| Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...to the base AB, the triangle must be equilateral. PROP. II. THEOREM. Two triangles are equal, which **have all the sides of the one equal to the corresponding sides of the other.** For let the triangle ACB be applied to DBF, in the same position. The point A being laid on D, and... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...equal to OB. Scholium. In the case of the rhombus, the sides AB, BC being equal, the triangles AOB, OBC **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 AOB, BOC are equal, and therefore, that... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...last figure) having its opposite sides respectively equal, viz. AB=DC, and AD =BC ; then will these **sides be parallel, and the figure a parallelogram....corresponding sides of the other ; therefore they are equal** ; therefore, the angle ADB, opposite the side AB, is equal to DBC, opposite CD ; therefore (67.) the... | |
| Adrien Marie Legendre - Geometry - 1830 - 344 pages
...last figure) having its opposite sides respectively equal, viz. AB=DC, and AD =BC ; then will these **sides be parallel, and the figure a parallelogram....BD, the triangles ABD, BDC, have all the sides of** tt^ one equal to the corresponding' sides of the other ; ' thejefpre they are equal ; therefore, the... | |
| John Playfair - Euclid's Elements - 1835 - 316 pages
...BD'+AC2. 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... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...respectively equal, viz. AB = DC, and AD = BC ; then will these sides be parallel, and the figure be **a parallelogram. For, having drawn the diagonal BD,...triangles ABD, BDC, have all the sides of the one equal to** " Br ' -. the corresponding sides of the other ; therefore they are equal, and the angle ADB, opposite'... | |
| John Playfair - Geometry - 1837 - 332 pages
...another. SCHOLIUM. In the case of the rhombus, the sides AB, BC, being equal, the triangles BEG, 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... | |
| Adrien Marie Legendre - Geometry - 1838 - 384 pages
...sides respectively equal, viz. AB=DC, and AD=BC ; then will these sides be parallel, and the figure be **a parallelogram. For, having drawn the diagonal BD,...triangles ABD. BDC, have all the sides of the one equal** ts the corresponding sides of the other ; therefore they are equal, and the angle ADB, opposite the... | |
| John Playfair - Euclid's Elements - 1842 - 332 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... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...ABCD, are equal, viz. AB to CD, and AD to BC, tlte equal sides will be parallel, and the figure will be **a parallelogram. For, having drawn the diagonal BD,...sides of the other ; ........ therefore they are equal** ; consequent- A ly the angle ADB, opposite the side AB, is equal to DBC, opposite CD ; (Prop. 10. Sch.;)... | |
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