| John Playfair - Euclid's Elements - 1833 - 346 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.... | |
| Euclid - 1835 - 540 pages
...of a triangle there be See N. drawn two straight lines to a point within the triangle, these sJiall **be less than the other two sides of the triangle,...two straight lines BD, CD be drawn from B, C, the** ends of the side BC of the triangle ABC to the point D within it ; BD and DC are less than the other... | |
| John Playfair - Geometry - 1836 - 148 pages
...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 drawn...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 - 488 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 drawn...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 - 290 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 be...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 - Euclid's Elements - 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.... | |
| Robert Simson - Geometry - 1838 - 434 pages
...greater than CA, and BC, CA greater than AB. Therefore any two sides, &c. Q,. ED PROP. XXI. THEOR. IF, **from the ends of the side of a triangle, there be...two straight lines BD, CD be drawn from B, C, the** ends of the side BC of the triangle ABC, to the point D within it ; BD and DC are less than the other... | |
| Euclides - 1838 - 264 pages
...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 drawn...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,... | |
| |