| Euclides - 1838 - 264 pages
...' Wherefore the greater angle, &c. Q. un PROP. XX. THEOR. Any two sides of a triangle are toget/ier **greater than the third side. 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... | |
| 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... | |
| 708 pages
...height of the fixed stars ? Is this what you really mean to assert to be as demonstrably true as that **any two sides of a triangle are together greater than the third side** ? Every mathematician would answer — it is : nay, more, that this very curve would carry a body from... | |
| 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. • '•'.>... | |
| Euclides - 1841 - 378 pages
...shown that it is not equal to AB; therefore AC is greater than AB. Wherefore the greater angle, &c. QED **PROP. XX. THEOR. Any two sides of a triangle are together...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 - Euclid's Elements - 1842 - 332 pages
...angle ABC would be less (18. 1.)than the angle ACB ; but it is not ; therefore the side AC is not -gj=^ **less than AB ; and it has been shewn that *-' it is...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 - 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... | |
| |