 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 207των George Washington Hull - 1897 - 398 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Adrien Marie Legendre - 1819 - 574 σελίδες
...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of Hie inscribed circles ; and their... | |
 | Adrien Marie Legendre - 1822 - 394 σελίδες
...of the inscribed circle. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons, Juming the same number of sides, are to each other as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; their surfaces are to each other as the squares of... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium.... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; and their... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...Admitting our principle, this proposition is included in that of art. 282. It is there demonstrated, that ' the perimeters of regular polygons of the same number of sides, are as the radii of their inscribed circles ; and their surfaces are as the squares of these same radii.'... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...Admitting our principle, this proposition is included in that of art. 282. It is there demonstrated, that ' the perimeters of regular polygons of the same number of sides, are as the radii of their inscribed circles ; and their surfaces are as the squares of these same radii.'... | |
 | Adrien Marie Legendre - 1828 - 346 σελίδες
...sides proportional ; consequently (102.) they -are similar. 264. Cor. The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces, as the squares of those sides (221.) 265. Scholium. The... | |
 | Timothy Walker - 1829 - 138 σελίδες
...given of a curved line (10) namely, that it is made up of infinitely small straight lines. 95. — The perimeters of regular polygons of the same number of sides are to each other as the radii of their circumscribed circles — . By the perimeter of a polygon we mean the sum of its sides. Then... | |
 | Timothy Walker - 1829 - 156 σελίδες
...(10) namely, 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 we say... | |
 | James Hayward - 1829 - 228 σελίδες
...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)... | |
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