 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 those sides and the projection of the other upon that side.  Plane and Solid Geometry - Page 168by Isaac Newton Failor - 1906 - 418 pagesFull view - About this book
 | Brookline (Mass.) - Brookline (Mass.) - 1881 - 672 pages
...work. 3. In any triangle, the square of the side 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. Prove. 4. To find a mean proportional between... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...less than the sum of the squares on the other two sides by twice the rectangle contained by either of those sides and the projection of the other side upon it. Hypothesis. ABC, any triangle having the angle at A acute ; CD, the perpendicular dropped from C on... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...§335 (in any Л the. square on the side opposite an acute Z is equivalent to the sum of the squares on the other two sides, diminished by twice the product of one of those sides and the projection of tlie other upon that side). Add these two equalities, and observe that BM = M С. . Then A~ff + AC?... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...square on the side opposite an acute anale equals the sum of the squares of the other two sides minus twice the product of one of those sides and the projection of the other upon that side. In the A ABC, let с be an acute Z., and PC the projection of AC upon BC. A To prove... | |
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...opposite an acute Z is equivalent to the sum of the squares on the other two sides, .diminished bg twice the product of one of those sides and the projection of the other upon that side). Add these two equalities, and observe that BM = MC. Then A~& + AG1 = 2 BM* + 2 A~Ж\... | |
 | George Albert Wentworth - Trigonometry - 1882 - 234 pages
...and the law may be stated as follows : The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle. § 38. LAW OF TANGENTS. By § 36, a : b = sin A : sin... | |
 | Henry Elmer Moseley - Universities and colleges - 1884 - 214 pages
...chords. 6. Prove that the square of a side of a triangle 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 and the projection of the other upon that side. 7. Two tangents drawn from the same point... | |
 | George Albert Wentworth - Trigonometry - 1884 - 330 pages
...and the law may be stated as follows : The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle. § 38. LAW OF TANGENTS. By § 36, a : b = sin A : sin... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...less than the sum of the squares on the other two sides by twice the rectangle contained by either of those sides and the projection of the other side upon it. HYPOTHESIS. A ABC, with £ C acute. CONCLUSION, c2 -f- zbj = a2 -f- b2. PROOF. By 295, ^_ b2 + j2 =... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...THEOREM. 341. 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 and the projection of the other side upon it. T> D Let C be an acute angle of the triangle... | |
| |
