The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... A Supplement to the Elements of Euclid - Page 278by Daniel Cresswell - 1819 - 410 pagesFull view - About this book
| 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
...(a) Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal... | |
| 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 DI5,... | |
| Euclides - 1855 - 230 pages
...BC the segments of the base (c). PROPOSITION XIV. THEOREM [1.]—If equal parallelograms (AB and BC) have an angle of the one equal to an angle of the other, their sides about the equal angles are reciprocally proportional (DB is to BE, as GB is to BF). [3.]... | |
| 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... | |
| Peter Nicholson - Cabinetwork - 1856 - 518 pages
...equal to the sum of the two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which have an angle of the one equal to an angle of the other, are to each other as the rectangle of the sides about the equal angles. Suppose the two triangles joined,... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have an angle of the one equal to an angle of the other. All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
| 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... | |
| Eucleides - 1860 - 396 pages
...If equal parallelograms have an angle of the one equal to an angle of the other. If parallelograms have an angle of the one equal to an angle of the other, and their sides about the equal angles reciprocally proportional. If parallelograms are about the diameter... | |
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