 | Webster Wells - Geometry - 1899 - 450 pages
...altitude. Find each of its dimensions. (Let x represent the altitude.) PROP. IX. THEOREM. 322. Two similar polygons are to each other as the squares of their homologous sides. B' Given AB and A'B' homologous sides of similar polygons AC and AC', whose areas are /iTand K', respectively.... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...altitude. Find each of its dimensions. (Let z represent the altitude.) PROP. IX. THEOREM. 322. Two similar polygons are to each other as the squares of their homologous sides. 3~ B A' B' Given AB and A'B' homologous sides of similar polygons AC and AC', whose areas are /fand... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...of their homologous sides. Consult Prop. 166, Cor. V. and Prop. 140. Proposition 178. Theorem. 214. Similar polygons are to each other as the squares of their homologous sides. K Hypothesis. AB and GH are homologous sides of the similar polygons ABCDEF and GHKMNO. Let their areas... | |
 | James Howard Gore - Geometry - 1899 - 266 pages
...SCHOLIUM. Two similar triangles are to each other as the squares of any two homologous lines. 264. COR. Two similar polygons are to each other as the squares of their homologous sides. triangles of one polygon will be to the sum of the triangles of the other as any one triangle of the... | |
 | William Taylor Campbell - Geometry - 1899 - 264 pages
...sides makes the area of the polygon four times as great; and so on. This is expressed by saying that " the areas of similar polygons are to each other as the squares of any two corresponding sides." The square of a number is the number multiplied by itself; thus the... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...meeting AC at x and y. Compare the areas of triangles ABC and Oxy. BOOK IV PROPOSITION X. THEOREM 631. Similar polygons are to each other as the squares of their homologous sides. C AE Let ABCDE and FGHIJ be two similar polygons. ABCDE CD* Toprove JGIHJ =iffProof. From the vertex... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...times as large as a given triangle and similar to it. PLANE OEOMETBT PROPOSITION XVII. THEOREM 371. Similar polygons are to each other as the squares of their homologous sides. A.' Hyp. AB and A'B' are homologous sides of two similar polygons BE and B'E', whose areas are S and... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...to it. A CAC Hyp. A ABC ~ A A'B'C'. To nrove A ABC AT? PLANE GEOMETRY PROPOSITION XVII. THEOREM 371. Similar polygons are to each other as the squares of their homologous sides. E E' Hyp. AB and A'B' are homologous sides of two similar polygons BE and B'E', whose areas are S and... | |
 | Arthur Schultze - 1901 - 260 pages
...triangle nine times as large as a given triangle and similar to it. PROPOSITION XVII. THEOREM 371. Similar polygons are to each other as the squares of their homologous sides. E' Hyp. AB and A'B' are homologous sides of two similar polygons BE and B'E', whose areas are S and... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...AFHI ^ ' AADE A FIJ A ADE , 9 v A FIJ ' AACD,.,. AJffl/' Cfl /9\ JV/ ABCDE FGHIJ 632. COROLLARY I. Similar polygons are to each other as the squares of their homologous diagonals. 633. COROLLARY II. In similar polygons homologous triangles are like parts of the polygons.... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
