| sir George Ramsay (9th bart.) - 1853 - 282 pages
...14. Alexander conquered Darius. 15. The three angles of a triangle are equal to two right lines. 16. **Any two sides of a triangle are together greater than the third side.** 17. The French Convention treated Louis XVI. cruelly. 18. The Chamber of Peers condemned Ney to death... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...AB ; therefore AC is greater than AB. "Wherefore the greater angle, etc. QED PROPOSITION XX. THEOB. **Any two sides of a triangle are together greater than the third side.** Produce BA to the point D, and make (3. i.) AD equal to AC, and join DC. Because DA is equal to AC,... | |
| Euclides - 1853 - 146 pages
...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 - 1854 - 1274 pages
...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 - Bible - 1854 - 496 pages
...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 - 262 pages
...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 - 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... | |
| John Hind - Trigonometry - 1855 - 546 pages
...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 - 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 adjacent... | |
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