| Euclides - 1855 - 270 pages
...be drawn to the given straight line, one upon , each side of the shortest line. : PROP. XX. THEOREM. **Any two sides of a triangle are together greater than the third side.** Let ABC be a triangle : any two of its sides are together greater than the third side ; viz., the sides... | |
| Thomas Reid - Intellect - 1855 - 528 pages
...this proposition, — Any two sides of a triangle are together equal to the third, — as of this, — **Any two sides of a triangle are together greater than the third;** yet the first of these is impossible. Perhaps it will be said, that, though you understand the meaning... | |
| Theology - 1856 - 984 pages
...force 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 pages
...this 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... | |
| Cambridge univ, exam. papers - 1856 - 252 pages
...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... | |
| Euclides - 1856 - 168 pages
...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... | |
| Middle-class education - 1857 - 70 pages
...straight 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 pages
...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... | |
| sir Thomas Dyke Acland (11th bart.) - 1858 - 270 pages
...straight 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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