| 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 similar, we... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...properties of triangles include, by implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. **Two triangles, which have an angle of the one equal...containing those angles proportional, are similar.** Let ABC, DEF, be two triangles, having the angle A equal to D ; then, if AB : DE :: AC : DF, the two... | |
| 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
...triangles. Thus, the properties of triangles include, by implication, those of all f1gures. BOOK IY. 109 D **PROPOSITION XX. THEOREM. Two triangles, which have...containing those angles proportional, are similar.** Let ABC, DEF, be two triangles, having the angle A equal to D ; then, if AB : DE : : AC : DF, the two... | |
| William Somerville Orr - Science - 1854 - 532 pages
...equal to au angle of the other, have their sides about the equal angles reciprocally proportional ; and **triangles which have an angle of the one equal to an angle of the other, and** their sides about those angles reciprocally proportional, are equal to one another. Let the triangles... | |
| Euclides - 1855 - 258 pages
...and hare their sides reciprocally proportional, they are equiangular. PROP. XV. ТНЕORЕМ. Equal **triangles which have an angle of the one equal to an angle of the other,** have their sides about the equal angles reciprocally proportional; and conversely, triangles which... | |
| Euclides - 1855 - 226 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.]... | |
| Peter Nicholson - Cabinetwork - 1856 - 482 pages
...but, since AB is 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.... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 pages
...figures may be divided into triangles, and any triangle into two right-angled triangles. Thus, the **properties of triangles include, by implication, those...of the other, and the sides containing those angles** proportioned, are similar. Let ABC, DEF, be two triangles, having the angle A equal to D; then, if... | |
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