| 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... | |
| Theology - 1856 - 984 pages
...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
...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 pages
...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
...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... | |
| 1858 - 380 pages
...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... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...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... | |
| Thomas Sutton - Photography - 1858 - 448 pages
...Petzval's arrangement ; for it appears that CO is greater than Cm. The proof of this is easy enough. Any two sides of a triangle are, together, greater than the third, therefore OC and CA are together greater than AO, and therefore than Km. Take away the common part... | |
| Euclides - 1858 - 248 pages
...given difference A D. The figure ABC therefore is the triangle required. PROP. 20.— THEOR. side. Any two sides of a triangle are together greater than the third CONSTRUCTION. — Pst. 2. A st. line may be lengthened out in a st. line. P. 3. From the greater line... | |
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