 | Euclides - 1821 - 294 pages
...rectangles under 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... | |
 | Euclid - 1822 - 179 pages
...rectangle under 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... | |
 | John Playfair - Geometry - 1829 - 186 pages
...base and the distance between the perpendicular and the obtuse angle. 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 under either of these sides and the distance... | |
 | Euclid - Euclid's Elements - 1833 - 183 pages
...rectangle under DC 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... | |
 | Euclides - 1840 - 82 pages
...opposite angle and the vertex of the obtuse angle. PROP. XIII. THEOR. In any triangle, the square of a side subtending an acute angle is less than the sum of the squares of the sides containing that angle, by twice the rectangle contained by either of those sides and the... | |
 | Euclides - 1840 - 194 pages
...AB and its external segment BD. PROP. XIII. THEOR. In any triangle (ABC) the square of a side (CB) subtending an acute angle, is less than the sum of the squares of the sides (CA, AB) containing that angle, by twice the rectangle contained by either of those sides... | |
 | George Roberts Perkins - Geometry - 1847 - 308 pages
...illustrated by aid of the annexed diagram : n"=9' PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle of the base and the distance of the perpendicular... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...the annexed diagram : 17 2 =9 2 +10 2+ 2.9X6. PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle of the base and the distance of the perpendicular... | |
 | Euclid - Geometry - 1853 - 176 pages
...to the rectangle under the other side and its produced part. The square on the side subtending that acute angle is less than the sum of the squares on the sides which contain that angle, by double the rectangle under the side to which the perpendicular is drawn,... | |
 | Robert Potts - 1855 - 1050 pages
...same base and on the same side of it, are between the same parallels. 4. 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 rectangle contained by either of them and the segment... | |
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In every triangle, the square on the side subtending an acute angle is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let... 
