| 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... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...BAC is equal to its alternate angle DCA, (Prop, xvu;) 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 equal to the side CD, the side AC common, and the contained angle BAC... | |
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