| John Hymers - Logarithms - 1841 - 244 pages
...sin Л а sin B b' It A = 90°, we still have, in conformity with the theorem, 6 sin В = . a 92. In any triangle, the square of any side is equal to the sum of the squares of the two other sides, diminished by twice the product of these sides and the cosine of the... | |
| John Hymers - Logarithms - 1858 - 324 pages
...but BA = BD — AD ; If A = 90° we still have in conformity with the theorem, с = a cos B. 92. In any triangle, the square of any side is equal to the sum of the squares of the two other sides, diminished by twice the product of these sides and the cosine of the... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...(94) or, as it may be written, a + b : a — b : : tan £ (A -\- B) : tan £ (A — B). (95) 113. In any triangle, the square of any side is equal to the sum of the squares of the two other sides, diminished by twice the rectangle of these sides multiplied by the... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...£) or, as it may be written, a-\-b : a — b : : tan £ (A + -B) : tan (94) — .B). (95) 113. ./« any triangle, the square of any side is equal to the sum of the squares of the two other sides, diminished by twice the rectangle of these sides multiplied by the... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...— B) ' « + 6 __ tan % (A + B) tan ^ (A — B) ' (94) (A -\- B) : tan £ (A — B). (95) B 113. In any triangle, the square of any side is equal to the sum of the squares of the two other sides, diminished by twice the rectangle of these sides multiplied by the... | |
| Dublin city, univ - 1878 - 498 pages
...circle : — (a). Any side is equal to twice the tangent from its middle point to the circle. (4). The square of any side is equal to the sum of the squares of the tangents from its extremities to the circle. 14. A square is described on the hypotheneuse... | |
| Simon Newcomb - Trigonometry - 1882 - 372 pages
...required parts of the triangle from the altitude. CASE III. Given the three sides. THEOREM III. In a triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides into the cosine of the angle... | |
| Webster Wells - Trigonometry - 1883 - 234 pages
...Since the result (80) may also be written a+b _ COt i Ü ХддЧ а — b tan b (A — В) 146. In any triangle the square of any side is equal to the sum of the squares of the other two sides, minus twice their product into the cosine of their included angle.... | |
| Webster Wells - Trigonometry - 1887 - 200 pages
...£ C a — b~tau$(A — B)' (51) 116. In any triangle, the square of any side is equal to the sum of the squares of the other two sides, minus twice their product into the cosine of their included angle. CASE I. When the included angle A is acute. 0 ъ, FIG. 1. There will be two cases, according as the... | |
| Webster Wells - Plane trigonometry - 1887 - 158 pages
...+ В = 180° - С, we have Thus formula (48) may be put in the form a + b _ cot ^ С '51-. 116. In any triangle, the square of any side is equal to the sum of the squares of the other two sides, minus twice their product into the cosine of their included angle.... | |
| |