| John Radford Young - Euclid's Elements - 1827 - 208 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 - 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 - 237 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... | |
| 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... | |
| 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... | |
| Benjamin Peirce - Geometry - 1847 - 150 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 Clinton Whitlock - Mathematics - 1848 - 324 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;... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...than CB ; then take AD equal to BC, and join DJB. Now, in the two triangles DAB and CBA, we have ^ A **equal to CB by construction, the side AB common, and...CB and CA, and therefore the triangle is isosceles.** 'IPROPOSITION VIII. .THEOREM. When two triangles have the three sides of the one respectively equal... | |
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