 | John Radford Young - 1827 - 246 σελίδες
...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 - 1837 - 216 σελίδες
...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 - 1837 - 410 σελίδες
...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 - 1844 - 268 σελίδες
...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... | |
 | Nathan Scholfield - 1845 - 894 σελίδες
...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... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...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... | |
 | George Roberts Perkins - 1847 - 326 σελίδες
...greater than CB ; then take AD equal to BC, and join DB. Now in the two triangles DAB and CBA, we have DA equal to CB by construction, the side AB common, and...CB and CA, and therefore the triangle is isosceles. PROPOSITION VIII. THEOREM. When two triangles have all the three sides of the one equal to all the... | |
 | Benjamin Peirce - 1847 - 204 σελίδες
...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 Clinton Whitlock - 1848 - 338 σελίδες
...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 - 1849 - 252 σελίδες
...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;... | |
| |
If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other... 
