 | George Roberts Perkins - Geometry - 1850 - 332 pages
...also be proportional to the sides GH, HK, (B. IV, Def. III.) Therefore, the two triangles ABC, GHK have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently these triangles are similar; and being... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...include, by implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having... | |
 | Euclid - Geometry - 1853 - 176 pages
...CONSEQUENCES. I. 34, cor. 2. . I.35. . . I.36. . . I. 46, cor. 1. I. 46, cor. 2. If two parallelograms have an angle of the one equal to an angle of the other. If parallelograms are between the same parallels, And upon the same base, Or upon equal bases. If two... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...by implication, those of all f1gures. BOOK IY. 109 D PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...other, have their sides about the equal angles reciprocally proportional : and parallelograms that have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another. Let the sides... | |
 | Euclides - 1855 - 230 pages
...equal to an angle of the other. If triangles are equiangular . If triangles are similar . . If equal triangles have an angle of the one equal to an angle of the other. If triangles have an angle in the one equal to an angle in the other, and their sides about the equal... | |
 | Euclides - 1855 - 270 pages
...compounded of the ratios which are the game with the ratios of the sides. Corollary 1. — Triangles which have an angle of the one equal to an angle of the other, are to one another as the rectangles contained by the sides about those angles. Corollary 2. — Equiangular... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...ratios (T. VI.) : BC : B'C' : : AC : A'C' : : AB : A'B'. GEOMETRY. THEOREM vIII. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. In the two triangles ABC, A'B'C',... | |
 | Peter Nicholson - Cabinetwork - 1856 - 518 pages
...also, the triangles DEF, ABC, are equiangular and similar. § THEOREM 51. 122. Two triangles which have an angle of the one equal to an angle of the other, and the sides about them proportionals, are similar. Let the angle A equal D, and suppose that AB :... | |
 | Euclid - 1859 - 150 pages
...àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, laa iariv iKtlva. Equal triangles which have an angle of the one equal to an angle of the other have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle... | |
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Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. 
