 | Euclides - 1821 - 294 pages
...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... | |
 | Euclid - 1822 - 222 pages
...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... | |
 | John Playfair - Geometry - 1829 - 210 pages
...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... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 pages
...another place. GEOMETRY. PROPOSITION XII. THEOREM. 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, by twice the rectangle contained by the base and the distance from the acute angle... | |
 | Euclides - 1840 - 82 pages
...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 part... | |
 | Euclides - 1840 - 192 pages
...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 (AB)... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...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 from... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...EF(jH is double of ABCD. PROPOSITION XII. THEOREM. 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, by twice the rectangle contained by the base and the distance from the acute angle... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...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 from... | |
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In any triangle, the square of the side opposite an acute angle is less than the sum of the squares of the... 
