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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.
Schultze and Sevenoak's Plane and Solid Geometry - Page 192
by Arthur Schultze, Frank Louis Sevenoak - 1918 - 457 pages

Treasurer's Report ...: Also, Reports of the Selectmen; the Trustees of the ...

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...

Elements of Geometry

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...

Elements of Geometry

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?...

Elements of Plane Geometry

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...

Elements of Plane and Solid Geometry

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\...

Plane and Spherical Trigonometry

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...

The College Student's Manual: A Hand-book of Reference for Professors ...

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...

Plane and Spherical Trigonometry: G. A. Wentworth ...

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...