 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...angles. THEOREM. 36. Two triangles are equal, 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. Demonstration. In the two triangles ABC, DEF (fig. 23), Fig. 23 let the angle A be equal to the angle... | |
 | Samuel Simon Schmucker - Psychology - 1842 - 262 pages
...demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz. : If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, they must be identical or equal in all respects. For it virtually consists in supposing... | |
 | Charles Waterhouse - Arithmetic - 1842 - 178 pages
...Demonstrably true: — 1. Two triangles are equal 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. 2. In an isosceles triangle, the angles opposite to the equal sides are equal. 3. Of the two sides... | |
 | Charles WATERHOUSE - Arithmetic - 1844 - 228 pages
...opposite the longer aids. 6. Two triangles ore equal 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. 7. Every triangle is half of a parallelogram of the same base and altitude. 8. In a right-angled triangle,... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...parallel, the angle BAC is equal to its alternate angle DCA (Prop. xvii)t; hence the two triangles, having two sides and the included angle of the one equal to two sides and the included angle of the other, namely, the side AB equal to. the side CD, the side AC common, and the contained angle... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...by the successive angles ACB, BCD, DCE, ECF. FCA. PROPOSITION V. THEOREM. If two triangles have two sides and the included angle of the one, equal to...two sides and the included angle of the other, each tc each, the two triangles will be equal Let the side ED be equal to the side BA, the side DF to the... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and C 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 (Prop. VI.), and the angle ACB to the angle CBD.... | |
 | Charles Davies - Logic - 1850 - 390 pages
...each, and the triangles themselves will be equal." Prop. V. " When two triangles have two Proposition sides and the included angle of the one, equal to...and the included angle of the other, each to each, the two triangles will be equal." Axiom I. " Things which are equal to the Axioms, same thing, are... | |
 | Charles Davies - Logic - 1850 - 402 pages
...to each, and the triangles themselves will be equal." Prop. V. " When two triangles have two tides and the included angle of the one, equal to two sides...and the included angle of the other, each to each, the two triangles will be equal." Axiom I. " Things which are equal to the same thing, are equal to... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...Triangles. ACD+BCD=ADC+BDC that is, the angle ACB=ADB. Now, the two triangles ACS and ADB have two sides and the included angle of the one equal to two sides and the in. eluded angle of the other, each to each : hence, the remaining angles will be equal (Th. iv) :... | |
| |
If 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, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal... 
