 In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the...  Elementary Course of Geometry ... - Page 33by Charles William Hackley - 1847 - 103 pagesFull view - About this book
 | Woolwich roy. military acad - 1884 - 148 pages
...a perpendicular be drawn from either of the acute angles to the opposite side produced, prove that the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle by twice the rectangle contained by the side upon... | |
 | George Johnston Allman - Geometry - 1889 - 266 pages
...squares on the sides which contain the acute angle ; (e). 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 it ; (/). In an isosceles triangle whose vertical angle is double the angle... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...a perpendicular be drawn from either of the acute angles to the opposite side produced, prove that the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle by twice the rectangle contained by the side upon... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...of\\.. 12 can be 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... | |
 | James Andrew Blaikie, William Thomson - Geometry - 1891 - 160 pages
...sides containing that 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.... | |
 | John Macnie - Geometry - 1895 - 386 pages
...PB2 + A~p,2^J3C~ + PC* + AP* — 2 rect. BC-PC. (Ax. 2) PROPOSITION XIII. THEOREM. 351. In an obtuse triangle, the square of the side subtending the obtuse...angle is greater than the sum of the squares of the other sides by twice the rectangle of either of these sides and the projection upon it of the other... | |
 | Education - 1899 - 824 pages
...a perpendicular be drawn from any of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing the obtuse angle, bv twice the rectangle contained by the side upon which when... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...perpendicular is drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when... | |
 | George Bruce Halsted - Geometry - 1904 - 313 pages
...foot to the acute angle A . 306. Theorem. In an 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 product of either of those sides and a sect from the foot of that side's altitude to the vertex of... | |
 | George Bruce Halsted - Geometry - 1904 - 324 pages
...c* -h*; :.a*-b*-abj+c*. 306. Theorem. In an 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 product of either of those sides and a sect from the foot of that side's altitude to the vertex of... | |
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