| Philip Kelland - 1843 - 147 páginas
...demonstrate to you the earlier theorems of Euclid's first Element. I can compel your assent to the truth of **the proposition, that " any two sides of a triangle are together greater than the third** side ;" and this without requiring from you any notion of a straight line at all. But I must stop here.... | |
| Charles Hutton - 1843
...Prove by means of the equations that connect the sides and angles of a spherical triangle, that (1.) **Any two sides of a triangle are together greater than the third.** (2.) The difference of two sides is less than the third. (3.) If three sides of a triangle be equal... | |
| 1844
...sides of the one shall be equal to the angle contained by the two sides equal to them of the other. 3. **Any two sides of a triangle are together greater than the third** side. 4. The straight lines which join the extremities of two equal and parallel straight lines towards... | |
| Scottish school-book assoc - 1845
...together less than AB, the circles would not intersect, and the construction, would be impossible ; hence **any two sides of a triangle are together greater than the third, which is** established in a different manner in (Prop. 13.) PROPOSITION V. — THEOREM. If two triangles, ABC... | |
| Royal Society of Edinburgh - 1880
...space : — That the greater side of every triangle has the greater angl* opposite, and conversely. **That any two sides of a triangle are together greater than the third** side. Also Euclid I. 21. Euclid I. 24 and 25. Euclid I. 26 (the second part). Also the usual propositions... | |
| Euclid, James Thomson - 1845 - 352 páginas
...not equal to AB : therefore AC is greater than AB. Wherefore, if two angles, &c. PROP. XX. THEOB. — **Any two sides of a triangle are together greater than the third** side.t * Let the learner compare thia proposition and the following with the 5th and G1h of this book.... | |
| Euclid - 1845 - 199 páginas
...; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROPOSITION XX. THEOR. — **Any two sides of a triangle are together greater than the third** side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the... | |
| Euclides - 1845
...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,... | |
| Sir J. Butler Williams - 1846 - 330 páginas
...than the true length : this follows from Euclid's 20th proposition of the first book, which proves **that any two sides of a triangle are together greater than the third.** Also, the frequent repetition of errors in the coincidence of the extremities of the chain with the... | |
| John Playfair - 1846 - 317 páginas
...and it has been shewn that it is not equal to AB ; therefore AC is greater than AB. PROP. XX. THEOR. **Any two sides of a triangle are together greater than the third** side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the... | |
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