| Sir John Leslie - Geometry, Analytic - 1809 - 524 pages
...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... | |
| Charles Hutton - Mathematics - 1818 - 646 pages
...and CB, taken together (by constr.) ; therefore AC 4- CB is also greater than AB. '; ED Carol. The **shortest distance between two points, is a single...line drawn from the one point to the other. THEOREM** X1. THE Difference of any Two Sides of a Triangle, is Less than the Third Side. Let ABC be a triangle... | |
| Sir John Leslie - Geometry, Plane - 1820 - 465 pages
...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 - Mathematics - 1822 - 618 pages
...AC and CD, or AC and CB, taken together (by constr.) ; therefore AC+CB is also greater than AB. <(. **ED Corol. The shortest distance between two points,...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 ;... | |
| James Mitchell - Mathematics - 1823 - 576 pages
...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 - Architecture - 1823 - 596 pages
...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... | |
| George Lees - 1826
...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... | |
| Euclides - 1826
...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 - 180 pages
...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.... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...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... | |
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