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" 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 and the projection of the other side upon it. "
Elements of Geometry: With Notes - Page 35
by John Radford Young - 1827 - 208 pages
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...of a straight line upon two parallel lines are equal. PLANE GEOMETRY. Proposition 151. Theorem. 186. 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 these...
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 55-59

United States Naval Academy - 1899 - 624 pages
...(internally) by the bisector of the opposite angle. Question 4. (a) State and prove the proposition that ' ' In any triangle the square of a side opposite an acute angle is equal to," etc. State the similar proposition for the square of a side opposite an obtuse angle. (b)...
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Questions Set at the Examinations, Volume 1905

College Entrance Examination Board - Universities and colleges - 1905 - 130 pages
...number of degrees contained in the sum of angles A and C. 2 Complete and prove the following statement : In any triangle the square of a side opposite an acute angle is equal to the sum of the squares . . . In the triangle ABC, AB=i, HC=8, and CA =5 ; find the projection...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...notations used in the following Propositions are in accordance with (230). PROPOSITION XXXVII. THEOREM 320. 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...
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Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...upon another line to which it is oblique is less than the line itself. PROPOSITION XII. THEOREM 659. In any triangle the square of a 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...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...notations used in the following Propositions are in accordance with (230). PKOPOSITION XXXVII. THEOREM 320. 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...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...notations used in the following Propositions are in accordance with (230). PROPOSITION XXXVII. THEOREM 320. 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...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...upon another line to which it is oblique is less than the line itself. PROPOSITION XII. THEOREM 659. In any triangle the square of a 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...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...a line 10 ft. long, divided internally in extreme and mean ratio. PROPOSITION 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 tivice the product of one of those...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...16, find p. Ex. 956. In A abc, if 6 = 15, p = 9, and c = 25, find o. PROPOSITION XXXVI. THEOREM 331. 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...
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