 | Euclides - 1834 - 518 pages
...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 - Geometry - 1836 - 148 pages
...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,... | |
 | 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.... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...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 - Euclid's Elements - 1837 - 290 pages
...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 - 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.... | |
 | Euclides - 1838 - 264 pages
...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 - Geometry - 1841 - 378 pages
...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 - 316 pages
...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 - Euclid's Elements - 1842 - 332 pages
...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.... | |
| |
If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. 
