 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...required, by a straight line drawn parallel to a given straight line. PROP. XX. (LXII.) To describe a polygon, similar to a given polygon, and having a given ratio to it. (LXIII.) Any regular polygon, inscribed in a circle, is a mean proportional between the inscribed and... | |
 | Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...and Supp. iv. 5.) the A BHG is the required part of the A ABC. PROP. LXV. 74. PROBLEM. To describe a polygon, similar to a given polygon, and having a given ratio to it. Upon any side of the given polygon describe (E. xlvi. 1.) a square; find (Supp. xxi. 6.) a square which... | |
 | Benjamin Peirce - Geometry - 1869 - 182 pages
...homologous to A or B, is the required polygon. Proof. For, by § 268, the similar polygons constructTo make a Polygon in a given Ratio to similar Polygons....For, by § 268, the similar polygons constructed upon JI and X, have the same ratio to each other as the squares upon A and X. 276. Corollary. In the same... | |
 | Benjamin Peirce - Geometry - 1865 - 184 pages
...B, and X, have the same ratio to each other as the squares upon A, B, and X. 273. Corollary. If Jl and B were the radii of two given c'rcles, X would,...polygon, and having a given ratio to it. Solution. Let Jl be a side of the given polygon. Find, by § 265, the side X of a square which is to the square,... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...to SF will have the same ratio to the square R, as n has to m. QEF PROPOSITION XXIII. PROBLEM. 353. To construct a polygon similar to a given polygon and having a given ratio to it. /^v ~VF\ / XN 4c \ s в— ° \ / m V__ J n A' В' Let R be the given polygon and - the given ratio.... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...QEF R / / \ \ -- /Vs. / / \ \ n Л ',-- ^ Г AB ° CONSTRUCTIONS. PROPOSITION XXIII. PROBLEM. 353. To construct a polygon similar to a given polygon and having a given ratio to it. Let -Й be tie given polygon and - the given ratio. m, It is required to construct a polygon similar... | |
 | George Albert Wentworth - 1884 - 264 pages
...their difference. 198. To construct a square which shall have a given ratio to a given square. 199. To construct a polygon similar to a given polygon, and having a given ratio to it. 200. To construct a triangle equivalent to a given polygon. 201. To construct a square equivalent to... | |
 | Euclides - 1884 - 434 pages
...triangle = a given regular hexagon. 6. Construct a regular hexagon = a given equilateral triangle. 7. Construct a polygon similar to a given polygon, and having a given perimeter. 8. Construct a polygon similar to a given polygon, and having a given ratio to it. 9. Through... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...proportionally). Therefore a2 : a? = m : n. By inversion, 3? : a2 = n : m. PROPOSITION XVIII. PROBLEM. 388. To construct a polygon similar to a given polygon and having a given ratio to it. A. BA! Let R be the given polygon and ~ the given ratio. To construct a polygon similar to R, which... | |
 | George Albert Wentworth - 1889 - 276 pages
...their difference. 198. To construct a square which shall have a given ratio to a given square. 199. To construct a polygon similar to a given polygon, and having a given ratio to it. 200. To construct a triangle equivalent to a given polygon. 201. To construct a square equivalent to... | |
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Problem. To construct a polygon similar to a given polygon, and having a given ratio to it. 
