| George Darley - Geometry - 1828 - 190 pages
...other the same ratio as the squares of their corresponding aides ; or yet more- briefly — Equiangular triangles are to each other as the squares of their corresponding sides. This mode of expressing the ratio of equiangular triangles is that which most frequently occurs in... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...DFE) ~ havln g et l ual Prop.35. Wherefore triangles, &c. PROP. LXXXIII. THEOR. 19. 6Eu. Equiangular triangles are to each other as the squares of their corresponding sides. Let ^NS ABC, DBF have the Z s A, B, C, = Z. s D, E, F respectively; then shall £\ ABC : ^ DEF : :... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...ACB : </\DFE Wherefore triangles, &c. PB : QB, CH : PI. PROP. LXXXIII. THEOR. 19. 6E u. Equiangular triangles are to each other as the squares of their corresponding sides. Let ^s ABC, DEF have the Zs A, B, C, = L s D, E, F respectively; then shall ^\ ABC : ^ DEF : : BC 8... | |
| D. M. Knapen - Measurement - 1849 - 300 pages
...Ans. 17.703 rods, very nearly. Similar triangles (that is, triangles whose angles are equal) are to each other as the squares of their corresponding sides, or as the squares of their altitudes ; and this rule, or statement, is true in respect to all similar superficies. 15. If the... | |
| William Harris Johnston - 1865 - 478 pages
...may be divided into triangles, all similar rectilinear figures are to one another in the same ratio as the squares of their corresponding sides, or as the squares of their perimeters. Thus, the area of any given triangle is to the area of any similar triangle, as the area... | |
| David Munn - Measurement - 1874 - 374 pages
...The area of the triangle whose sides are 15, 18, 21, s x 12 x 9 x 6, or 54 ^6. Then as the areas of similar triangles are to each other as the squares of their corresponding sides, we have x2 54 = 754 V6 3 J6 Again, for the other sides, we have <54 .76 i82 60 100 and . , . ' 70 ^6... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...similar triangles, homologous altitudes are to each other as any pair of homologous sides. XXVI. Theorem. The areas of two similar triangles are to each other as the squares of two homologous sides or altitudes. abc. ABC : abc = HYPOTH. A ABC ~ To IJE PROVED. AB2 : a&2. PROOF.... | |
| George Albert Wentworth - Geometry - 1888 - 264 pages
...equalities, AABC_ABxAC AADE ADxAE §370 q. ED COMPARISON OF POLYGONS. PROPOSITION VIII. THEOREM. 375. The areas of two similar triangles are to each other as the squares of any two homologous sides. Let the two triangles be ACS and A'CB'. A ACB AJ? Draw the perpendiculars... | |
| Edward Albert Bowser - Geometry - 1890 - 420 pages
...equal ^57^ . D .A. r> O A ABC BC BC BC' ' ' ' A A'B'C' ~ B'C' X B'C' - g^c'' • Q•KD• 378. Cor. The areas of two similar triangles are to each other as the squares of any two homologous lines. EXERCISES. 1. ABC is a triangle. AE and BF, intersecting in G, are drawn... | |
| Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...angle in each equal, are to each other as the product ofthe sides including those equal angles. 21. Similar triangles are to each other as the squares of their corresponding aides. 22. The perimeters of similar polygons are to each other as any two corresponding sides, and... | |
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