 | 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... | |
 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...are similar, because the line M m is drawn parallel to the side BC in the triangle ABC (page 82); and as the areas of similar triangles are to each other as the areas of the squares upon the corresponding sides (lee page 134) we have the proportion triangle ABC... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 212 pages
...because the line Mm is drawn parallel to the side BC in the triangle ABC (Query 16, Sect. II.) ; and as the areas of similar triangles are to each other as the areas of the squares upon the corresponding sides (Query 8, page 97), we have the proportion triangle... | |
 | Charles Davies - Geometrical drawing - 1840 - 264 pages
...opposite equal angles 1 Are these sides proportional 1 PLANE GEOMETRY. Properties of Polygons. 13. The areas of similar triangles are to each other as the squares described on their homologous sides. The similar triangles ABC, and DEF, are to each Other, as the... | |
 | 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... | |
 | Education - 1850 - 488 pages
...Hollingworth. Let x = the distance of the first' perpendicular measured from the acute angle of the triangle ; then as the areas of similar triangles are to each other as the squares of their like sides, we have . , .-. x = 1-732, and the distance of the other perpendicular is in like... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...right angle is a mean proportional between the parts of the hypotenuse (Def. 2, Sec. X). THEOREM VIII. The areas of similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles of which the angles A and... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...= 2 1 ^ — 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... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...ietraedrons are to each other as the squares of their edges. This is only a corollary of the theorem that the areas of similar triangles are to each other as the squares of their sides. 641. Corollary — The areas of homologous faces of similar tetraedrons are to each... | |
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Show that the areas of similar triangles are to each other as the squares of the homologous sides. 
