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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. "
Elements of Plane and Solid Geometry - Σελίδα 186
των George Albert Wentworth - 1877 - 398 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Plane Geometry

Edith Long, William Charles Brenke - 1916 - 276 σελίδες
...119. Theorem XI. In any triangle the square on the side opposite an acute angle is equal to the sum of the squares on the other two sides, diminished by...one of those sides and the projection of the other side upon it. Give the proof of this on the same plan as in the preceding theorem, noting that we now...

Plane and Solid Geometry

William Betz - 1916 - 507 σελίδες
...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 those sides and the projection of the other upon it. FH;. 1 FIG. 2 Given, in the triangle ABC, that p is the projection of the side 6 upon the side...

Plane Geometry

Jacob William Albert Young, Lambert Lincoln Jackson - 1916 - 312 σελίδες
...GEOMETRY PROPOSITION VI. THEOREM 375. In any triangle the square on the side opposite to an acute angle is equivalent to the sum of the squares on the other two sides diminished by twice the rectangle of either of those sides and the projection of the other upon it. FiG. 1 Given triangle ABC...

Plane Geometry

John Charles Stone, James Franklin Millis - 1916 - 278 σελίδες
...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 it. DB Hypothesis. — In A ABC, Z. A is acute, a, b, and e are the sides opposite A, B, and (7, respectively,...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1918 - 457 σελίδες
...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...one of those sides and the projection of the other side upon it. Given in A abc, p the projection of b upon c, and the angle opposite a an acute angle....

Solid Geometry

Claude Irwin Palmer - 1918 - 177 σελίδες
...side opposite the obtuse angle is equivalent to the sum of the squares of the other two sides, plus twice the product of one of those sides and the projection of the other side upon it. § 381. Theorem. In any triangle, the square of a side opposite an acute angle is equivalent...

Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 σελίδες
...side opposite the obtuse angle is equivalent to the sum of the squares of the other two sides, plus twice the product of one of those sides and the projection of the other side upon it. Given the obtuse triangle ABC, the angle ACB being obtuse, and d and AD being the projections...

Drill Book in Plane Geometry

Robert Remington Goff - 1922
...side opposite an obtuse angle of a triangle equals the sum of the squares of the other two sides plus twice the product of one of those sides and the projection of the other upon it. 341. Group articles 282, 339, and 340 under one general statement. 342. The sum of the squares...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1913 - 457 σελίδες
...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...one of those sides and the projection of the other side upon it. Given in A abc, p the projection of 6 upon c, and the angle opposite a an acute angle....

Essentials of Plane Geometry

David Eugene Smith - 1923 - 296 σελίδες
...square of the side opposite an acute •angle of any triangle is equal to the sum of the squares of the other two sides diminished by twice the product...one of those sides and the projection of the other side upon it. BA Given the A ABC with an acute ZA, and a' and V, the projections of a and 6 respectively...




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