 | Euclides - 1865 - 402 pages
...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... | |
 | Robert Potts - 1865 - 528 pages
...AB ; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROPOSITION XX. THEOREM. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle. Then any two sides of it together shall be greater than the third side,... | |
 | John Morley - Conduct of life - 1867 - 308 pages
...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 - Euclid's Elements - 1867 - 426 pages
...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 - Geometry - 1868 - 132 pages
...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 - 876 pages
...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 - 898 pages
...©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 - Geometry - 1903 - 384 pages
...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 (A.M.I.C.E.) - Geometry - 1903 - 300 pages
...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 - Geometry - 1904 - 60 pages
...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... | |
| |
Any two sides of a triangle are together greater than the third side. 
