 | Sir John Leslie - 1809 - 542 ページ
...sides AB and BC are together greater than the third AC. PROP. XVII. THEOR. The- difference between two sides of a triangle is less than the third side. Let the side AC be greater than AB, and from it cut off a part AE equal to AB ; the remainder EC is less... | |
 | Sir John Leslie - 1820 - 482 ページ
...sides AB and BC are together greater than the third side AC. PROP. XV. THEOR. The difference between any two sides of a triangle is less than the third side. • Let the side AC be greater than AB, and from it cut off a part AE equal to AB ; the remainder EC is less... | |
 | Charles Hutton - 1822 - 616 ページ
...it, must necessarily be greater, o.. ED THEOREM X. THE Sum of any Two Sides of a Triangle is Greater than the Third Side. Let ABC be a triangle ; then will the . lum of .ny two of its side* be greater than the third side, as for instances, AC -J-cB greater than... | |
 | James Mitchell - 1823 - 666 ページ
...limitation arises from a known geometrical problem, though it is not found in Muclid's " Elements;" viz. "The difference of any two sides of a triangle is less than the third side." PROS. 4. Giving the hypothenuse of aright-angled triangle, and the side of its inscribed square, to... | |
 | Peter Nicholson - 1823 - 210 ページ
...KL, FL, FQ. Then, by hypothesis, the angle KML=fML, KM=/M, and LM is common, the base LK is =Li/; but the difference of any two sides of a triangle is less than the third ;* therefore FL — LK, or FL - L/, is less than FK, or F/, or FM -/M, or FQ -/Q. Hence/L is greater... | |
 | Euclides - 1826 - 226 ページ
...and the sides вс, CA, greater than AB. Therefore two sides of every triangle, &c. Deductions. 1. The difference of any two sides of a triangle is less than the third side. 2. Two sides of a triangle are together greater than twice the line from the vertex bisecting the base.... | |
 | Euclid - 1826 - 234 ページ
...and the sides вс, CA, greater than AB. Therefore two sides of every triangle, &c. Deductions. 1 . The difference of any two sides of a triangle is less than the third side. 2. Two sides of a triangle are together greater thaa twice the line from the vertex bisecting the base.... | |
 | George Lees - 1826 - 276 ページ
...is less than the more remote ; there can be two equal lines, but there cannot be more than two. 5. The difference of any two sides of a triangle is less than the third side. 6. If, from the vertex of a triangle, two straight lines be drawn, one of which is perpendicular to... | |
 | Euclid, Dionysius Lardner - 1828 - 542 ページ
...should be adopted as a geometrical axiom (55). (99) It follows immediately from this proposition, that the difference of any two sides of a triangle is less than the remaining side. For the sides AC and BC together are greater than AB ; let the side AC be taken from... | |
 | William Grier - 1836 - 384 ページ
...any two of its sides be greater than the third side; as, for instance, AC + CB greater than AB. 1 1. Let ABC be a triangle ; then will the difference of...sides, as AB — AC, be less than the third side BC. 12. Let the line EF cut the two parallel lines AB, CD; then will the angle AEF be equal to the alternate... | |
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AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. 
