| 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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