| Robert Simson - 1806 - 518 páginas
...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 - 1809 - 524 páginas
...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 - 1811 - 128 páginas
...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... | |
| Charles Butler - 1814
...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
...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... | |
| Olinthus Gregory - 1816 - 244 páginas
...GB :: BF : BE ; which agrees with the proposition. PROP. XVII. 17. In any plane triangle it will be, **as twice the rectangle under any two sides, is to...the cosine of the angle contained by the two sides.** Let ABC be a plane triangle. From A, C one extremity of the base AB, draw AD perpendicular to the opposite... | |
| Euclides - 1816 - 528 páginas
...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 - 1827 - 513 páginas
...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 - 1834 - 427 páginas
...base made by a perpendicular let fall from the vertical angle. 18. In any plane triangle it will be, **as twice the rectangle under any two sides, is to...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
...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... | |
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