| John Hind - 1855 - 328 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
...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
...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
...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
...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
...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
...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 - 234 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
...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
...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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