| Euclides - 1862 - 140 pages
...— Therefore, any two sides, &.c. Q. JE. D. PROPOSITION 21.— THEOREM. If from the ends of the side of a triangle there be drawn two straight lines to...of the triangle, but shall contain a greater angle. (References— Prop. I. 16, 20; ax. 4.) Hypothesis. — Let ABC be a triangle, and from ths points... | |
| Euclides - 1862 - 172 pages
...ends of a side of a triangle there be drawn tioo straight lines to a point within the triangle ; then these shall be less than the other two sides of the triangle, but shall contain a greater angle. (References — i. 16, 20; ax. 4.) Let the two straight lines BD, CD, be drawn from B, C, the ends... | |
| University of Oxford - Education, Higher - 1863 - 316 pages
...rectilineal figure, and having an angle equal to a given rectilineal angle. 3. If from the ends of the side of a triangle there be drawn two straight lines to...than the other two sides of the triangle, but shall confine a greater angle. 4. Divide a given straight line into two parts so that the rectangle contained... | |
| Euclides - 1863 - 122 pages
...(ABC), there be drawn two straight lines to a point (D) within the triangle, these (BD and CD) together shall be less than the other two sides of the triangle, but shall contain a greater angle. Produce BD to E. Then, tie two Bides BA, AE, of the triangle unequals add EC. Therefore the two sides... | |
| Henry White - 1864 - 156 pages
...a rhombus, and give Euclid's 12th axiom (relating to parallel lines). 2. If from the ends of a side of a triangle there be drawn two straight lines to...of the triangle, but shall contain a greater angle. 3. What is meant by a corollary? State and prove the corollaries to the proposition in which it is... | |
| Euclides - 1864 - 448 pages
...greater than AB. Therefore any two sides, &e. QED PROPOSITION XXI. THEOREM. If from the ends of a side of a triangle, there be drawn two straight lines to...of the triangle, but shall contain a greater angle. Let ABC be a triangle, and from the points B, C, the ends of the side BC, let the two straight lines... | |
| Robert Potts - 1865 - 528 pages
...greater than AB. Therefore any two sides, &c. QED PROPOSITION XXI. THEOREM. If from the ends of a tide of a triangle, there be drawn two straight lines to...within the triangle; these shall be less than the otlier two sides of the triangle, but shall contain a greater angle. Let ABC be a triangle, and from... | |
| Euclides - 1865 - 80 pages
...equal to AB ; therefore AC is greater than AB. PROPOSITION XXI. TIIEOR. If from the ends of one side of a triangle there be drawn two straight lines to a point within the triangle, these two straight lines are less than the two sides of the triangle, but contain a greater angle. Let the... | |
| Euclides - 1865 - 402 pages
...greater than AB. Therefore, any two sides, &c. QED PROP. XXI.— THEOREM. If from the ends of a side of a triangle there be drawn two straight lines to a point within the triangle; then these shall be less than the other two sides of the triangle, but shall contain a greater angle.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...greater than AB. Wherefore, any two sides &c. QED PROPOSITION 21. THEOREM. If from, the ends of the side of a triangle there be drawn two straight lines to...of the triangle, but shall contain a greater angle. Let ABC be a triangle, and from the points B, O, the ends of the side BC, let the two straight lines... | |
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