 | Sir John Leslie - Geometry, Plane - 1809 - 522 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 - 394 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 - 336 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 - 394 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 - Euclid's Elements - 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 - 372 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 - 268 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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BD the two triangles ABD, BDC, have all the sides of the one equal to the corresponding... 
