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" The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (Book IV. "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 109
by Charles Davies - 1849 - 359 pages
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...equal. 4. This is obvious from 3. 5. By definition of similar polygons. 420 535. Theorem. The perimeter of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Given the regular polygons AB • • • and A'B • • • of the same...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...equal. . 4. This is obvious from 3. 5. By definition of similar polygons. 534. Corollary. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. 535. Theorem. The perimeter of two regular polygons of the same number...
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Plane Geometry: Experiment, Classification, Discovery, Application ...

Clarence Addison Willis - Geometry, Modern - 1922 - 320 pages
...of a regular hexagon whose apothem is 34.64? THE SECOND STEP IN CLASSIFICATION 336. Theorem I. — The perimeters of two regular polygons of the same number of sides are proportional to the radii of the polygons. Hypothesis. — Regular polygons 0 and 0', of the same number...
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Plane Geometry: Experiment, Classification, Discovery, Application ...

Clarence Addison Willis - Geometry, Modern - 1922 - 318 pages
...a regular hexagon whose apothem is 34.64? THE SECOND STEP IN CLASSIFICATION 336. Theorem I.-—The perimeters of two regular polygons of the same number of sides are proportional to the radii of the polygons. Hypothesis.—Regular polygons 0 and 0', of the same number...
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The Reorganization of Mathematics in Secondary Education: A Report of the ...

National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...external segment. 21. Parallelograms or triangles of equal bases and equal altitudes are equal. 22. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apothems. Solid Geometry In the following list the precise wording and the...
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Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...Post. 1 §§ 278, 224 § 271, Post. 9 §134,1 §213 §205 §210 §205 Ax. 5 281. Corollary. The areas of two regular polygons of the same number of sides are to each other as the squares on the radii of the circumscribed circles, and also as the squares on the radii of the...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P:P'— OD : O'D' = AO:A'o'. QED 417. 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. 1315. The lines joining the mid-points of the radii of...
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The Teaching of Mathematics in the Elementary and the Secondary School

Jacob William Albert Young - Mathematics - 1924 - 484 pages
...external segment. 21. Parallelograms or triangles of equal bases and equal altitudes are equal. 22. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apot hems, Notes." I. The list I is typical, not exhaustive. 2. Concerning...
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A Geometry Reader

Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...Group 91 283. Prop. V. Two regular polygons of the same number of sides are similar. 285. Prop. VII. The perimeters of two regular polygons of the same number of sides are to each other as their apothems or their radii. 284. Prop. VI. An equilateral polygon inscribed in a circle. 286. Prop. VIII....
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...the same number of sides are similar. 7. Two circles arc to each other as their radii. a. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides, or as the squares of their radii. b. The areas of two circles arc to each...
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