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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, minus twice the product of one of these sides and the projection of the other side upon it. "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 190
1898 - 208 pages
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...XXVIII. 68 1 In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular let fall upon this side...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...XXVIII. 68. In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular let fall upon this side...
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Treasurer's Report ...: Also, Reports of the Selectmen; the Trustees of the ...

Brookline (Mass.) - Brookline (Mass.) - 1881 - 674 pages
...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 two given straight lines. Proof of work....
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...THEOREM VII. 259. In any triangle, the square on the side opposite an acute angle. 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 c be an acute Z., and...
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Elements of Plane and Spherical Trigonometry with Logarithmic and ..., Volume 1

Simon Newcomb - Logarithms - 1882 - 188 pages
...III. Given the three sides. THEOREM III. In a triangle the square of any side is equal to the sum, of the squares of the other two sides minus twice the product of these two sides into the cosine of the angle included oy them. In symbolic language this theorem is...
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The College Student's Manual: A Hand-book of Reference for Professors ...

Henry Elmer Moseley - Universities and colleges - 1884 - 214 pages
...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 to the circumference of a circle include...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...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 AB C, and let CD he the projection of the side AC upon...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...opposite to 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 upon that side. A FIG. 1. Fio. 2. PROPOSITION XI.— THEOKEM. 32. If two chords intersect within a...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...opposite to 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 P a B other upon that side. PROPOSITION XI.-THEOREM. 32. If two chords intersect within a circle, their...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...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 upon it. 163. Theorem. In an obtuse triangle the square of the side opposite the obtuse angle is equal...
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