 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.  Robbin's New Plane Geometry - Page 173by Edward Rutledge Robbins - 1915 - 264 pagesFull view - About this book
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...dropped from the middle point of the arc on the tangent and chord, respectively, are equal. 4. Prove that 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... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...THEOREM 277. 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. D B fig. 1. Fig. 2. D Given C an acute Z of A ABC,... | |
 | James William Nicholson - Trigonometry - 1898 - 204 pages
...the following is the 56 Translation: The square of any side of any triangle is equal to the sum of the squares of the other two sides, minus twice the product of these sides into the cosine of their included angle. While all other trigonometric relations of the... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...the projection of CD upon AB. 162 NUMERICAL PROPERTIES OF FIGURES. PROPOSITION XXIX. THEOREM. 375. 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 % the projection... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...perpendicular to line CD, the projection of line AB upon line CD is line A'B'. PROP. XXV. THEOREM 277. 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... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...extremities of the first line. Thus, PR is the projection of CD upon AB. PROPOSITION XXIX. THEOREM. 375. 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... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...X BF. f + (7£ 2 = AB(AF + BF) = AB\ §367 QED -^ PROPOSITION XXIX. THEOREM. ••»* „ 375. Zn 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... | |
 | F. J. Beck - 1899 - 288 pages
...proportion, they are in proportion taken by composition. , 6. What is a plane? How is a plane determined? 7. In any triangle, the square of the side opposite an acute angle is equal to Complete the theorem. 8. A's farm is square, and the diagonal is 200 rods; how many acres has he? 9.... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...THEOREM 277. 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. D Fig. 1. B Given C an acute Z of A ABC, and CD... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...parallel lines are equal. PLANE GEOMETRY. Proposition 151. Theorem. 186. 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 these sides and the projection... | |
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