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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 211
by George Albert Wentworth - 1888 - 386 pages

Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...angles equal and their homologous 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....

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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...

Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...angles equal and their homologous 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....

Elements of Geometry...: Translated from the French for the Use of the ...

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 number of sides are to each other as their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium....

Elements of Geometry and Trigonometry: With Notes

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 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...

Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 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 we say that the perimeter ABCDEF (fig....

Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 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)...

First lessons in Plane Geometry. Together with an application of them to the ...

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...