| Euclides - 1834
...than AB. Therefore, any two sides, &c. QED PROPOSITION XXI. See N. THEOR. — If from the ends of the **side of a triangle, there be drawn two straight lines...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 - 1836 - 114 sider
...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 two straight lines...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,... | |
| 1836 - 472 sider
...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.... | |
| Euclides - 1837 - 88 sider
...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 two straight lines...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 - 1837 - 240 sider
...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 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.... | |
| John Playfair - 1837 - 318 sider
...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
...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 two straight lines...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,... | |
| Euclides - 1841 - 351 sider
...BC, CA greater than AB. Therefore any two sides, &c. UED PROP. XXI. THEOR. If from the ends of the **side of a triangle, there be drawn two straight lines...be less than the other two sides of the triangle,** out shall contain a greater angle. Let ABC be a triangle, and from the points B, C, the ends of the... | |
| Euclides - 1842
...вc, CA greater than AB. Therefore any two sides, &c. QED PROP. XXI. THEOR. IF from the ends of the **side of a triangle there be drawn two straight lines...within the triangle, these shall be less than the** two other sides of the triangle, but shall contain a greater angle. Let the two straight lines BD,... | |
| John Playfair - 1842 - 317 sider
...from B to C ; therefore BC is less than BA+AC or BA+AC>BC. PROP. XXI. THEOR. 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.... | |
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