 | John Playfair - Geometry - 1829 - 210 pages
...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 distance between the acute angle and the perpendicular drawn from the opposite... | |
 | Euclides - 1834 - 518 pages
...obtuse-angled triangles, &c. Q. £. D. PROPOSITION XIII. See N. THEOR. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...triangle, the square of the side sub- . tending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these tides, and the straight line intercepted between the perpendicular, let fall upon it from the opposite... | |
 | Euclides - 1838 - 264 pages
...BC-CD. Therefore, in obtuse angled triangles, &c. QED PROP. Xm. THEOR. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, ly twice the rectangle contained by either of these sides, and... | |
 | Euclides - 1840 - 82 pages
...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 of it intercepted between the perpendicular let fall on it from the opposite... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...BC AD2 to both, we find, as before, AB*=BC'+AC'=2(BC X CD). Hence, In every triangle the square of the side subtending either of the acute angles, is less than the sum of the squares of the other two sides, by twice the rectangle contained by either of these sides... | |
 | Euclides - 1845 - 546 pages
...Therefore in obtuse-angled triangles, &c. QED PROPOSITION XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...Therefore, in obtuse angled zHs, &c. PROP. XLVIII. THEOR. 13. 2 Ea. In every triangle^ the square of the side sub-tending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle^ the square of the side sttbtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either oj these sides, and the straight line intercepted between the perpendicular let fall upon it from the... | |
 | Education - 1847 - 508 pages
...one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides containing• that angle by twice the rectangle contained by either of those sides, aud... | |
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In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute... 
