 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 it.  Essentials of Geometry - Page 110by Alfred Hix Welsh - 1883 - 267 pagesFull view - About this book
 | Geometry, Plane - 1911 - 192 pages
...circles, one inscribed in, and the other circumscribed about, an equilateral triangle? JUNE, 1909 1. 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... | |
 | David Eugene Smith - Geometry - 1911 - 358 pages
...This formula evidently comes from that of Pythagoras by doubling the sides of the squares. 1 THEOREM. 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... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...of an isosceles triangle upon the base is equal to one half the base. PROPOSITION XX. THEOREM 420. 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... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...discussion for a right triangle ? 454. Prop. XXVIII may be stated in the form of a theorem as follows : 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 these sides and the projection... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...of an isosceles triangle upon the base is equal to one half the base. PROPOSITION XX. THEOREM 420. 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... | |
 | Arkansas Education Association - Education - 1912 - 270 pages
...effective implement for attacking many of the theorems of Geometry. Consider the theorem, "In any oblique 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 two sides and the projection... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...hypotenuse diminished by the square on 'he other side. 199. Theorem VII. In any triangle the square on the side opposite an acute angle is equal to the sum of the squares on t/ie other two sides diminished by twice the product of one of those sides and the projection... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...6 = 15, p = 9, and c = 25, find o. PROPOSITION XXXVI. THEOREM 331. 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 of one of those sides and the projection... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...6 = 15, p = 9, and c = 25, find a. PROPOSITION XXXVI. THEOREM 331. 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 of one of those sides and the projection... | |
 | Herbert Ellsworth Slaught - Logarithms - 1914 - 296 pages
...the answer to this question is contained in the following two propositions of geometry : Theorem 1. 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... | |
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