| Euclides - 1840
...side opposite to or subtending the greater angle is greater than the side opposite the less angle. **PROP. XX. THEOR. Any two sides of a triangle are together greater than the third side.** COR..—Hence the difference between any two sides of a triangle is less than the third side. • '•'.>... | |
| Euclides - 1841 - 351 sider
...to AB: neither is it less; because then the angle ABC A would be less* than the angle ACB; but it is **not: therefore the side AC is not less than AB; and...Let ABC be a triangle: any two sides of it together** shall be greater than the third side, viz. the sides BA, AC greater than the side BC; and AB, BC greater... | |
| John Playfair - 1842 - 317 sider
...less than AB ; 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...Let ABC be a triangle ; any two sides of it together** arc greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB, . BC greater... | |
| Chambers W. and R., ltd - 1842
...A proposition is first stated in general terms : take, for instance, the 20th proposition — '• **Any two sides of a triangle are together greater than the third side."** This is but bare assertion : to advance a step farther, Euclid places the figure referred to, namely,... | |
| Philip Kelland - 1843 - 147 sider
...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... | |
| John Playfair - 1844 - 317 sider
...-rT" less than AB; 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** suie. Let ABC be a triangle ; any two sides of it together arc greater than the third side, viz. the... | |
| 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 the... | |
| Royal Society of Edinburgh - 1880
...: — 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... | |
| 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,... | |
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