 | Sir J Butler Williams - Surveying - 1855 - 306 pages
...the true length : this follows from Euclid's 20th proposition of the first book, which proves that any two sides of a triangle are together greater than the third. Also, the frequent repetition of errors in the coincidence of the extremities of the chain with the... | |
 | 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... | |
 | 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 equal to AC the... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
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Any two sides of a triangle are together greater than the third side. 
