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" Similar triangles are to each other as the squares of their homologous sides. "
Elements of Geometry and Trigonometry: With Notes - Page 62
by Adrien Marie Legendre - 1822 - 367 pages
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A Treatise on Land Surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1855 - 436 pages
...length of AD is derived from the area of a triangle being equal to its base by half its altitude. Since similar triangles are to each other as the squares of their homologous sides, ABC' : DBE : : AB2 : BD2 ; whence BD = AB J 51? — AB -— . Y Aħ>u Y m T n The construction of Fig....
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 482 pages
...ABC : AB x AC. tria. ADE : : AB x AC : AD x AE. THEOREM 55. 126. Similar triangles are to one another as the squares of their homologous sides. Let the angle A be equal to the angle D, and the angle B equal to E. Then AB : DE :: AC : DF (119) and AB : DE :: BC : EF therefore,...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1856 - 478 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 : DBK : : AB' : BD> ; whence BD = AB J ^ = AB The construction of Fig. 363 is founded on the proportion...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

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...
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Elements of Geometry and Trigonometry

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 Fi then...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

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...
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Outlines of Mathematical Science for the School Room

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,...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

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 homologous...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

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....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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 altitudes....
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