 | George Lees - 1826 - 276 sider
...equal sides of the triangle. 2. The square of the base of an isosceles triangle, is equal to twice the rectangle contained by either side, and by the...the opposite angle and the extremity of the base. 3. If the vertical angle of a triangle be two-thirds of a right angle, the square of the base will... | |
 | Henry Parr Hamilton - 1826 - 354 sider
...of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular...let fall upon it from the opposite angle., and the acute angle." (Eve. II. IS). Since the triangle may be either acute angled, or obtuse angled, or right... | |
 | Robert Simson - 1827 - 546 sider
...of the sides containing that angle, by twice the rectangle contained by either of these 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, and the angle at B one of its acute angles, and upon BC, one... | |
 | Pierce Morton - 1830 - 584 sider
...that angle, by twice the rectangle, contained by either of these sides, and that part of it, which is intercepted between the perpendicular let fall upon it from the opposite angle, and the given angle : greater, when the given angle is greater than a right angle, and less, when it is less.... | |
 | Euclides - 1834 - 518 sider
...twice the rectangle contained by either of these sides, and the straight line intercepted bi-twecn the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles ; and upon BC, one... | |
 | Euclid - 1835 - 540 sider
...of t 'fie sides containing that angle by twice the rectangle contained by either of these 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, and the angle at B one of its acute angles, and upon BC, one... | |
 | 1835 - 684 sider
...that angle, by twice the rectangle contained by either of these sides, and that part of it which is intercepted between the perpendicular, let fall upon it from the opposite angle, and the acute angle; greater if the given angle is greater than a right angle, and less if it is less . . .22... | |
 | John Playfair - 1836 - 148 sider
...of the sides containing that angle, by twice the rectangle contained by either of these .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, and the angle at B one of its acute angles, and upon BC, one... | |
 | Euclides - 1837 - 112 sider
...of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular...let fall upon it from the opposite angle, and the acute angle. Fig. 1. Fig. 3. Steps of the Demonstration to Case 1st. (in which AD falls within the... | |
 | Andrew Bell - 1837 - 290 sider
...squares of BC, CA, by twice the rectangle BC • CD. PROPOSITION XIII. THEOREM. of these sides, and the straight line intercepted between the perpendicular...let fall upon it from the opposite angle, and the acute angle. Let ABC he any triangle, and the angle at B one of its acute angles, and upon BC, one... | |
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In every triangle, the square of the side subtending 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 sides, and the straight line intercepted between the perpendicular... 
