| 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... | |
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