 | L J V. Gerard - 1874 - 428 pagina’s
...angles are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which have an angle of the one equal to an angle of the other, have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pagina’s
...the two triangles are equal, ABxAC=POxOQ, therefore ^? - 29 \)L .AO that is, equal triangles which have an angle of the one equal to an angle of the other, have the sides ahout the equal angles reciprocally proportional. Cor. 3. — Hence also equiangular... | |
 | Euclid - 1876 - 240 pagina’s
...as EA is to AB). [2.] And if triangles (ABC and ADE) have an angle in the one equal to an angle in the other, and their sides about the equal angles...equal to one another. CONSTRUCTION. Let the sides CA, AD, be placed contiguous, in the same straight line, with the triangles on opposite sides of CD... | |
 | Sir George Greenhill - 1876 - 318 pagina’s
...equal angles reciprqcally proportional ; and triangles which have one angle of the one equal to one angle of the other and their sides about the equal angles reciprocally proportional are equal to one anothen If ABC, ADE be two such triangles placed so that BA, AE are in a straight... | |
 | Aaron Schuyler - 1876 - 384 pagina’s
...proportionality of sides involve equality of angles. 230. Proposition XXI.— Theorem. Two triangles having an angle of the one equal to an angle of the other, and tlie including sides proportional, are similar. In the triangles, ABC, DEF, let A = D, and AB : DE... | |
 | Richard Wormell - 1876 - 268 pagina’s
...same demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then the sides which contain the angle of the first are the extremes of a proportion of which the sides... | |
 | 1876 - 646 pagina’s
...polygons. Prove that two triangles are similar when they are mutually equiangular. 2. Two triangles having 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. 3. To inscribe A circle... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 pagina’s
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two... | |
 | Elias Loomis - 1877 - 458 pagina’s
...the point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they have an angle of the one equal to an angle of the other, and the sides including those angles proportional. Let the triangles ABC, DEF have the angle A of the one... | |
 | Dalhousie University - 1888 - 212 pagina’s
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles have an angle of the one equal to an angle of the other, and have their areas proportional to the squares of the side* opposite these equal angles, they must be... | |
| |
... 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. 
