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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
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PLANE AND SOLID GEOMETRY

ISAAC NEWTON FAILOR - 1906
...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...one of those sides and the projection of the other side upon it. Fig. 1 Fig. 2 HYPOTHESIS. In the A ABC, the £ B is acute, and BD is the projection of...

Exercises in Concrete Geometry: With Supplementary Discussions

David Sands Wright - 1906 - 84 σελίδες
...described on the side of a triangle opposite an acute angle is equal to the sum of the squares described on the other two sides diminished by twice the product of one of those sides by the projection of the other side upon it. Problem. To find the area of a triangle, when the three...

Exercises in Geometry

Grace Lawrence Edgett - 1909 - 81 σελίδες
...square of the side opposite an acute angle, in any triangle, 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. 10. In any obtuse-angled triangle the square...

Practical Algebra, 2d Course by Jos. V. Collins, Βιβλίο 2

Joseph Victor Collins - 1911 - 303 σελίδες
...opposite an acute aiujle in a triangle is equal to the sum of the squares of the other two sides dimmished by twice the product of one of those sides and the projection of the other on that side. To prove a3 = 62 + я3 — 2 cm. PROOF. а2=1? + 1Ш' (§61.) = P2+ (cm)2 =p2 + C2 _...

The Teaching of Geometry

David Eugene Smith - 1911 - 339 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 one of those sides by the projection of the other upon that side. THEOREM. A similar statement for the obtuse triangle....

Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - 1911 - 233 σελίδες
...side opposite an acute angle is equal to the sum of the squares of the other two sides diminished % twice the product of one of those sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute...

The Elements of Plane and Spherical Trigonometry

John Gale HUN (and MAC INNES (Charles Ranald)), Charles Ranald MacInnes - 1911 - 205 σελίδες
...~ tan |(C + А)' 53. Law of Cosines. The square on one side of any triangle is equal to the sum of the squares on the other two sides diminished by twice the product of these sides times the cosine of the angle between them. To prove a2 = 61 + c2 — 2bc cos A. ELEMENTS...

The Elements of Plane and Spherical Trigonometry

John Gale Hun, Charles Ranald MacInnes - 1911 - 205 σελίδες
...: tan КС + A). 53. Law of Cosines. The square on one side of any triangle is equal to the sum of the squares on the other two sides diminished by twice the product of these sides times the cosine of the angle between them. To prove a» - 6r + c2 - 26c cos A. ma. ; Similarly...

College Entrance Examination Papers in Plane Geometry

1911 - 178 σελίδες
...triangle the square on the side opposite an acute angle is equivalent 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. 4. Prove that regular polygons of the same...

Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 332 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. FIG. 1 FIG. 2 Given, in the triangle ABC, that p is the projection of the side b upon the side...




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