| Popular educator - 1852
...D. Therefore, if from a point without a given straight line, &c. QE.D. PROPOSITION XX.— THEOREM. **Any two sides of a triangle are together greater than the third** side. In fig. 20, let ABO be a triangle; MI. SO. any two of its sides are together greater than the... | |
| John Hind - 1855 - 328 páginas
...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... | |
| Thomas Reid - 1855 - 492 páginas
...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 - 1855
...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.,... | |
| 1856
...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... | |
| 1856
...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
...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... | |
| 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... | |
| Middle-class education - 1857
...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.... | |
| 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,... | |
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