| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...angles equal and their homologous sides proportional ; therefore they are similar (162). 264. Corollary. **The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are** as the squares of these sides (221). 265. Scholium. The angle of a regular polygon is deteruiined by... | |
| Adrien Marie Legendre - Geometry - 1825 - 280 pages
...angles equal and their homologous sides proportional ; therefore they are similar (162). 264. Corollary. **The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are** as the squares of these sides (221). 265. Scholium. The angle of a regular polygon is determined by... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...angles equal and their homologous sides proportional ; therefore they are similar (162). 264. Corollary. **The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are** as the squares of these sides (221). 265. Scholium. The angle of a regular polygon is determined by... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...angles equal, and their homologous sides proportional ; consequently (102.) they -are similar. 264. **Cor. The perimeters of two regular polygons of the...other as their homologous sides, and their surfaces,** as the squares of those sides (221.) 265. Scholium. The angle of a regular polygon, like the angle... | |
| James Hayward - Geometry - 1829 - 172 pages
...circumscribed circles; and ON, on, are radii of the inscribed circles. We therefore say—The areas of regular **polygons of the same number of sides, are to each other as** the squares of the radii of the circumscribed circles, and also of the inscribed circles. (on)* 0 (boc)... | |
| Timothy Walker - Geometry - 1829 - 158 pages
...that it is made up of infinitely small straight lines. 95. THEOREM. — The pe.rime.le.rs of regular **polygons of the. same number of sides are to each other as** the radii of their circumscribed circles. By th^orimeter of a polygon we mean the sum of its sides;^Snen... | |
| Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...perimeter of that figure. The above proportion may therefore be expressed in shorter terms; namely, **the perimeters of two regular polygons of the same number of sides, are to each other** in the proportion of the radii of the inscribed or circumscribed circles. 2. The areas of two regular... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 190 pages
...perimeter of that figure. The above proportion may therefore be expressed in shorter terms ; namely, **the perimeters of two regular polygons of the same number of sides, are to each other** in the proportion of the radii of the inscribed or circumscribed circles. 2. Tlie areas of two regular... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 206 pages
...each other in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas **of two regular polygons of the same number of sides, are to each other as** the areas of the squares constructed upon the radii of the inscribed or circumscribed circles. 36.... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 190 pages
...Two regular polygons of the same number of sides are similar figures. 34. The sums of all the sides **of two regular polygons of the same number of sides, are to each other** in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular... | |
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