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" In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it. "
Elements of Geometry: Plane geometry - Page 148
by Andrew Wheeler Phillips, Irving Fisher - 1896
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...vertex of their included angle to the opposite side is 4; required the third side. THEOREM XIII. In any triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of (he other two sides phis twice the rectangle contained by one of these sides and the projection...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...that are divided internally or externally in medial section. In obtuse.angled triangles, the square on the side opposite the obtuse angle is equal to the sum of the squares on the other two sides increased by twice the rectangle contained by either of those sides...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...AD2 = AB*, and CD2 + AD2 = AC2 : hence, AB3 = BC2 + AC2 - 2BCxCD; PROPOSITION XIII. THEOREM. In any obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the base and the other side, increased by twice the rectangle of the base and the distance...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...right triangles, by § 338, and JD2+ (752= JO2. AB2= BC2+AC2- 2 BC x CD. PROPOSITION XII. THEOREM. 342. In an obtuse-angled triangle, the square of the side...opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection...
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...the product of one of these sides and the projection of the other upon it. 163. Theorem. In an obtuse triangle the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...the product of one of these sides and the projection of the other upon it. 163. Theorem. In an obtuse triangle the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...of the squares of the tsvo numbers diminished by twice their product. Proposition 27. Theorem. 331. In an obtuse-angled triangle, the square of the side...opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by twice the product of one of these sides by the projection...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...the squares of the two numbers diminished by twice their product. Proposition 27. Theorem. 331. In nn obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by twice the product of one of these nides by the projection...
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Manual of Plane Geometry: On the Heuristic Plan, with Numerous Extra ...

George Irving Hopkins - 1891 - 210 pages
...squares of the perpendicular, and then combine the terms by using Theorem 360 (a). 364. In an obtuse triangle the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, plus twice the product of one of those sides and the projection of...
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Examinations Papers

1891 - 644 pages
...that part together with the square on the other part. 6. In an obtuse-angled triangle the square on the side opposite the obtuse angle is equal to the sum of the squares on the other sides together with twice the rectangle contained by one of them and by the straight...
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