 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.  Robbin's New Plane Geometry - Page 173by Edward Rutledge Robbins - 1915 - 264 pagesFull view - About this book
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...CD2 = BC2, and also that AD2 + CD2 = AC2, we shall obtain BC2 = AB2 + AC2 + 2 AB x AD. THEOREM XvI. 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, diminished ly twice the product of one of these sides, Iy the projection... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...CD2 = BC2, and also that AD2 + CD2 = AC2, we shall obtain BC2 = AB2 + AC2 + 2AB x AD. THEORRM XVI. 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, diminished by twice the product of one of these sides, by the projection... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...square BCGF, are equivalent to the sum of the squares ABHL, ACI K. PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...square BCGP, are equivalent to the sum of tlie squares ABHL, ACIK. PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...are equivalent to the sum of the squares ABHL, ACI K. BOOK IV. ' PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | 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... | |
 | James Fraser (bp. of Manchester.) - 1866 - 480 pages
...altitudes are proportional to their bases. (Book IV., Prop. 3.) 8. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of tne base and the other side, diminished by brice (he rectangle of the base and the distance... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...BCGF, are equivalent to the sum of the squares ABHL, ACIK. BOOK IV. PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | 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
...square of either of the two small sides. Fig. 78. B m 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... | |
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