other as the squares of their sides. § 446 .-. y? = O2 + 72 + 82. Ex. 381 .-. x = Ve2 + 72 + 82 = V36 + 49... | |
 | Thomas Franklin Holgate - 1901 - 462 σελίδες
...circles; that is, as the radii of the polygons, or as the apothems of the polygons. 351. COROLLARY II. The perimeters of two regular polygons of the same number of sides are in the same ratio as their radii, or as their apothems. Let Si and 83 be the lengths of the sides in... | |
 | Arthur Schultze - 1901 - 260 σελίδες
...OD: O'D'= AO: A'O'. (W h y?) But P: P' = AB: A'B' = AD: A'D'. (Why ?) 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1902 - 394 σελίδες
...= OD : O'D' = AO: A'O'. (Why ?) But P:P' = AB:A'B' = AD:A'D'. (Why?) 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. « Ex. 948. The lines joining the midpoints of the radii of... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1901 - 394 σελίδες
...= AO: A'O'. But P:P' = AB:A'B' = AD:A'D'. (398) (Why?) (Why?) (Why?) 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1901 - 396 σελίδες
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P:P'=OD: O'D' = AO : A'O'. QED 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a... | |
 | 1902 - 762 σελίδες
...from three given points and from a given straight line. When is it impossible to do so ? Q. Prove that the perimeters of two regular polygons of the same number of sides are to one another as the radii of their circumscribing circles. Prove that in a given circle the perimeter... | |
 | John Alton Avery - 1903 - 136 σελίδες
...to any vertex of a regular polygon bisects the angle at the vertex. 143. The perimeters of regular polygons of the same number of sides are to each other as any two homologous sides. 144. Find the area of a square inscribed in a circle whose radius is 6. 145.... | |
 | Fletcher Durell - 1904 - 382 σελίδες
...homologous sides proportional. Hence K and K' are similar. Art. 321. QED PROPOSITION VI. THEOKEM 434. I. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their areas... | |
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