| William Guy Peck - Conic sections - 1876 - 366 pages
...meet at C'. Lay off EA' equal to EA, and draw the arc DA'. The rightangled triangles AED and A'ED, **have two sides and the included angle of the one,...and the included angle of the other, each to each;** hence, they are equal in all their parts; therefore, the angle EA'D is equal to EAD, and the side DA'... | |
| William Guy Peck - Conic sections - 1876 - 366 pages
...draw the arc DA'. The right• angled triangles AED and A 'ED, have two sides and the included atigle **of the one, equal to 'two sides and the included angle of the other, each to each** ; hence, they are equal in all their parts ; therefore, the angle EA'D is equal to EAD, and the side... | |
| Edward Olney - Geometry - 1877 - 239 pages
...form of quadrilateral.] PROPOSITION XV. 301, Theorem,—Two parallelograms having two sides and tin **Included angle of the one equal to two sides and the included angle of the other, each to each,** are equal. DEM.—Let AC and EC be two parallelograms, with AD = EH, AB = EF, and A = E; then are they... | |
| Elias Loomis - Geometry - 1877 - 443 pages
...because AB is equal to CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD **have two sides and the included angle of the one equal to two sides' and the included angle** of the other; therefore the side AC is equal to BD (Pr. 6), and the angle ACB to the angle CBD. And,... | |
| Thomas Hunter - 1878
...AF and FE are also equal (const.), and the angles AFC and EFB are equal (Prop. XVII.). Therefore the **two triangles have two sides and the included angle...and the included angle of the other, each to each,** and are every way equal (Prop. IV.); the angle EBF is equal to the angle FCA. But DBG is greater than... | |
| Elias Loomis - Geometry - 1880 - 443 pages
...therefore, A and B are mutually equilateral. PROPOSITION XII. THEOREM. If two triangles on equal spheres **have two sides and the included angle of the one equal to two sides and the included** anrjle of the other each to each, their third sides will be equal, and their other angles will be equal... | |
| William Frothingham Bradbury - Geometry - 1880 - 240 pages
...angle DBC—CDB; therefore the whole angle ABC = ADC; therefore the triangles ABC and ADC, having two **sides and the included angle of the one equal to two sides and the included angle** of the other, are equal (80). 89. Scholium. In equal triangles the equal angles are opposite the equal... | |
| Simon Newcomb - Geometry - 1881 - 399 pages
...Or, because QU= QW (I.), TQ+QU= TU> TW. 6. Comparing with (4), TU> TV. QED 45 THEOREM XIX. 108. If **two triangles .have two sides and the included angle...the one equal to two sides and the included angle** of the other, they are identically equal. Hypothesis. ABC&n&MNP, two triangles in which PM = CA. PN... | |
| Edward Olney - Geometry - 1883 - 333 pages
...PROPOSITION XXI. 704. Theorem.—On the same sphere, or on equal spheres, two spherical triangles having two **sides and the included angle of the one equal to two...and the included angle of the other, each to each,** are equal, or symmetrical and equivalent. DEMONSTRATION. Let ABC and A'B'C' be two spherical triangles,... | |
| Alfred Hix Welsh - Geometry - 1883 - 267 pages
...required triangle. For, all triangles constructed with the given data must be equal, since they would **have two sides and the included angle of the one equal to two sides and the included angle** of the other. \ QEF PROBLEM XI. One side of a triangle and its adjacent angles being given, to construct... | |
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