 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...straight line intercepted without the triangle between the perpendicular and the obtuse angle. In every triangle the square of the side subtending an acute angle is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 520 pages
...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 the base and the distance from the vertex... | |
 | Benjamin Greenleaf - Geometry - 1861 - 628 pages
...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 the base and the distance from the vertex... | |
 | Dublin city, academic inst - 1862 - 32 pages
...with thé square of the other part. 6. In an acute angled triangle the square of the side opposite the acute angle is less than the sum of the squares of the sides about that angle by twice the, rectangle under the base, and the distance from the acute angle... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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 the base and the distance from the vertex... | |
 | McGill University - 1865 - 332 pages
...square of a line is four times the square of its half. 2. In any triangle the square of a side opposite an acute angle is less than the sum of the squares of the sides containing it by twice the rectangle under either of them and the intercept between the acute angle and the foot... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...(ax. 2). But AD2+CD2=AC2, and BD2+CD2=BC2 (th. 34). Therefore AC2=AB2+BC2+2AB. BD. QED THEOREM XXXVII. In any triangle, the square of the side subtending an acute angle is less than the squares of the base and the other side by twice the rectangle of the base and the distance of the perpendicular... | |
 | Benjamin Greenleaf - Geometry - 1868 - 338 pages
...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 the base and the distance from the vertex... | |
 | Dublin city, univ - 1871 - 366 pages
...the other part. (a). Calculate the lengths of the segments of a line whose length is 10 inches. 8. In any triangle the square of the side subtending an acute angle is less than the squares of the sides containing the acute angle by twice the rectangle contained by one of the sides... | |
 | Edward Sang - Geometry - 1875 - 150 pages
...angle is greater than the sum of the squares of the containing sides ; the square of the subtense of an acute angle is less than the sum of the squares of the containing sides ; in either case by twice the rectangle under one of the containing sides and the... | |
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In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the... 
