 AA' and BB' be perpendicular to line CD, the projection of line AB upon line CD is line A'B'. PROP. XXV. THEOREM 277. 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...  Elements of Plane Geometry - Page 136by Franklin Ibach - 1882 - 196 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... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...twice the rectangle contained by either side and the projection on it of the other side. THEOR. n. In any triangle the square on the side opposite an acute angle is less than the squares on the other two sides by twice the rectangle contained by either side and... | |
 | 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
...the foot of the perpendicular С P ; that is, D P. GEOMETRY. BOOK IV. PROPOSITION IX. THEOREM. 335. In any triangle, the square on the side opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by twice the product of one... | |
 | James Maurice Wilson - 1878 - 450 pages
...CB* + BD* + 2CB. BD, (by n. 6,) therefore AC* = AB* + BC*+iCB. BD. SECT. I.] THE TRIANGLE. THEOREM u. In any triangle the square on the side opposite an acute angle is less than the squares on the other two sides by twice the rectangle contained by either side and... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...XXVIII. 68. 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... | |
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