 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
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...expressed in a more easily remembered form. In obtuse_angled triangles the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing it by twice the rectangle contained by either of these sides and the projection of... | |
 | 1891 - 644 pages
...twice the rectangle contained by the whole and that part together with the square on the other part. 6. In an obtuse-angled triangle the square on the side opposite the obtuse angle is equal to the sum of the squares on the other sides together with twice the rectangle contained by one... | |
 | James Andrew Blaikie, William Thomson - Geometry - 1891 - 160 pages
...angle. Use Euc. I. 47 and I. 24. 20. In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing that angle. 21. Enunciate and prove the converses of the two preceding theorems. 22.... | |
 | Euclid - Geometry - 1892 - 460 pages
...straight line given on page 97, the student will see that this proposition may be enunciated as follows : In an obtuse.angled triangle the square on the side...angle is greater than the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by either of those sides, and the... | |
 | George Bruce Halsted - Geometry - 1896 - 208 pages
...its altitude. 519. Theorem. In any triangle, the square on a side opposite any acute angle is less than the sum of the squares on the other two sides...the rectangle contained by either of those sides and a sect from the foot of that side's altitude to the vertex of the acute angle. Proof. Let a, b, c denote... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...triangle, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side opposite the obtuse angle is greater than the sum of the srjuares on tlte other sides, by twice tite rectangle contained by the side on which, when produced,... | |
 | Nathan Fellowes Dupuis - Geometry - 1894 - 313 pages
...— b^ + c1 + 2bcl. .'. The square on the side opposite the obtuse angle in an obtuseangled triangle is greater than the sum of the squares on the other two sides by twice the rectangle on one of these sides and the projection of the other side upon it. The results of 2 and 3 are fundamental... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...triangle, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side opposite the obtuse angle is greater than the sum of tJie squares on the other sides, by twice the rectangle contained by the side on which, when produced,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...point. Fig. 4 is the most general, approaching the others as P recedes to a greater distance. Theorem 9. In an obtuse-angled triangle the square on the side opposite the obtuse angle equals the sum of the squares on the other two sides together with twice the rectangle of either side... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...general, approaching the others as P recedes to a greater distance. 90 EQUALITY OF POLYGONS. Theorem 9. In an obtuse-angled triangle the square on the side opposite the obtuse angle equals the sum of the squares on the other two sides together with twice the rectangle of either side... | |
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