 | Robert Simson - Trigonometry - 1806 - 548 pages
...plane triangle, 8cc. QED PROP. V. FIG. 9, 10. IN any plane triangle, twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides, and the square of the base as the radius is to the co-sine of the angle included by... | |
 | Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...In any triangle, as twice the rectangle under two sides, is to the difference between their squares and the square of the base, so is the radius, to the cosine of the contained angle. In the triangle ABC, 2AB x BC : AB' + AC* — BC' R:Cos,BAC. For let fall the perpendicular... | |
 | Francis Nichols - Plane trigonometry - 1811 - 162 pages
...sides is to the difference between the sum of the squares of those sides and the square of the base, as the radius to the cosine of the angle contained by the two sides. Let ABC be any triangle; 2 AB. BC : difference between AB2+BC2 and AC2 :: R : cos. B. A A B D C B CD From A draw... | |
 | Charles Butler - Mathematics - 1814 - 528 pages
...the angles are found by this proposition. 71. In a plane' triangle, twice the rectangle contained by any two sides, is to the difference of the sum of the squares of these two sides and the square of the base, as radius to the co-sine of the angle contai-ned by the... | |
 | Charles Butler - 1814 - 582 pages
...angles are found by this proposition. 71- In a plane triangle, twice the rectangle contained bjacj two sides, is to the difference of the sum of the squares of these two sides and the square of the base, as radius to the co-sine of the angle contained by the... | |
 | Euclides - 1816 - 592 pages
...plane triangle, &c. Q. E, D. PROP. V. FIG. 9. and 10. IN any triangle, twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides, and the square of the base, as the radius is to the cosine of the angle included by... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...plane triangle, Sic. QED PROP. V. FIG. 9 and 10. In any triangle, twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides, and the square of the base, as the radius is to the cosine of the angle included by... | |
 | Olinthus Gregory - Mathematics - 1834 - 480 pages
...difference of the segments of the base made by a perpendicular let fall from the vertical angle. 18. In any plane triangle it will be, as twice the rectangle...the cosine of the angle contained by the two sides. Cor. When unity is assumed as radius, then if A c, AB, B c, are the sides of a triangle, this prop,... | |
 | Euclides - 1834 - 518 pages
...plane triangle, &c. Q. JE. a. PROPOSITION V. In any triangle, twice the rectangle contained by any tn-n sides, is to the difference of the sum of the squares of these two sides, and the square of the base, as the radius is to the cosine of the angle included by... | |
 | John Playfair - Geometry - 1836 - 148 pages
...Therefore, in any plane triangle, &c. QED PROP. V. In any triangle, twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides, and the square of the base, as the radius is to the co-sine of the angle included... | |
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In any plane triangle, as twice the rectangle under any two sides is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides. 
