 | Edward Olney - Geometry - 1872 - 562 pages
...shortest distance between two points is a straight line. 2 To. COR. 2. — TJie difference bet 'ween any two sides of a triangle is less than the third side. DEM. — Let a, b, and e be the sides. By Corollary 1st, a + b > e. Therefore, transposing, a > e —... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...triangle is also equiangular. 5. Any side of a triangle is less than the sum of the other Y. two. 6. The difference between any two sides of a triangle is less than the other side. T. The side in a right-angled triangle opposite the right angle is the longest. 8. In every... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...any point within it to the opposite sides are together greater than the semi-perimeter of the A . 19. The difference between any two sides of a triangle is less than the third side. 20. Find the shortest path from a given point in one of two straight lines to the other, and then back... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...away either of the sides AS, SC, as SC, for example, there will remain (A. 5), AC - SC < AS; that is, the difference between any two sides of a triangle is less than the third side. Scholium. In order that any three given lines may represent the sides of a triangle, the sum of any... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...equilateral triangle is also equiangular. 5. Any side of a triangle is less than the sum of the other two. 6. The difference between any two sides of a triangle is less than the other side. 7. The side in a right-angled triangle opposite the right angle is the longest. 8. In every... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...letting fall a perpendicular from any angle on the opposite side. Cor. — Hence the difference of any two sides of a triangle is less than the third side. For since AB and BC are greater than AC, if BC be taken from both, we shall have (ax. 5.) AB greater... | |
 | Edward Atkins - 1874 - 426 pages
...within, then the line bisecting the third angle will pass through the same point. 22. The difference of any two sides of a triangle is less than the third side. 23. If the angles at the base of a right-angled isosceles triangle be bisected, the bisecting line... | |
 | Edward Atkins - 1876 - 130 pages
...within, then the line bisecting the third angle will pass through the same point. 22. The difference of any two sides of a triangle is less than the third side. 23. If the angles at the base of a right-angled isosceles triangle be bisected, the bisecting lino... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...point A may be to the line BC. It may be easily shewn from this proposition, that the difference of any two sides of a triangle is less than the third side. Prop. xxn. When tlie sum of two of the lines is equal to, and when it is less than, the third line;... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...PHEOR. 12. Any two sides of a triangle are together greater than the third side. COR. The difference of any two sides of a triangle is less than the third side. THEOR. 13. If from the ends of the side of a triangle two straight lines are drawn to a point within... | |
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The difference between any two sides of a triangle is less than the third side. 
