 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...the antecedent and consequent (B. IV. Prop. 8), we shall have ABC : DEC : : AC.CB : DC.CE. PROP. XX. THEOREM. Two similar triangles are to each other as the squares of their homologous sides. Let ABC, DEF, be the similar triangles, having the angles A, B, C, respec- Fig- 77. lively equal to D,... | |
 | Charles WATERHOUSE - Arithmetic - 1844 - 228 pages
...in the other, are to each other as uie rectangles of the sides, which contain (he equal angles. 11. Two similar triangles are to each other as the squares of their homologous sides. 12. The surface of a triangle is equal to its perimeter, multiplied by half the radius of the inscribed... | |
 | Anna Cabot Lowell - Geometry - 1846 - 206 pages
...ABC = GEH, and EH2=BC2; therefore triangle ABC : triangle DEF = Bcf : EF2 ; that is, the surf aces of similar triangles are to each other as the squares of their homologous sides. For example, if BC = £ EF then triangle ABC = } DEF. If the homologous sides of two similar triangles... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...couplet, we have triangle ABC : triangle ADF : : AB.AC : AD.AF. PROPOSITION XII. THEOREM. Equiangular or similar triangles are to each other as the squares of their homologous sides. Let ABC, DFG be two equiangular triangles, AB and DF being two like sides ; then will the triangle ABC... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...by § 251, the area of ABC: the area of A'B C' = AB* : A'B". 267. Corollary. Hence, by § 197 & 198, similar triangles are to each other as the squares of their homologous altitudes, and as the squares of their perimeters. 268. Theorem. Similar polygons are to each other... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...the antecedent and consequent of the first couplet, we have PROPOSITION XVI. THEOREM. Equiangular or similar triangles are to each other as the squares of their homologous sides. Let ABC, DFG be two equiangular triangles, AB and DF being two like sides; then will the triangle ABC be... | |
 | Alonzo Gray - Physics - 1850 - 422 pages
...times, 1,4, 9, 16, 25, &c. If, therefore, we can ascertain how far a * This is on the principle that similar triangles are to each other as the squares of their homologous sides. By another principle we have AB X BC to ADxDE, as the triangles themselves. What figure may represent... | |
 | Charles Davies - Logic - 1850 - 400 pages
...general relation of the magnitudes, which is measured by the Ratio. For example : we Example, say that " Similar triangles are to each other as the squares of their homologous sides." Whatdo we mean by that ? Just this : Formula of That the area of a triangle Is to the area of a similar... | |
 | John Benjamin Henck - Railroad engineering - 1854 - 270 pages
...for Л G above, we have Л G = —¿— c, . Moreover, since Л F = — - — x А С, and because similar triangles are to each other as the squares of their homologous sides, we have the triangle Л FG — ("~1)2 x A CL. But Л CL : A CD = CL : CD = n — l : n, or Л CL =... | |
 | 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... | |
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Similar triangles are to each other as the squares of their homologous sides. 
