 | Thomas Perronet Thompson - 1833 - 168 σελίδες
...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 - 1833 - 346 σελίδες
...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 σελίδες
...; 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 - 1836 - 148 σελίδες
...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,... | |
 | 1836 - 488 σελίδες
...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 - 1836 - 488 σελίδες
...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 - 1837 - 112 σελίδες
...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 - 1837 - 290 σελίδες
...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 - 1837 - 332 σελίδες
...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 σελίδες
...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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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. 
