 | Thomas Simpson - 1821 - 426 sider
...above ACB. . ED PROPOSITION XI. Jin the base of any plane triangle is to the sum of the two sides, so is the difference of the sides to the difference of the segments of the base, made by a perpendicular falling from the vertical angle. - For, Let ABC be the proposed triangle,... | |
 | William Nicholson - 1821 - 356 sider
...IV. In any plane triangle, as the base, or greater side, is to the sum of the other two sides ; so is the difference of the sides to the difference of the segments of the base, made by a perpendicular let fall from the angle opposite to the base : and if half the difference... | |
 | Peter Nicholson - 1823 - 210 sider
...triangle, to the opposite side, which is the base ; then, as the base is to the sum of the two sides, so is the difference of the sides to the difference of the segments of the base. For, (theorem 62, page 56) AC*-CD*=AD* and, again, (theorem 62) BC*- CD*=BD*. Subtract the second... | |
 | Pierce Morton - 1830 - 584 sider
...the base, or of the base produced, may be stated thus : — the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base, or sum of the segments of the base produced. For it is shown (1. 38.) that the difference of... | |
 | William Galbraith - 1834 - 454 sider
...any plane triangle, when the three sides are given, I. As the base Is to the sum of the sides ; So is the difference of the sides To the difference of the segments of the base made by a perpendicular upon it, or upon it produced from the opposite angle. It may perhaps be... | |
 | John Playfair - 1837 - 332 sider
...the sides, and therefore (16. 6.) the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base. PROP. VI. THEOR. In, any triangle, twice the rectangle contained by any two sides is to the difference... | |
 | Thomas Holliday - 1838 - 404 sider
...given to find the angles. Rule.—As the base or greatest side is to the sum of the other two sides, so is the difference of the sides to the difference of the segments of the base made by a perpendicular, let fall from the greater angle upon the base. Then half this difference... | |
 | John Playfair - 1842 - 332 sider
...the sides, and therefore (16. 6.) the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base. PROP. VI. THEOR. In any triangle, twice the rectangle contained by any two sides is to the difference... | |
 | Euclid, John Playfair - 1846 - 334 sider
...the sides, and therefore (16. 6.) the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base. PROP. VI. THEOR. In any triangle, twice the rectangle contained by any two sides is to the difference... | |
 | Horatio Nelson Robinson - 1851 - 96 sider
...gives the following general principle : In any triangle, as the base is to the sum of the sidesy so is the difference of the sides to the difference of the segments of the base, From y-\-z, Take y— 2; Difference 2z. That is : From the base,, subtract the difference of... | |
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... the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base. 
