 | Euclides - 1853 - 146 sider
...the point A. B For, if not, let it fall otherwise, if possible, as FGDH, and join AF, AG. And because two sides of a triangle are together greater than the third side, (1. 20.) 1. AG, 6F, are greater than FA; but FA is equal (I. Def. 15.) to FH, both being from the same... | |
 | Popular educator - 1852 - 1272 sider
...straight line A 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 - 496 sider
...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... | |
 | Euclides - 1855 - 270 sider
...lines can 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...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... | |
 | Thomas Reid - 1855 - 528 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 - 540 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... | |
 | Sir J Butler Williams - 1855 - 306 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... | |
 | Euclides - 1856 - 168 sider
...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 - 984 sider
...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 - 252 sider
...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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Any two sides of a triangle are together greater than the third side. 
