In any triangle, the square of the 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 and the projection of the other side upon it. Plane Geometry - Page 197by John Charles Stone, James Franklin Millis - 1916 - 278 pagesFull view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by **twice the product of one of those sides and the projection of the other upon** that side. A Lot C be an acute angle of the triangle ABC, and DC the projection of AC upon B C. We... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...opposite the obtuse angle is equivalent to the sum of the squares of the other two sides increased by **twice the product of one of those sides and the projection of the other** on that side. A Let С be the obtuse angle of the triangle ABC, and С D be the projection of A С... | |
| William Frothingham Bradbury - Geometry - 1877 - 262 pages
...XXVIII. 68 1 In a triangle the square of a side opposite an acute angle is equivalent to the sum of **the squares of the other two sides minus twice the product of one of** these sides and the distance from the vertex of this acute angle to the foot of the perpendicular let... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...aide opposite the obtuse Z is cquivalent to the sum of the squares on the other two sides increased by **twice the product of one of those sides and the projection of** thе other on that side) ; and A~C* = STC* + AM* — 2MCX MD, §335 (in any Д the square on the side... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...[acute'] angle is equal to the sum of the squares of the other two sides [,£jj twice the rectangle **of one of those sides, and the projection of the other upon it.** HYPOTH. In the triangles ABC, the angle ACB is obtuse in Fig, 1, and acute in Figs. 2 and 3 (produced)... | |
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