 In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.  The Elements of Geometry - Page 107by George Bruce Halsted - 1885 - 366 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...before, AB2=BC2+ AC2— 2BC X CD. THEOREM. 192. In any triangle, having an obtuse angle, the square of the side opposite the obtuse angle, is greater than the sum of the squares of the sides containing it, by twice the rectangle contained by either of the latter sides, and the... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...AB2=BC2 + AC2 —SBC x CD. PROPOSITION XIII. THEOREM. .In every obtuse angled triangle, the square of the side opposite the obtuse angle is greater than the sum of the squares of the other two sides by twice the rectangle contained by the base and the distance from the obtuse... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...any triangle, the square of the side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular drawn to that side from the... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...the square of the side subtending either of the acute angles, is less than the sum of the squares of the other two sides, by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall upon it from the opposite... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...any triangle, the square of a side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular drawn to that side from the... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...=BC 2 +AC 2 —2BCxCD. D DB PROPOSITION XIII. THEOREM. In every obtuse angled triangle, the square of the side opposite the obtuse angle is greater than the sum of the squares of the other two sides by twice the rectangle contained by the base and the distance from the obtuse... | |
 | Euclid - Geometry - 1853 - 176 pages
...obtuse-angled triangle (ABC) to the opposite side (BC) produced, the square on the side (AB) subtending the obtuse angle is greater than the sum of the squares on the two sides (BC and CA), which contain the obtuse angle, by double the rectangle under the side (BC),... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...sides about the right angle. THEOREM XL. In any obtuse-angled triangle, the square on the side opposiie the obtuse angle is greater than the sum of the squares...sides, by twice the rectangle contained by either side about the obtuse angle, and the part of this side produced to meet the perpendicular drawn to... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...the square root of the sum of the squares of the two sides about the right angle. THEOREM XL. In any obtuse-angled triangle, the square on the side opposite...sides, by twice the rectangle contained by either side about the obtuse angle, and the part of this side produced to meet the perpendicular drawn to... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...of the equal sides. 500. Find the obtuse angle of a triangle when the square on the side opposite to the obtuse angle is greater than the sum of the squares on the sides containing it, by the rectangle of the sides. 501. Construct a rectangle equal to a given square... | |
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