| Jeremiah Day - Measurement - 1831 - 394 pages
...a different way, by the following proposition. THEOREM B. In a plane triangle, twice the product of **any two sides, is to the difference between the sum...the squares of those sides, and the square of the** third side, as radius to the cosine of the angle included between the two sides. In the triangle ABC,... | |
| John Playfair - Euclid's Elements - 1832 - 358 pages
...the base. QED PROP. VI. THEOR. In any triangle, twice the rectangle contained by any two sides is !o **the difference between the sum of the squares of those...the base, as the radius to the cosine of the angle** included by the two sides. LetABCbeanytriangIe,2AB.BCis to the difference 'between ABa+BCa and AC*... | |
| Euclid - 1835 - 540 pages
...&c. QED PROP. VI. FIG. 9. & 10. In any triangle, twice the rectangle contained by any two adjacent **sides is to the difference between 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 - 1835 - 544 pages
...&c. QED PROP. VI. FIG. 9. & 10. In any triangle, twice the rectangle contained by any two adjacent **sides is to the difference between 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 - Euclid's Elements - 1836 - 488 pages
...of the sides to the difference of the segments of the base. QE Don PROP. VI. t . . In any trianglei **twice the rectangle contained by any two sides is...the base, as the radius to the cosine of the angle** included by the two sides. Let ABC be any triangle, 3AB.BC is to the difference between AB2 + BC2 and... | |
| Mathematics - 1836 - 488 pages
...opposite angles, to the tangent of half their difference. In a plane triangle, twice the product of **any two sides, is to the difference between the sum...the squares of those sides, and the square of the** third side, as radius to the cosine of the angle included between the two sides. CONIC SECTIONS. 16th... | |
| John Playfair - Geometry - 1836 - 148 pages
...to the tangent of half their difference. 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... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...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...the base, as the radius to the cosine of the angle** included by the two sides. • Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2... | |
| Jeremiah Day - Geometry - 1838 - 416 pages
...a different way, by the following proposition. THEOREM B. In a plane triangle, twice the product of **any two sides, is to the difference between the sum...the squares of those sides, and the square of the** third side, as radius to the cosine of the angle included between the two sides. In the triangle ABC,... | |
| Jeremiah Day - Geometry - 1839 - 434 pages
...a different way, by the following proposition. THEOREM B. In a plane triangle, twice the product of **any two sides, is to the difference between the sum...the squares of those sides, and the square of the** third side, as radius to the cosine of the angle included between the two sides. In the triangle ABC,... | |
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