 | George Roberts Perkins - Geometry - 1856 - 460 pages
...perpendiculars which determine this projection. THEOREM Xv. In any obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of either of the sides containing the... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...perpendiculars which determine this projection. THEOREM XV. In any obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of either of the sides containing the... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...Z52 = BCZ + AC2 - 2BC x CD ; PROPOSITION XIII. THEOREM. In any obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the base and the other side, increased ~by twice the rectangle of the base and the distance... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...A& = AC* : hence, ~ X CD ; PROPOSITION XIII. THEOREM. In any obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the sqitares of the base and the other side, increased by twice the rectangle of the base and the distance... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...having an obtuse angle. An acute-angled triangle is one having three acute angles. PROPOSITION III. In obtuse-angled triangles, the square on the side opposite the obtuse angle is greater than the squares on the sides containing it by twice the rectangle contained by either of those... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...BC2 + which was to be proved. PROPOSITION Xm. THEOREM. N In any obtuse.angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of t/>e base and the other side, increased by twice the rect> angle of the base and the distance... | |
 | Richard Wormell - 1876 - 268 pages
...on AD ; Then the rectangle AG = the square on С D. THEOREM LIV. In any obtuse-angled triangle, tl1e square on the side opposite the obtuse angle is equal to the sum of the squares on the sides containing the obtuse angle, together with twice the rectangle contained by either... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...x AE, which was to be proved. PROPOSITION X, THEOREM. In any obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the rectangle of the base and the distance from... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...AB=a, and AC=5y then (a-\-b) PROPOSITION XIX. — THEOREM. In an obtuse-angled triangle the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides and twice the rectangle contained by the base and the distance from... | |
 | Richard Pears Wright - 1882 - 136 pages
...diminished by twice the product of either of these sides and the projection of the other upon it. Rule 2. In obtuse-angled triangles, the square on the side...opposite the obtuse angle is equal to the sum of the squares on the sides which contain it increased by twice the product of either of these sides and the... | |
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In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it. 
