 | Adrien Marie Legendre - 1819 - 574 pàgines
...in a triangle ABC (fig. 110), if the angle C be acute, the square of the side opposite to it will be less than the sum of the squares of the sides containing it, and, AD being drawn perpendicular to BC, the difference will be equal to double the rectangle BC x... | |
 | Euclides - 1821 - 294 pàgines
...the whole produced line and, side. PROP. 13. THEOR, In any triangle the square of the side subtending an acute angle, is less than the sum of the squares of the sides containing that angle, by twice the rectunyle under either of them and the segment between the acute angle and... | |
 | Euclid - 1822 - 222 pàgines
...DC and CB. PROP. XIII. THEOR. In any triangle (ABC) the square of the side (AB) Fi^. 25. subtending an acute angle is less than the sum of the squares of the sides(AC and CB), containing that angle by twice the rectangle under either of them (AC), and the segment... | |
 | Adrien Marie Legendre - 1825 - 276 pàgines
...In a triangle ABC (fig. 110), if the angle C be acute, the square of the side opposite to it will be less than the sum of the squares of the sides containing it, and, AD being drawn perpendicular to BC, the difference will be equal to double the rectangle BC X... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 pàgines
...In a triangle ABC (fig. 110), if the angle C be acute, the square of the side opposite to it will be less than the sum of the squares of the sides containing it, and, AD being drawn perpendicular to BC, the difference will be equal to double the rectangle BC x... | |
 | John Radford Young - 1827 - 228 pàgines
...of the parts into which the perpendicular from the vertex divides the base. PROPOSITION XI. THEOREM. In any triangle, the square of a side opposite an acute angle is less than the squares of the base and of the other side, by twice the rectangle contained by the base and the part... | |
 | Adrien Marie Legendre - 1828 - 346 pàgines
...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 distance from the obtuse angle to the foot a perpendicular... | |
 | John Playfair - 1829 - 210 pàgines
...Therefore, in any &c. QED PROPOSITION XIII. THEOREM. In any triangle the square of the side subtending an acute angle is less than the sum of the squares of the two sides containing that angle, by twice the rectangle contained by either of those sides and the... | |
 | Adrien Marie Legendre - 1830 - 344 pàgines
...another place. THEOREM. 191. In any triangle, the square of the side opposite either of the acute angles, is less than the sum of the squares of the sides containing it, by twice the rectangle contained by either of ilie latter sides and the distance from the acute angle to the foot, of a perpendicular... | |
 | Euclid - 1833 - 216 pàgines
...and CB. PROP. XIII. THEOPv. In any triangle {ABC) tie square of the side (AB), Fig. 25. subtending an acute angle, is less than the sum of the squares of the sides (AC and CB) containing that angle, by twice the rectangle under either of them (AC) and the segment... | |
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In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides... 
