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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 and Solid Geometry: Suggestive Method

George Clinton Shutts - 1912 - 376 σελίδες
...side opposite an obtuse angle of a triangle equals the sum of the squares of the two other sides plus twice the product of one of those sides and the projection of the other upon it. Given a A with sides a, b, c, side a being opposite an obtuse angle, and m being the projection...

Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 332 σελίδες
...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 those sides and the projection of the other iipon it. Given, in the triangle ABC, that p is the projection of the side b upon the side a, and that...

Plane and Solid Geometry: Teacher's Edition

George Albert Wentworth - 1912 - 590 σελίδες
...general manner : In any triangle the square on the side opposite In any triangle the square on any side is equivalent to the sum of the squares on the other two sides diminished, if the side is opposite an acute angle, and increased, if the side is opposite an obtuse angle, by...

Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - 1912 - 376 σελίδες
...side opposite an acute angle of a triangle equals the sum of the squares of the two other sides minus the product of one of those sides and the projection of the other upon it. Given a A with the sides a, b, c, side a being opposite an acute angle and m being the projection...

Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - 1912 - 488 σελίδες
...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 these sides and the projection of the other side upon it. Ex. 726. If the sides of a triangle are 7,...

Solid Geometry

Walter Burton Ford, Charles Ammerman - 1913 - 107 σελίδες
...Theorem VII. In any triangle the square on the side opposite the acute angle is equal to the sum of the squares on the other two sides diminished by twice...of those sides and the projection of the other upon it. 200. Theorem VIII. In any obtuse triangle the square on the side opposite the obtuse angle is equal...

Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - 1913 - 321 σελίδες
...Theorem VII. In any triangle the square on the side opposite the acute angle is equal to the sum of the squares on the other two sides diminished by twice...of those sides and the projection of the other upon it. Given the A ABC in which C is an acute angle. Let a, b, c be the sides opposite the angles A, B,...

Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - 1913 - 213 σελίδες
...Theorem VII. In any triangle the square on the side opposite the acute angle is equal to the sum of the squares on the other two sides diminished by twice...of those sides and the projection of the other upon it. Then, in Why? Why? Why? FIG. 139 Given the A ABC in which C is an acute angle. Let a, b, c be the...

Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - 1913 - 470 σελίδες
...other pair. PROPOSITION XI. THEOREM 341. In any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares on the other...diminished ~by twice the product of one of those sides ~by the projection of the other upon that side. c c DB FIG. 1 FIG. 2 Given the triangle ABC, A being...

Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - 1913 - 470 σελίδες
...= AB2. PROPOSITION XI. THEOREM 341. In any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares on the other...diminished ~by twice the product of one of those sides by the projection of the other upon that side. o G c DB FIG. 1 FIG. 2 Given the triangle ABC, A being...




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