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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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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 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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Elementary Synthetic Geometry of the Point, Line and Circle in the Plane

Nathan Fellowes Dupuis - Geometry - 1889 - 370 pages
...obtuseangled triangle is greater than the sum of the squares on tlic other two sides by iwice the rectangle on one of these sides and the projection of the other side upon it. The results of 2 and 3 are fundamental in the theory of triangles. These results are but one ; for,...
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Elements of Plane and Spherical Trigonometry

Edwin Schofield Crawley - Trigonometry - 1890 - 184 pages
...pairs of sides. (83) FIG. 21 bis. о 63. //( any 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 sides and the cosine of the included angle. We are to prove a2 = I', + ca — 2bc cos A. In one...
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Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...respective sides. 363. 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 those sides and the projection of the other upon that side. If C be the acute angle, then by a glance...
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A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...sin B : sin C. 96. Law of Cosines. — In any 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 sides and the cosine of the included angle. In an acute-angled triangle (see С first figure)...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the projection of the other side upon it. EXERCISES. The following theorem should be noticed ; it is proved by the help of n. 1. I. If four points...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - Trigonometry - 1892 - 194 pages
...sin B : sin С. 56. Law of Cosines. — In any 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 sides and the cosine of the included angle. In 'an acute-angled triangle (see С first figure)...
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Elementary Geometry

William Chauvenet - 1893 - 340 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 other upon that side. PROPOSITION XI.—THEOREM. 32. If two chords intersect within a circle, their...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 394 pages
...In any triangle, the square of the side opposite an acute angle is equal to the sum of the syuares of the other two sides, minus twice the product of...sides and the projection of the other side upon it. Fig. 2. Let C be an acute angle of the triangle ABC, and draw AD perpendicular to CB, produced if necessary....
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Journal of the Michigan Schoolmasters' Club, Volume 22; Volumes 31-40

Michigan Schoolmasters' Club - Education - 1894 - 554 pages
...AC/BC lowing: "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...one of these sides and the projection of the other upon it." From the previous ex|>eriment the details of this one are obvious. This work would give a...
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