| 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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