| Charles Hutton - Mathematics - 1816 - 610 pages
...points, is a single right line drawn from the one point to the other. THEOREM XI. THE Difference of **any Two Sides of a Triangle, is LesS than the Third Side.** Let ABC be a triangle ; then will the difference of any two sides, as AB — AC, be less than the third... | |
| Sir John Leslie - Geometry, Modern - 1820 - 488 pages
...and BC, the two 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... | |
| Charles Hutton - Mathematics - 1822 - 616 pages
...points, is a single right line drawn from the one point to the other. THEOREM XI. THK Difference of **any Two Sides of a Triangle, is Less than the Third Side.** Let ABC be a triangle ; then will the difference of any two sides, as AB — AC, be less than the third... | |
| James Mitchell - Mathematics - 1823 - 666 pages
...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... | |
| Euclid - 1826 - 234 pages
...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.... | |
| Euclides - 1826 - 226 pages
...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.... | |
| George Lees - 1826 - 276 pages
...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, James Thomson - Geometry - 1837 - 410 pages
...greater than CA, and BC, CA greater than AB. Therefore, any two sides, &c. Cor. Hence the difference of **any two sides of a triangle, is less than the third...For, since BA and AC are together greater than BC,** from each of these take AC; then (I. ax. 5.) BA is greater than the excess of BC above AC. PROP. XXI.... | |
| Charles Reiner - Geometry - 1837 - 246 pages
...by the greater side. 14. Any two sides of a triangle are together greater than the third side. 15. **The difference between any two sides of a triangle is less than the third side.** 16. The three sides of every triangle are together greater than double the length of any one side.... | |
| Euclides - 1840 - 192 pages
...19). But BD = BA + AC (const.), which are therefore greater than the third side BC. COR. — Hence **the difference between any two sides of a triangle is less than the third side. For** the greater of those two sides is equal to the less side and the difference between them ; but, by... | |
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