 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...another. SCHOLIUM. In the case of the rhombus, the sides AB, BC, being equal, the triangles BEC, DEC, have all the sides of the one equal to the corresponding sides of the other, and are therefore equal : whence it follows that the angles BEC, DEC, are equal ; and, therefore, that... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...to EB. Scholium. In the case of the rhombus, the sides AB, BC being equal, the triangles AEB, EBC, have all the sides of the one equal to the corresponding sides of the other, and are therefore equal: whence it follows that the angles AEB, EEC, are equal, and therefore, that... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...Because the alternate angles ABE, BCD CD Cor. If the side AB is equal to AC, the triangles AEB, AEC have all the sides of the one equal to the corresponding sides of the other, and are consequently equal ; hence the angle AEB will equal the angle AEC, and therefore the diagonals... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...sides be parallel, and the .4 figure will be a parallelogram. For, draw the diagonal BD. Then, the two triangles ABD, BDC, have all the sides of the one equal to all the sides of the other, each to each : therefore, the two triangles are equal (Th. viii) ; hence,... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...sides be parallel, and the figure will be a parallelogram. For, draw the diagonal BD. Then, the two triangles ABD, BDC, have all the sides of the one equal to all the sides of the other, each to each : therefore, the two triangles are equal (Th. viii) ; hence,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...quadrilateral, having its opposite sides respectively equal, viz.: AB—DC, and AD—BC] then will these sides be parallel, and the figure a parallelogram. For, having drawn the diagonal BD the two triangles ABD, BDC, have all the sides of the one equal to the corresponding sides of the other;... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...sides be parallel, and the 4 ^ figure will be a parallelogram. For, draw the diagonal BD. Then, the two triangles ABD BDC, have all the sides of the one equal to all the sides of the other, each to each : therefore, the two triangles are equal (Th. viii) ; hence,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...quadrilateral, having its opposite sides respectively equal, viz. : AB=DC, and AD=BC '; then will these sides be parallel, and the figure a parallelogram. For, having drawn the diagonal BD "Q p the two triangles ABD, BDC, have all the sides of the one equal to the corresponding sides of... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...quadrilateral, having its opposite sides respectively equal, viz.: AB=DC, and AD=BC; then will these sides be parallel, and the figure a parallelogram. For, having drawn the diagonal BD DC the two triangles ABD, BDC, have all the sides of the one equal to the corresponding sides of the... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...the diagonals of every parallelogram, &c. Cor. If the side AB is equal to AC, the triangles AEB, AEC have all the sides of the one equal to the corresponding sides of the other, and are- consequently equal ; hence the angle AEB will equal the angle AEC, and therefore the di agonals... | |
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BD the two triangles ABD, BDC, have all the sides of the one equal to the corresponding... 
