 | Thomas Keith - Navigation - 1810 - 478 pages
...AC = AD and BC = BD, by 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... | |
 | Daniel Cresswell - Geometry - 1816 - 352 pages
...is equal to CBF (Art. 97.), and the side CB to CA. Hence, in the two spherical triangles CAD, CDB, the three sides of the one are equal to the three sides of the other, each to each ; therefore, (Art. 86.) the angle CBD is equal to the angle CAD ; and the angle CBF has been shewn to be equal to... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...equal quantities, AG, AB, we shall have GC < BC, or EF< BC. THEOREM. 43. Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (Jig. 23), AC = DF,^g 23BC=EF ; then the angles will be equal,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...equal quantities, AG, AB, we shall have GC <[ BC, or EF<BC. THEOREM. 43. 7V0o triangles are equal, when the three sides of the one are '< equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) JtC = DF, ^6- 23BC — EF ; then the angles will be... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...equal quantities, AG, AB, we shall have GC < BC, or EF<BC. THEOREM. 43. 7\»o triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) AC - DF, F'g.23BC = EF ; then the angles will be equal,... | |
 | Thomas Keith - Navigation - 1826 - 504 pages
...then AC=AD and BC=BD, by construction, also AB is common to the two triangles ABC and ABD, 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, If о be the centre... | |
 | John Martin Frederick Wright - Euclid's Elements - 1829 - 206 pages
...included angle are equal each to each in the triangles. In prop. 8, the three sides of one triangle are equal to the three sides of the other, each to each. In prop. 26, two angles and a side adjacent in one triangle, are equal to two angles and a side adjacent,... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...to the square of В С, and MN is equal to В С (25. Cor.). Therefore, in the triangles ABC, LMN, the three sides of the one are equal to the three sides of the other, each to each ; and, consequently, the angle В А С is (7.) equal to the angle MLN, that is, to a right angle.*... | |
 | Mathematics - 1835 - 684 pages
...to the square of В С, and MN is equal to В С (25. Cor.). Therefore, in the triangles ABC, LMN, the three sides of the one are equal to the three sides of the other, each to each ; and, consequently, the angle В А С is (7.) equal to the angle MLN, that is, to a right angle.*... | |
 | John Playfair - Geometry - 1836 - 148 pages
...have the side DA equal to EA (Def. 54. 1.), DF equal to EF, by the construction, and FA •common ; the three sides of the one are equal to the three sides of the other, and therefore the triangles are equivalent (7. 1.) ; and the angle DAF is equal to the angle EAF ;... | |
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THEOREM. 43. 7\»o triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. 
