 | Thomas Holliday - Surveying - 1838 - 404 pages
...perpendicular to the base. A scalene triangle has all its sides and angles unequal. See fig. 7. Note 1. Any two sides of a triangle are together greater than the third side. 2. The greatest side of every triangle is opposite the greatest angle; and the greatest angle is also... | |
 | 1839 - 92 pages
...day passed on tolerably smoothly with one exception, that when the doctor (arguing very soundly that any two sides of a triangle are together greater than the third side) was taking a shorter cut across a field, his career was stopped about midway by his horse inserting... | |
 | Euclides - 1840 - 82 pages
...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. • '•'.>... | |
 | Chambers W. and R., ltd - 1842 - 744 pages
...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 - Algebra - 1843 - 168 pages
...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 - Mathematics - 1843 - 570 pages
...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 - Euclid's Elements - 1844 - 338 pages
...-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... | |
 | Education - 1844 - 688 pages
...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 - Science - 1880 - 864 pages
...: — 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 - 444 pages
...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,... | |
| |
Any two sides of a triangle are together greater than the third side. 
