| 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 third... | |
| John Cumming - 1854
...are not equally important. Two and two are four, is a truth ; the sun rises and sets, is a truth ; **any two sides of a triangle are together greater than the third side,** is a truth ; the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares... | |
| John Playfair - 1855 - 318 sider
...than AB ; and it has been shewn that it is not equal to AB ; therefore AC is greater than AB. — — **PROP. XX. THEOR. Any two sides of a triangle are together...Let ABC be a triangle ; any two sides of it together** arc greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB, BC greater... | |
| 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., the sides BA, AC, are greater than the... | |
| Sir J Butler Williams - 1855 - 272 sider
...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 - 1855 - 492 sider
...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... | |
| 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... | |
| 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... | |
| 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... | |
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