 | Elias Loomis - Conic sections - 1849 - 252 pages
...each other as the rectangles of the sides which contain the equal angles. PROPOSITION XXIV. THEOREM. Similar triangles are to each other as the squares described on their homologous sides. Let ABC, DBF be two simi- A lar triangles, having the angle A equal to D, the angle B equal to E, and C equal... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...also shows the length of the radius of the inscribed circle. Now, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk. IV. Th. xx), we have I2 : tabular area : : any side squared : area. Hence, to find the area of... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...also shows the length of the radius of the inscribed circle. Now, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk. IV. Th. xx), we have 1 : tabular area : : any side squared : area. Hence, to find the area of... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...Consequently (B. n., p. 4, c.), ;2 ADC : DEF :: AC : DF. Therefore, the similar triangles BAC, EDF, are to each other as the squares described on their homologous sides A Cf DF, or as the squares described on any other two homologous sides. PROPOSITION XXVI. THEOEEM.... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...polygons, they may be divided into an equal number of similar triangles. THEOREM XX1. Similar polygons arc to each other as the squares described on their homologous sides. Let ABODE and FGNIK, be two similar polygons ; then will they be to each other as the squares described... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...antecedent ABC, is to its consequent FGH (B. n., p. 10), or as AB is to FG (P. 25) ; hence, similar polygons are to each other as the squares described on their homologous sides. Cor. If three similar figures are described on the three sides of a right•angled triangle, the figure... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...also shows the length of the radius of the inscribed circleNow, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk- IV Th- xx), we have I2 : tabular area : : any side squared : areaHence, to find the area of a... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...each other as tne rectangles of the sides which contain the equal angles. PROPOSITION XXIV. THEOREM. Similar triangles are to each other as the squares...similar triangles, having the angle A equal to D, the angle B equal to E, and C equal to F ; then the triangle ABC is to the triangle DEF as the square... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...n., p. 2), BA : DA : AE : AC: consequently, DC and BE are parallel (p. 16). PROPOSITION XXV. THEOEEM. Similar triangles are to each other as the squares...two similar triangles, having the angle A equal to Z>, and the angle B=E: then will the triangle BAC be to the triangle EDF, as a% square described on... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...angles. PROPOSITION XXIV. THEOREM. Similar triangles are to each other as the squares described in their homologous sides. Let ABC, DEF be two similar triangles, having the angle A equal to D, the angle B equal to E, and C equal to F ; then the triangle ABC is to the triangle DEF as the square... | |
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Two similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E. 
