 | Euclides - 1838 - 264 pages
...BC, CA, by twice the rectangle BC-CD. Therefore, in obtuse angled triangles, &c. QED PROP. Xm. THEOR. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, ly twice the rectangle contained by either of these sides,... | |
 | Geometry - 1843 - 376 pages
...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 rectangie contained by the base and the distance from the obtuse angle to the foot of the perpendicular... | |
 | Euclides - 1845 - 546 pages
...twice the rectangle BC, CD. Therefore in obtuse-angled triangles, &c. QED PROPOSITION XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides,... | |
 | Nathan Scholfield - 1845 - 894 pages
...side AB opposite the obtuse angle, (see last figure,) is equal to a' + c' + 2 ex, that is, greater than the sum of the squares of the other two sides, by 2cx, which agrees with propositions XXVI and XXVII, B. IV, El. Geom ; by these propositions we may... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...side AB opposite the obtuse angle, (see last figure,) is equal to a3 + c3 + 2 ex, that is, greater than the sum of the squares of the other two sides, by 2cx, which agrees with propositions XXVI and XXVII, B. IV, EL Geom ; by these propositions we may determine... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...side AB opposite the obtuse angle, (see last figure,) is equal to a" + c2 + 2 ex, that is, greater than the sum of the squares of the other two sides, by 2cx, which agrees with propositions XXVI and XXVII, B. IV, El. Geom ; by these propositions we may... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
.... CD. 1 \ CD 8 + DA 8 = CA S , Therefore, in obtuse angled zHs, &c. PROP. XLVIII. THEOR. 13. 2 Ea. In every triangle^ the square of the side sub-tending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides,... | |
 | Education - 1847 - 508 pages
...rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides containing• that angle by twice the rectangle contained by either of those sides,... | |
 | Alpheus Crosby - Geometry - 1847 - 190 pages
...side of a triangle subtending an OBTUSE angle is GREATER, and of any side subtending an ACUTE angle LESS, than the sum of the squares of the other two sides, by twice the rectangle of either of these sides into the distance between a perpendicular let fall upon it from the opposite... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...THEOREM. In any obtuse-angled triangle, the square of the side subtending the obtuse angle is greater than the sum of the squares of the other two sides, by twice the rectangle of the base and the distance of the perpendicular from the obtuse angle. g Let ABC be a triangle, obtuseangled... | |
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In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute... 
