 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
 | James Hayward - Geometry - 1829 - 228 pages
...oblique-angled triangle, the square of the side opposite an acute angle, is equivalent to the sum of the squares of the other two sides, minus twice the rectangle contained by one of the sides adjacent to this angle, and the distance of this angle from the foot of the perpendicular... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...CD2 = BC2, and also that AD2 + CD2 = AC2, we shall obtain BC2 = AB2 + AC2 + 2 AB x AD. THEOREM XvI. 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 ly twice the product of one of these sides, Iy the projection... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...CD2 = BC2, and also that AD2 + CD2 = AC2, we shall obtain BC2 = AB2 + AC2 + 2AB x AD. THEORRM XVI. 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, by the projection... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...square BCGP, are equivalent to the sum of tlie squares ABHL, ACIK. PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...square BCGF, are equivalent to the sum of the squares ABHL, ACI K. PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...are equivalent to the sum of the squares ABHL, ACI K. BOOK IV. ' PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | James Fraser (bp. of Manchester.) - 1866 - 480 pages
...altitudes are proportional to their bases. (Book IV., Prop. 3.) 8. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of tne base and the other side, diminished by brice (he rectangle of the base and the distance... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...BCGF, are equivalent to the sum of the squares ABHL, ACIK. BOOK IV. PROPOSITION XII. — THEOREM. 244. In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle contained by... | |
 | André Darré - 1872 - 226 pages
...square of either of the two small sides. Fig. 78. B m H THEOREM. 91. 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, minus twice the product of one of these sides by the projection on... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...the side of a square are incommensurable. PRorosrrioN xii. THEOBEM. In any triangle, the square of a side opposite an acute angle, is equal to the sum of the squares of the base and the other side, diminished by twice the rectangle of tht base and the distance... | |
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