 | Isaac Sharpless - Geometry - 1879 - 282 pages
...(7 * + CB * by 25(7. CD. Proposition 8. Theorem.—In every triangle the square of the side opposite an acute angle, is less than the sum of the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the line between the acute angle and the foot of... | |
 | Joseph Wollman - 1879 - 120 pages
...produced, a perpendicular be drawn from the opposite angle ; the square of the side subtending the acute angle is less than the sum of the squares of the sides containing the acute angle, by twice the rectangle contained by the side on which the perpendicular falls, and... | |
 | 1882 - 376 pages
...draw a right line bisecting the area of the triangle. 4. In any triangle, prove that the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle under either of these sides and the intercept... | |
 | 1882 - 486 pages
...therefore the triangle DHK is also one-fourth of ABC. (QED) 8. In any triangle, prove that the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle by twice the rectangle contained by either of these sides, and the... | |
 | James Andrew Blaikie, William Thomson - Geometry - 1891 - 160 pages
...squares of the sides of the figure FGHKED is 8BC2. See Ex. 11 (3). 19. In any triangle the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle. Use Euc. I. 47 and I. 24. 20. In an obtuse-angled triangle the... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...AB, together with twice the square on BC. BOOK II. PROPOSITION 13. In any triangle, the square on a side subtending an acute angle, is less than the sum of the squares on the other sides, by twice the rectangle contained by either of these sides, and the part of the... | |
 | 1894 - 786 pages
...World.vict akerofth« Baltic and the ' a"79 °f the happier d, ?reat Worl 6. In any triangle the square on a side subtending an acute angle is less than the sum of the squares on the sides containing that angle by twice a certain rectangle. Specify the rectangle and prove the... | |
 | John Macnie - Geometry - 1895 - 390 pages
...projection, and PB is the projection of AB. PROPOSITION XII. THEOREM. 350. In any triangle, the square of a side subtending an acute angle is less than the sum of the squares of the other sides by twice the rectangle contained by either of these sides and the projection upon it of... | |
 | 1898 - 830 pages
...base, it bisects every parallel to the base (4 marks'). 4. Prove that in any triangle the square of a side subtending an acute angle is less than the sum of the squares of the other sides by twice the rectangle contained by either of those sides and the straight line intercepted... | |
 | 1899 - 166 pages
...must be satisfied in each of the first two parts of the Paper.) 1. In any triangle, the square on a side subtending an acute angle, is less than the sum of the squares on the other sides, by twice the rectangle contained by either of these sides, and the part of the... | |
| |
In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the... 
