 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...respectively equal to ED, EF, r , . _, 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... | |
 | Nathan Scholfield - 1845 - 894 pages
...not, a right angle. Scholium. "It 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... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...AG equal to DE, also AH equal 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 :... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...AG equal to DE, also AH equal 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 B... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...similarly arranged. 630. Corollary — Two tetraedrons are equal when one face and the adjacent diedrals of the one are respectively equal to those parts of the other, and they are similarly arranged. 631. When tetraedrons are composed of equal parts in reverse order,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...AG equal to DE, also AH equal 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 B... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...rectangle and a rhombus, has the properties of all these figures. PROPOSITION XXXVI.— THEOREM. 119. Two parallelograms are equal when two adjacent sides and the included angle of the one are equal to two adjacent sides and the included angle of the other. Let AC, A'C', have... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...and the square are the only parallelograms which can be inscribed in a circle (348). EQUALITY. 370. Theorem — Two parallelograms are equal when two...are respectively equal to those parts of the other. 372. Corollary. — Two squares are equal when a side of the one is equal to a side of the other. APPLICATIONS.... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...rectangle and a rhombus, has the properties of all these figures. PROPOSITION XXXVI— THEOREM. 119. Two parallelograms are equal when two adjacent sides and the included angle of the one are equal to two adjacent sides and the included angle of the other. Let AC, A'C', have... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...the diagonals of a parallelogram are equal, the figure is a rectangle. PROPOSITION XL. THEOREM. 123. Two parallelograms are equal when two adjacent sides and the included angle of one are equal respectively to two adjacent sides and the included angle of the other. In the parallelograms... | |
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Theorem. — Two parallelograms are equal when two adjacent sides and the included angle in the one, are respectively equal to those parts in the other. 
