| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...their homologous sides proportional ; 'consequently they are einrilai (Book IV. Def. 1.). • . _' J **Cor. The perimeters of two regular polygons of the...surfaces are to each other as the squares of those** sidei (Book IV. Prop. XXVII.). Scholium. The angle of a regular polygon, like the angle ot an equiangular... | |
| Adrien Marie Legendre - Geometry - 1837 - 372 pages
...question have their angles equal, and their homologous sides proportional ; consequently they are similai **(Book IV. Def. 1.). Cor. The perimeters of two regular...other as the squares of those sides (Book IV. Prop.** XXVIL). Scholium. The angle of a regular polygon, like the angle ot an equiangular polygon, is determined... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...214, 215, 216, 217, 218, 219, 220, 221, and 228. , , 232. Theorem. The homologous sides of regular **polygons of the same number of sides are to each other as** the radii of their circumscribed circles, -and also as the radii of their inscribed circles. Demonstration.... | |
| Adrien Marie Legendre - Geometry - 1838 - 386 pages
...are equal, and likewise the sides ab, be, cd, &c. (Def.) ; it is plain that AB : ab : : BC : be : : **CD : cd, &c. ; hence the two figures in question have...the squares of those sides (Book IV. Prop. XXVII.).** Scholium. The angle of a regular polygon, like the angle of an equiangular polygon, is determined by... | |
| Adrien Marie Legendre - Geometry - 1839 - 372 pages
...the angles C and c, &c. are equal. Again, since the polygons are regular, the sides AB, BC, CD, &c. **are equal, and likewise the sides ab, bc, cd, &c....the squares of those sides (Book IV. Prop. XXVII.).** Scholium. The angle of a regular polygon, like the angle of an equiangular polygon, is detennined by... | |
| Adrien Marie Legendre - Geometry - 1841 - 235 pages
...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... | |
| Geometry - 1843 - 404 pages
...the angles C and c, &c. are equal. Again, since the polygons are regular, the sides AB, BC, CD, &c. **are equal, and likewise the sides ab, bc, cd, &c....XXVII.). PROPOSITION II. THEOREM. Any regular polygon may** be inscribed in a circle, and circumscribed about one. Let ABCDE &c. be a regular polygon : describe... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...area of a circle is equal to its circumference multiplied by half its radius.* PROP. VII. THEOREM. **The perimeters of two regular polygons of the same number of sides, are to each other as** the radii of the circumscribed circles : and their areas are to each other, as the squares of those... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...each other as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; **and their surfaces are to each other as the squares of those** radii. Let AB he a side of one of the polygons, O the centre, and conse- a— quently OA the radius... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...; consequently they are similar (B. FV, Def. 3). Cor. The perimeters of two regular polygons having **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 (B. IV, Prop. xvi). (84.) It has been shown (... | |
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