 | 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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Any two sides of a triangle are together greater than the third side. 
