| Benjamin Donne - 1796 - 118 pages
...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 - 482 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 - 1816 - 294 pages
...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
...the other, coincide entirely ; thus two circles having the same radius arc equal ; and two triangles **having the three sides of the one equal to the three sides of the other, each to each,** are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. .fc **having the three sides of the one equal to the three sides of the other, each to each,** are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...equivalent, however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. **having the three sides of the one equal to the three sides of the other, each to each,** are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles... | |
| Adrien Marie Legendre - Geometry - 1825 - 280 pages
...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 - 1826 - 266 pages
...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 - 228 pages
...parts ; they are not different, therefore, but equal; and \ve 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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