| Euclides - Geometry - 1841 - 378 pages
...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...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,... | |
| John Playfair - Euclid's Elements - 1844 - 338 pages
...AB 2 =BC 2 +AC 2 +2BC.CD ; that is, AB 2 is greater than BC 2 +AC 2 by 2BC.CD. BC PROP. XIII. THEOR. In every triangle the square of the side subtending...sides, and the straight line intercepted between the perpendicular,let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle,... | |
| Euclides - 1845 - 546 pages
...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, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,... | |
| Euclides - 1848 - 52 pages
...intercepted without the triangle between the perpendicular and the obtuse angle. PROP. XIII. THEOREM. In every triangle, the square of the side subtending...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. PROP. XIV. PROBLEM. BOOK... | |
| Great Britain. Council on Education - Education - 1848 - 596 pages
...of the side subtending either of the acute angles is less than tbe square of the sides containing it by twice the rectangle contained by either of these...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. (The first case only of... | |
| Great Britain. Committee on Education - 1848 - 606 pages
...of the side subtending either of the acute angles is less than the square of the sides containing it by twice the rectangle contained by either of these...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. (The first case only of... | |
| J. Goodall, W. Hammond - 1848 - 390 pages
...the side subtending either of the acute angles is less than the square of the sides, containing it by twice the rectangle contained by either of these...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. (The first case only of... | |
| London univ - 1852 - 358 pages
...given rectilineal angle. 4. In every acute-angled triangle the square of the side subtending either of the acute angles is less than the squares of the...contained by either of these sides, and the straight line in- _ tercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.... | |
| Euclid, John Playfair - Geometry - 1853 - 336 pages
...therefore, AB2=BC2+AC2+2BC.CD; that is, AB2 is greater than BC2+AC2 by 2BC.CD. ^ ^ PROP. XIII. THEOR. In every triangle the square of the side subtending...perpendicular, let fall upon it from the opposite angle, and ihn acute , angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC,... | |
| Euclides - Geometry - 1853 - 334 pages
...the side subtending either of the acute angles is less than the squares of the sides including this angle, by twice the rectangle contained by either...sides, and the straight line intercepted between the acute angle and the perpendicular drawn to this side, produced if necessary, front the opposite angular... | |
| |