 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...as their bases ; and in general they arc to each other as the product of their bases and altitudes. Similar triangles are to each other as the squares of their homologous sides. 17. Two triangles which have an angle equal in each, arc to each other as the products of the including... | |
 | 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... | |
 | 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... | |
 | 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 homologous... | |
 | 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 altitudes.... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...DE will be parallel to _B(7, and we shall have, • AD : AB : : AE : AC ; hence (B. H, P. IV.), we have, ADE : ABE : : ABE : ABC ; PROPOSITION XXV. THEOREM....angle A being equal to the angle D, B to E, and C to F. then will the triangles be to each other as the squares of any two homologous sides. Because the... | |
 | William Chauvenet - Mathematics - 1872 - 382 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 BC* DC A'B'C' B'C" Let AD, A'D', be the altitudes.... | |
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Similar triangles are to each other as the squares of their homologous sides. 
