 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...on equal spheres, are equal in all their parts, when two sides and the included angle of the one are equal to two sides and the included angle of the other, each to each. Let ABC, EFG, be two triangles having the side AB=UF, the side AC— EG, and the angle BA C=FEG•,... | |
 | Anthony Dumond Stanley - Sphere - 1854 - 130 pages
...these two sides. Now DCE is equal to this triangle, two sides and the included angle of the one being equal to two sides and the included angle of the other, each to each ; since CE and DE are supplements of AE and BE, and the angle CED is equal to AEB. Since then CDE is... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...on equal spheres, are equal in all their parts, when two sides and the included angle of the one are equal to two sides and the included angle of the other, each to each. Let ABC, EFG, be two triangles having the side AB=EF, the side AC=EG, and the angle BAC—FEG; then... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...themselves will bo equal." Prop. V. " When two triangles have two sides, and the included angle of the une equal to two sides and the included angle of the other, each to each, the two triangles will be equal. "Axiom 1. Things which are equal to tho same thing are equal to each... | |
 | Elias Loomis - Conic sections - 1861 - 244 pages
...right angles. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included angle of t/ie one, equal to two sides and the included angle of the other > each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal,... | |
 | Charles Davies - 1863 - 436 pages
...is equal to the angle CEB\ THEOREM IVIf two triangles have two sides and the included angle of tie one, equal to two sides and the included angle of the other, each to each, the two triangles will be equalLet the triangles ABC and DEF have the side AC equal to DF, CB to FE,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...angles. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included angle of fie une, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will b? equal, and their other angles will be equal,... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...TRIANGLES. PROPOSITION TL 284. Theorem. — Two triangles which have two sides and the 'included angle of one equal to two sides and the included angle of the other, each to each, are equal. DEM.— Let ABC and DEF be two triangles, having AC = DF, AB = DE, and angle A = angle D... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...On the same or equal spheres, two spherical triangles having two sides and the included angle of (he one equal to two sides and the included angle of the other, each to each, are equal, or sym+ metrical and equivalent. DEM.— Let ABC and A'B'C', Fig. 337, be two spherical... | |
 | William Guy Peck - Conic sections - 1876 - 412 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 DA' to DA. But, the sine... | |
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B : hence the two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each : hence, the two triangles are equal (Th. 
