| Benjamin Donne - 1796
...the line DF will coincide with AC, and EF with BC. THEOREM 16. If two triangles have three sides of **one equal to the three sides of the other, each to each,** thefe triangles are equal in every rcfpeft. — 8 E. 1, or 17 D. 1. Ciť For if the triangle DEF be... | |
| Thomas Keith - Navigation - 1810 - 420 pages
...construetion, also AB is common to the two triangles ABC and ADB, therefore the three sides of the one are **equal to the three sides of the other, each to each. The** angles -which are opposite to the equal sides in each triangle are equal. For, Produce the sides BC... | |
| Daniel Cresswell - Geometry, Descriptive - 1816 - 294 pages
...triangles, which are equal to them, are equal to one another. (2l6.) COR. 2. Hence, if two spherical **triangles have the three sides of the one equal to the three sides of the other,** or two sides and the included angle in the one, equal to two sides and the included angle, in the other,... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...will be equal to the arc EJVG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will **have the three sides of the one equal to the three sides of the other, each to each,** namely, AC = EO, CD= OG and AD = EG; therefore these triangles are equal (43); hence the angle ACD... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...the figure will be a parallelogram. Demonstration. Draw the diagonal BD ; the two triangles ABD, BDC, **have the three sides of the one equal to the three sides of the other, each to each,** they are therefore equal, and the angle ADB opposite to the side AB is equal to the angle DBC opposite... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...will be equal to the arc ENG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will **have the three sides of the one equal to the three sides of the other, each to each,** namely, AC— EO, CD = OG and AD = EG ,. therefore these triangles are equal (43) ; hence the angle... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...line AD from the vertex A to the point D the middle of the base BC ; the two triangles ABD, ADC, will **have the three sides of the one, equal to the three sides of the** qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction... | |
| George Lees - Algebra - 1826 - 207 pages
...base at right angles. OF GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, **have the three sides of the one equal to the three sides of the other, each to each,** viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let AB be that side... | |
| Thomas Keith - Navigation - 1826 - 442 pages
...through two given points on the surface of the sphere. Hence, the three sides of the one triangle being **equal to the three sides of the other, each to each, the** triangles are equal. (Prop, vu.) Secondly, let the triangles be situated on contrary sides of the centre... | |
| James Hayward - Geometry - 1829 - 172 pages
...coincide in all their parts ; they are not different, therefore, but equal; and we say, universally, **When two triangles have the three' sides of the one equal to the three sides of the other** respectively, the angles will also be equal, respectively, and the two triangles will be equal in all... | |
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