 | William Nicholson - 1809 - 722 pages
...one another: hence, 1. All similar triangles have the sides about their angles proportional. ?. All similar triangles are to one another as the squares of their homologous sides. SIMILAR bodies, in natural philosophy, are such as have their particles of the same kind and nature... | |
 | William Nicholson - Natural history - 1821 - 384 pages
...one another: hence, 1. All similar triangles have the sides about their angles proportional. 2. All similar triangles are to one another as the squares of their homologous sides. SIMILAH bodies, in natural philosophy, are such as have their particlei of the same kind and nature... | |
 | William Nicholson - Natural history - 1821 - 382 pages
...one another : hence, 1. All similar triangles have the sides about their angles proportional. 2. All similar triangles are to one another as the squares of their homologous sides. • SIMILAR bodies, in natural philosophy, are such as have their particles of the same kind and nature... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...ADxAE. the triangle ADE : AD x AE. the triangle ABC : AB x AC. : AB x AC : AD x AE. THEOREM 64. 162. Similar triangles are to one another as the squares of their homologous sides. Let the angle A be equal to the angle D, and A the angle B equal to E. Then AB : DE •: AC : DF (155)... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...duplicate ratio of two straight lines is the same with the ratio of their squares (37. Cor. 2.) it appears that similar triangles are to one another as the squares of their homologous sides. PROP. 43. (Eue. vi. 20.) Similar rectilineal figure» are to one another in the duplicate ratio of... | |
 | Mathematics - 1835 - 684 pages
...duplicate ratio of two straight lines is the same with the ratio of their squares (37. Cor. 2.) it appears that similar triangles are to one another as the squares of their homologous sides. PROP. 43. (Eue. vi. 20.) Similar rectilineal figures are to one another in the duplicate ratio of their... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...sides. M. — Now, express, in words, the relation which similar triangles have to one another. P. — Similar triangles are to one another as the squares of their homologous sides. SUBSTANCE OF SECTION VIII. 1. Triangles between the same parallels are to one another as their bases.... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...M.—Now, express, in words, the relation which similar triangles have to one another. P.—Similar triangles are to one another as the squares of their homologous sides. SUBSTANCE OF SECTION VIII. 1. Triangles between the same parallels are to one another as their bases.... | |
 | Euclides - 1838 - 264 pages
...upon a given straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another as the squares of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Joseph Denison - Mechanics - 1841 - 210 pages
...are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the similar triangles are to one another as the squares of their homologous sides. E But the spaces described in the times ab, ad, are as the squares of ab, ad ; that is, as the squares... | |
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The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig. 
