| Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...(A) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of **the squares of the other two sides, minus twice the product of** those two sides, and the cosine of the angle included by them. First, let the triangle А В С be... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...opposite to an acute angle is equal to the sum of the squares of the other two sides diminished by **twice the product of one of these sides and the projection of the other** upon that side. Let (7 be an acute angle of the triangle ABC, A Pthe projection of A upon BC by the... | |
| Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...(А) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of **the squares of the other two sides, minus twice the product of** those two sides, and the cosine of the anale included by them. First, let the triangle А В С be... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...the sum of the squares of the two remaining sides is equal to twice the rectangle contained by either **one of these sides and the projection of the other side upon** that side. Fig- 35. F'g- 36. Let ABC be any triangle, then the square of any side, as AC, shall be... | |
| André Darré - 1872 - 226 pages
...H THEOREM. 91. In any triangle the square of a side opposite an acute angle is equal to the sum of **the squares of the other two sides, minus twice the product of one of these sides** by the projection on it of the other. Def. The projection of one line on another is the part of the... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...opposite to an acute angle is equal to the sum of the squares of the other two sides diminished by **twice the product of one of these sides and the projection of the other** •upon that side. Let C be an acute angle of the triangle ABC, P the projection of A upon BC by the... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...opposite to the obtuse angle is equal to the sum of the squares of the other two sides, increased by tunce **the product of one of these sides and the projection of the other** upon that side. Let C be the obtuse angle of the triangle ABC, -j^ P the projection of A upon BC (produced);... | |
| Harvard University - 1874 - 668 pages
...opposite to an acute angle is equal to the Bum of the squares of the other two sides diminished by **twice the product of one of these sides and the projection of the other** upon that side. 7. The area of a trapezoid is equal to the product of its altitude by half the sum... | |
| Henry Nathan Wheeler - Trigonometry - 1876 - 204 pages
...of half their difference . . 78 § 73. The square of any side of a triangle is equal to the sum of **the squares of the other two sides, minus twice the product of** those sides into the cosine of their included angle 73 § 74. Formula for the side of a triangle, in... | |
| Henry Nathan Wheeler - 1876 - 128 pages
...— C)' 6 — c tani(B — C)' § 73. The square 'of any side of a triangle is equal to the sum of **the squares of the other two sides, minus twice the product of** those sides into the cosine of their included angle. FIG. 43. FIG 44. Through c in the triangle ABC... | |
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