 | John Hind - 1855 - 540 sider
...excluded. The circumstances here pointed out, are nothing more than what have all along been assumed, that any two sides of a triangle are together greater than the third : but it thus appears that the Algebraical Formulae are sufficient of themselves to determine the consistency... | |
 | Euclides - 1856 - 168 sider
...opposite the greater of the two AB, AC, or, in other words, AC is greater than A B. XXI.— EUCLID I. 20. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle (Fig. 14), take any side BA and produce it at one extremity to D,- making AD equal to AC the adjacent... | |
 | Cambridge univ, exam. papers - 1856 - 252 sider
...angles at the base, prove that the locus of the vertex is a hyperbola, and find its asymptotes. 1. ANY two sides of a triangle are together greater than the third side. If a polygon with only salient angles be situated inside another polygon, the perimeter of the former... | |
 | 1856 - 984 sider
...of its conclusions. They who can deny them, * Jxdtptndent for June 28, 1855. may as well deny that any two sides of a triangle are together greater than the third side, or the truth of any other demonstrable proposition.* What was the peculiar characteristic nature of... | |
 | 1856 - 422 sider
...restriction is plain, when we consider that he had previously proved in his Prop. XX., Book I. that any two sides of a triangle are together greater than the third. This, however, is manifest without demonstration, if we adopt Archimedes's definición of a straight... | |
 | Middle-class education - 1857 - 70 sider
...line. What figure would be formed by placing two equilateral triangles base to base ? 81. Prove that any two sides of a triangle are together greater than the third side. Is the same proposition true of the angles of a triangle ? Give reasons for your answer. 32. Prove... | |
 | JOHN GRAY - 1857 - 784 sider
...each ? 5. If a : b : : c : d show that a + b : J : : c + d : d and that am : b" : : C" : d" EUCLID. 1. Any two sides of a triangle are together greater than the third side. the squares of the sides containing it by twice the rectangle contained by the side upon which, when... | |
 | Elias Loomis - 1858 - 256 sider
...difference. Let two circumferences cut each other in the point A. Draw the radii CA, DA ; then, because any two sides of a triangle are together greater than the third side (Prop. VIII., B. I.), CD must be less than the sum of AD and AC. Also, DA must be less than the sum... | |
 | 1858 - 380 sider
...plane rectilineal angle, and show how to bisect one, that is, to divide it into two equal angles. 2. Any two sides of a triangle are together greater than the third side. Is the same proposition true of the angles of a triangle? 3. What is a parallelogram? Prove that the... | |
 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 sider
...line. What figure would be formed by placing two equilateral triangles base to base ? 31. Prove that any two sides of a triangle are together greater than the third side. Is the same proposition true of the angles of a triangle? Give reasons for your answer. 32. Prove geometrically... | |
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Any two sides of a triangle are together greater than the third side. 
