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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 areas are to each other as the squares of those sides (Prop. "
A Text-book of Geometry - Page 215
by George Albert Wentworth - 1888 - 386 pages
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Pennsylvania School Journal, Volume 56

Education - 1907 - 656 pages
...according to its reading we would find ourselves doing the impossible. As for example take the theorem, " The perimeters of two regular polygons of the same...and also as the radii of their inscribed circles." The phrase " Of the same number of sides " might be omitted and the untrained pupil would scarcely...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apothems. AMB A' M' B' Given the regular polygons with perimeters p...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...— •— st. 2s ( 193), and are, therefore, equal. .-. ABCDEF ~ GHIKLM. 363 QED 471. COK. 1. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The area of...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...= w~ st. 2s ( 193), n and are, therefore, equal. .-. ABCDEF ~ GHIKLM. 363 0. ED 471. COR. 1. The perimeters of two regular polygons of the same number of sides are to each oiher as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...respectively ; what is the ratio of their perimeters ? of their areas ? PROPOSITION VIII. THEOREM 638. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. E A' F' E' Given regular polygons ABCDE and A'B'C'D'E' having the...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...inches and 72 inches, respectively ; what is the ratio of their areas ? PROPOSITION VIII. THEOREM 538. The perimeters of two regular polygons of the same number of sides are to each otlIer as their radii or as tlIeir apothems. E' Given regular polygons ABCDE and A'B'C'D'S' having...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...sides are proportional. and having the difference of its base and altitude equal to a given line. 4. The perimeters of two regular polygons of the same number of sides are in.the same ratio as the radii of the inscribed or circumscribed circles. 5. To construct a circle...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...the sides of the polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides ; and the areas of two regular polygons of the same number of sides are to...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...tangents drawn at the points of division form a regular polygon circumscribed about the circle. 538. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. 541. I. The perimeter and area of a regular polygon inscribed in...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...the circle into two arcs having the ratio 1:3 (1:5, 2:3, 3 : 7, 7 : 8). PROPOSITION VI. THEOREM 454. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apothems. Given two regular polygons, each having n sides, and with the...
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