 | Euclides - 1865 - 402 sider
...BDC greater than ttxe angle BAC. Therefore, if from the ends, &c. QED PROP. XXII.— PROBLEM. To mahe a triangle of which the sides shall be equal to three given straight lines, but of which any two whatever must be greater than the third. (References — Prop. I. 3 ; post. 3; ax.... | |
 | Robert Potts - 1865 - 528 sider
...namely, A and B greater than C; A and C greater than B ; and B and C greater than A. It is required to make a triangle of which the sides shall be equal to ../,/.', C, each to each. A B C Take a straight line DE terminated at the point D, but unlimited towards... | |
 | John Playfair - 1855 - 350 sider
...angle CEB ; much more then is the angle BDC greater than the angle PROP. XXII. PROS. To -construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of tfiese lines must be greater than the third (20. 1.). Let A, B, C be the three given •traight lines,... | |
 | Euclid, Isaac Todhunter - 1867 - 424 sider
...angle CEB of the triangle ABE is greater than the angle BAE. But it has been shewn that the angle BDC is greater than the angle CEB; much more then is the angle BDC greater than the angle BAC. Wherefore, if from the ends &c. QED PROPOSITION 22. PROBLEM. To make a triangle of which the sides... | |
 | Euclid, Isaac Todhunter - 1867 - 426 sider
...angle CEB of the triangle ABE is greater than the angle BAE. But it has been shewn that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC. Wherefore, if from the ends &c. QED PROPOSITION 22. PROBLEM. To make a triangle of which the sides... | |
 | Robert Potts - 1868 - 434 sider
...and it has been demonstrated, that the angle BDCis greater than the angle CEB; much more therefore is the angle BDC greater than the angle BAC. Therefore, if from the ends of the side, &c. QED PROPOSITION XXII. PROBLEM. To mala a triangle of which the tides skull be equal to... | |
 | Edinburgh univ - 1868 - 336 sider
...ALGEBRA. 23^ October 1867. 1. To bisect a given rectilineal angle. 2. To construct (when possible) a triangle of which the sides shall be equal to three given straight lines. State the condition under which it is possible. 3. If a straight line be divided into any two parts,... | |
 | Euclides - 1870 - 270 sider
...P. 20. 5 Add. 6 Ax. 4. 7 D. 3. 8 9 a fort. P. 16. 10 P. 16. 11 it fort. Recap. 12 PBOP. 22.— PROR To make a triangle, of which the sides shall be equal to three given st. lines, but any two whatever ^ of these must be greater than the third. SOL. — P. 3. From the... | |
 | Euclides, James Hamblin Smith - 1872 - 376 sider
...than the perimeter of the triangle, and greater than half the perimeter. PROPOSITION XXII. PROBLEM. To make a triangle, of which the sides shall be equal to three given straight lines, any two of which are greater than the third. Let A, B, C be the three given lines, any two of which... | |
 | Lewis Sergeant - 1873 - 182 sider
...either of the interior opposite angles. Prove this. (See Geom., Prop. 14.) 5. Show how to construct a triangle of which the sides shall be equal to three given straight lines. (See Geom., Prop. 20.) Why must any two be greater than the third ? Show by figure what will happen... | |
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To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i. 
