 | William Mitchell Gillespie - Surveying - 1857 - 538 pages
...AD is derived from the area of a triangle being equal to its base by half its altitude. (527) Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...: : AE : AC ; hence (B. II., P. IV.), w(j have, ADE : ABE : : ABE : ABC ; PROPOSITION XXV. THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let the triangles ABC and DEF be similar, the angle A being equal to the angle D, B to E, and C to... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...— a I. \ / Substituting these in the equation of the area, it becomes, 391. Theorem. — The areas of similar triangles are to each other as the squares of their homologous lines. HC area BCD. In a similar manner, prove that the areas have the same ratio as the squares of... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...implies a general relation of the magnitudes, which is measured by the Ratio. For example : we say that " Similar triangles are to each other as the squares of their homologous sides." What do we mean by that? Just this : That the area of a trinngle Is to the area of a similar triangle,... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...and omitting the common factor AHC, we have, or, ABC:DEF::ACXSC:DFXFE. Therefore, etc. THEOREM XVI. Similar triangles are to each other as the squares of their homologous sides. Let ABC and A DE be two similar triangles ; then will they be to each other as the squares of any two... | |
 | William Mitchell Gillespie - Surveying - 1869 - 550 pages
...AD is derived from the area of a triangle being equal to its base by half its altitude. (527) Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD' ; whence BD = AB J 55? — AB J "* . y ABC ym -f- n The construction of Fig.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...theorems, and the sum of these areas will be the area of the polygon. PROPOSITION VII.— THEOREM. 20. Similar triangles are to each other as the squares of their homologous sides. Let ABC, A'B'C' be similar tri- •* angles; then, ABC BC2 D' C' DC A'B'C' B'C'* Let AD, A'D', be the... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...whose adjacent sides are 2 and 3, and then draw a square of the same area. 111. Theorem.— The areas of similar triangles are to each other as the squares of their homologous sides. ILL.— The meaning of this is, that if ABC and DEF are similar, and any side of ABC is 2 times as... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides. It is illustrated in the preceding examples. Ex. Construct a triangle with one of its sides 2 in length.... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...AB : : AE : AC ; hence (B. H, P. IV.), we have, ADE : ABE : : ABE : ABC ; PROPOSITION XXV. THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let the triangles ABC and DEF be similar, the angle A being equal to the angle D, B to E, and C to... | |
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Similar triangles are to each other as the squares of their homologous sides. 
