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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

The Student's Guide to Accountancy

Lawrence Robert Dicksee - Accounting - 1907 - 128 pages
...the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by one of those sides and the projection of the other side upon it. Q. 8. — Prove that the opposite angles of any quadrilateral inscribed in a circle are together equal...

A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908 - 286 pages
...sum of the squares on the sides containing that angle diminished by twice the rectangle contained by one of those sides and the projection of the other side upon it. 227 THEOREM 56. In any triangle the sum of the squares on two sides is equal to twice the square on...

Plane Geometry

Fletcher Durell - Geometry, Plane - 1909 - 360 pages
...THEOREM 349. In any oblique triangle, the square of a 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 time sides by the projection of the other side upon it. KB. 2 Given acute ZC in A ABC, and DC the projection...

Exercises in Geometry

Grace Lawrence Edgett - Geometry - 1909 - 104 pages
...incommensurable. 9. The square of the side opposite an acute angle, in any triangle, 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. 10. In any obtuse-angled triangle the square...

Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...XXXVII. THEOREM. 398. 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 diminished by twice the product of one of those sides by the projection of the other upon that side. Given the A ABC, £ A being acute and CD J. AB. To prove...

Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...triangle the square on the side opposite an acute angle is equivalent to the sum of the squares on the other two sides diminished by twice the product of one of those sides by the projection of the other upon that side. c a' DB FIG. 1 FIG. 2 Given the triangle ABC, A being...

Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...side opposite an acute angle is equal to the sum of the squares of the other two sides diminished % twice the product of one of those sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove...

The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 358 pages
...squares. 1 THEOREM. 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 by the projection of the other upon that side. THEOREM. A similar statement for the obtuse triangle....