In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the... The Element of Geometry - Page 29by John Playfair - 1836 - 114 pagesFull view - About this book
| John Playfair - Mathematics - 1806 - 320 pages
...square of the side subtending the obtuse aigle is greater than the squares of the sides contain ng **the obtuse angle, by twice the rectangle contained...perpendicular falls, and the straight line intercepted** between the perpendicular and the obtuse angle. a 12. 1. b4.! c 47. 1. Let ABC b( an obtuse angled... | |
| Charles Hutton - Mathematics - 1811 - 406 pages
...+ BC . AC — BC = AB.AD + BD in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the **Square of the Side subtending the Obtuse Angle, is Greater than the** Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the... | |
| Charles Hutton - Mathematics - 1812 - 620 pages
...AC+BC . AC — BC =AB . AD + BD in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the **Square of the Side subtending the Obtuse Angle, is Greater than the** Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the... | |
| John Mason Good - 1813 - 714 pages
...angles to the opposite side produced, the square of the side subtending the obtuse angle is greatcf **than the squares of the sides containing the obtuse...triangle between the perpendicular and the obtuse angle.** Prop. XIII. Theor. In every triangle, the square of the side subtending any of the acute angles, is... | |
| Euclides - 1814 - 560 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the **square of the side subtending the obtuse angle is...produced, the perpendicular falls, and the straight line** intercopted without the triangle between the perpendicular and the obtuse angle. Because the straight... | |
| Euclides - 1816 - 588 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the **square of the side subtending the obtuse angle is...triangle between the perpendicular and the obtuse angle.** : ABC be an obtuse angled triangle, having the obtuse angle ACS, and from the .point A. let AD be drawn"... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...triangles, if a perpendicular be drawn front any of i the acute angles to the opposite side produced, the **square of the side subtending the obtuse angle is...perpendicular falls, and the straight line intercepted** between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle, having the obtuse... | |
| John Mason Good - 1819 - 800 pages
...angles to the opposite side produced, the square of the side subtending the obtuse anule it greatt-i **than the squares of the sides containing the obtuse angle, by twice the rectangle contained** br the side upon which, when produced, the perpendicular falls, and the straight line intercepted without... | |
| Charles Hutton - Mathematics - 1822 - 616 pages
...BC . AC — BC = AB . AB -f- BB in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the **Square of the Side subtending the Obtuse Angle, is Greater than the** Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the... | |
| Euclides - 1826 - 226 pages
...to the square of AH. Which was to be done. PROPOSITION XII. THEOREM. In obtuse angled triangles, the **square of the side subtending the obtuse angle is greater than the squares,** which are made by the sides containing the obtuse angle by twice the rectangle contained under one... | |
| |