| Euclides - 1865
...to AB ; therefore AC is greater than AB. Wherefore, in any triangle, &c. QED PROP. XX.— THEOREM. **Any two sides of a triangle are together greater than the third** side, (References — Prop. I. 3, 5, 19 ; ax. 9.) Let ABC be a triangle. Then any two sides of it together... | |
| John Morley - 1867 - 290 páginas
...minds to any book they read are any less positive that it is a good book or a bad book, than they are **that any two sides of a triangle are together greater than the third** side. There is something delightful in the perfect conclusiveness and authority with which they pronounce... | |
| Euclid, Isaac Todhunter - 1867 - 400 páginas
...AB. Therefore AC is greater than AB. Wherefore, the greater angle &c. QED PROPOSITION 20. THEOREM. **Any two sides of a triangle are together greater than the third** side. Let ABC be a triangle : any two sides of it are together greater than the third side ; namely,... | |
| James Maurice Wilson - 1868
...the circles would not intersect. This limitation might be anticipated from the theorem before proved, **that any two sides of a triangle are together greater than the third** side. alone to effect what is performed in practice generally by means of the sector or protractor,... | |
| 1868
...another upon one side of it are either two right angles or are together equal to two right angels 20 3. **Any two sides of a triangle are together greater than the third** side 20 4. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles... | |
| 1903
...©cfdjaftSfttl beeinflufet. PURE MATHEMATICS I. (Geometry and Trigonometry.) Time — Three hours. 1. Prove **that any two sides of a triangle are together greater than the third.** A triangle is described upon a given base and with its vertex in a given straight line. Find the position... | |
| Charles Godfrey, Arthur Warry Siddons - 1903 - 355 páginas
...triangle to any point in the base is less than either of the equal sides of the triangle. THEOREM 18. **Any two sides of a triangle are together greater than the third** side. Data To prove that (1) Coiistructioi: Proof fig. 140. ABC is a triangle. (1) BA + AC>BC, (2)... | |
| Joseph Harrison - 1903 - 250 páginas
...notation used in connection with triangles. We here give some fundamental properties of triangles. (a) **Any two sides of a triangle are together greater than the third** side. — Or, Any side of a triangle is greater than the difference between the other two. In symbols... | |
| John Charles Stone - 1904 - 40 páginas
...apprehending the relations existing between these facts. When Euclid's followers were criticised for teaching **that " any two sides of a triangle are together greater than the third** side," as teaching that which even the beasts of the field know, the reply was, " We are not seeking... | |
| American Association for the Advancement of Science - 1904
...Theory of Functions. Moreover, underneath all this even is the assumption of the theorem, Euclid I, 20: **"Any two sides of a triangle are together greater than the third** side;" upon which proposition, which the Sophists said even donkeys knew, Hubert has thrown brilliant... | |
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