| John Radford Young - Euclid's Elements - 1827 - 246 pages
...and join GH. fa/ V Then the triangles GBH, DEF are equal, since two sides and the included angle in the one are respectively equal to two sides and the included angle in the other ; hence, and by hypothesis, AB : BC : : GB : BH, that is, the sides BA, BC of the triangle... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Demonstration. In the two triangles ABC, D£JP(ng.31), let the angle A be equal to the... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...respect equal. They are proved to be such in the fourth proposition, u In , tivo sides and the contaHied angle of the one are respectively equal to two sides and the contained angle of the other : in the eighth, when the three sides of the one are equal to the three... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...consequently they are equal. (Ax. 13.) Hence, universally, Any two triangles are every way equal, when two sides and the included angle of the one, are respectively equal to two sides and the included angle of the other. PROPOSITION VI. THEOREM. If two triangles ABC, DEF, have two angles and the interjacent... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...respect equal. They are proved to be such in the fourth proposition, when two sides and the contained angle of the one are respectively equal to two sides and the contained angle of the other: in the eighth, when the three sides of the one are equal to the three... | |
| Nathan Scholfield - 1845 - 894 pages
...has been proved (Prop. VIII.) that two triangles are equal, when two sides and the included angle in the one, are respectively equal to two sides and the included angle in the oilier ; we may now infer further, that two triangles are equivalent or equal in surface, when... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Proof. In the two triangles ABC, DEF, (fig. 31), let the angle Jl be equal to the angle... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...construction, the side AB common, and the angle CAB equal to the angle CBA by hypothesis ; therefore two sides and the included angle of the one are respectively equal to two sides and the included angle of the other ; consequently the triangle DAB is equal to the triangle CBA (Prop. in). But a part cannot... | |
| George Clinton Whitlock - Mathematics - 1848 - 338 pages
...and a increase or decrease together. Cor. 2. Two spherical triangles are equal : (537) 1°. When two sides and the included angle of the one are respectively equal to the two sides and the included angle of the other ; and therefore, FOR A SIDE. 265 Fig. 120a. 2°.... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...to DF, and join GH. Then the triangles AGH, DEF are equal, since two sides and the included angle in the one, are respectively equal to two sides and the included angle in the other (Prop. VI., BI). But, by hypothesis, AB : DE : : AC : DF; therefore AB : AG : : AC : AH;... | |
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