 | 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 (AB)... | |
 | Euclides - 1841 - 378 pages
...twice the rectangle BC, CD. Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOR. In every triangle, the square of the side subtending an acute angle, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides,... | |
 | Euclides - 1845 - 544 pages
...the square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the square of the side subtending an acute angle is less than the squares of the sides which contain that angle. 21. This will be found to be that particular case of... | |
 | George Roberts Perkins - Geometry - 1847 - 308 pages
...The above principle may be illustrated by aid of the annexed diagram : n"=9' PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending...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 William Hackley - Geometry - 1847 - 248 pages
...Therefore, by substitution in the last equality but one. AC2 = AB2 + BC2 + 2AB . BD. QED B2 THEOREM XXIX. In any triangle, the square of the side subtending an acute angle is less than the squares of the other two sides, by twice the rectangle of one of the sides containing the acute angle... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...the square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the square of the side subtending an acute angle is less than the squares of the sides which contain that angle. 21. This will be found to be that particular case of... | |
 | Charles Davies - Trigonometry - 1849 - 384 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
...may be illustrated by aid of the annexed diagram : 17 2 =9 2 +10 2+ 2.9X6. PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending...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... | |
 | Thomas Lund - Geometry - 1854 - 522 pages
...twice the rectangle BC, CD. 47. PROP. XXV. In every triangle the square of the side opposite to any acute angle is less than the sum of the squares of the aides forming that angle by twice the rectangle contained by either of these sides and that part of... | |
 | Robert Potts - 1855 - 1050 pages
...3. Equal triangles, on the same base and on the same side of it, are between the same parallels. 4. In any triangle the square of the side, subtending...squares of the sides containing that angle, by twice the rectangle contained by either of them and the segment between the acute angle anil, the perpendicular... | |
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In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the... 
