| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...triangle. For if thoy did, there would be two of its sides together not greater than the third. THEOREM — **If from the ends of the side of a triangle, there be drawn two straight lines to a point** milhin the triangle, these See Note *hall together be less than the two sides of thejirst triangle,... | |
| John Playfair - Euclid's Elements - 1833 - 333 pages
...Therefore any two sides, &c. QED PROP. XXI. THEOR. If from the ends of one side of a triangle, tJiere **be drawn two straight lines to a point within the triangle, these** two lines shall he less than the other two sides of the triangle, but shall contain a greater angle.... | |
| Euclides - 1834 - 518 pages
...; and BC, CA greater than AB. Therefore, any two sides, &c. QED PROPOSITION XXI. See N. THEOR. — **If from the ends of the side of a triangle, there...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 BD,... | |
| John Playfair - Geometry - 1836 - 114 pages
...is impossible ; and, therefore, ACB is not a right angle. Therefore, From, &c. QED PROP. XII. THEOR. **If from the ends of the side of a triangle there be...be less than the other two sides of the triangle.** Let the two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC,... | |
| Mathematics - 1836 - 472 pages
...Any two sides of a triangle are together greater than the third side. XXI. If from the ends of one **side of a triangle, there be drawn two straight lines to a point within the triangle, these** two lines shall be less than the other two sides of the triangle, but shall contain a greater angle.... | |
| John Playfair - Euclid's Elements - 1836 - 488 pages
...point within the triangle, these two lines shall be less than the other two sides of the triangle, biit **shall contain a greater angle. Let the two straight lines BD, CD be drawn from B,** <I, the ends of the side BC of the triangle ABC, to the point D within it ; BD and DC are less than... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...that similarly each of the other pairs of sides is > the remaining side. PROPOSITION XXI. Theorem. **If from the ends of the side of a triangle there be...of the triangle, but shall contain a greater angle.** • Steps of the Demonstration. 1. Prove that BA + AC > BE + EC, 2. that BE + EC > CD + DB, 3. that... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...that the sides AB, BC, are greater than CA, and BC, CA, greater than AB. PROPOSITION XXI. THEOREM. **If from the ends of the side of a triangle, there...straight lines to a point within the triangle, these** two lines shall he less than the other two sides of the triangle, but shall contain a greater angle.... | |
| John Playfair - Geometry - 1837 - 332 pages
...than CA, and BC, CA greater than AB. SCHOLIUM. 23 E PROP. XXI. THEOR. If from, the ends of one si'le **of a triangle, there be drawn two straight lines to a point within the triangle, these** two lines shall be less than the other two sides of the triangle, but shall contain a greater angle.... | |
| Euclides - 1838 - 264 pages
...lew than the third Mr.." and reason as follows: " For, since BA and AC are together PROP. XXI. THEOR. **If from the ends of the side of a triangle there be...to a point within the triangle, these shall be less** man the other two sides of the triangle, but shall contain a greater angle. Let ABC be a triangle,... | |
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