| Elias Loomis - Conic sections - 1849 - 252 pages
...similar. Wherefore, two triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they **have an angle of the one equal to an angle of the other,** and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of... | |
| 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
...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 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 - 136 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... | |
| William Somerville Orr - Science - 1854
...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... | |
| Charles Davies - Geometry - 1854 - 436 pages
...triangles include, 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... | |
| Euclides - 1855
...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
...ABC ; therefore, 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 :... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...series of equal 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',... | |
| Euclides - 1859
...rpiywvwv, 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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