 | John Playfair - 1819 - 354 pages
...betrvetri the perpendicular, let fall upon it front the opposite angle, and the acute angle. Let ABC be auy triangle, and the angle at B one of its acute angles, and upon BCT, one of the sides containing it, let fall the perpendicular (12. 1.) AD from the opposite angle... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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 perpendiculai let fall upon it from the opposite angle, and the acute angle.* Let ABC be any triangle,... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...angle by twice the rectangle contained by either of these sides, and the straight line inteicepted between the perpendicular let fall upon it from the...acute angle. Let ABC be any triangle, and the angle at В one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular... | |
 | Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...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...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 angled, the... | |
 | George Lees - 1826 - 276 pages
...the base of an isosceles triangle, is equal to twice the rectangle contained by either side, and by the straight line intercepted between the perpendicular, let fall upon it from 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...line intereepted between the perpendieular, let fall upon it from the opposite angle, and the aeute angle. Let ABC be any triangle, and the angle at B one of its aeute angles, and upon BC, one of the sides eontaining it, let fall the perpendieular (12. 1.) AD from... | |
 | John Playfair - Geometry - 1829 - 210 pages
...distance between the acute angle and the perpendicular drawn from the opposite angle to that side. Let ABC be any triangle, and the angle at B one of its acute angles; on BC, one of the sides containing B, let fall the perp. Af) from the opposite angle A; the square... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...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 pages
...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...angles ; and upon BC, one of the sides containing it, • 12. 1. let fall the perpendicular' AD from the opposite angle: the square of AC, opposite to the... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...oftJie acute angles, is less than t he squares of the sides containing that angle by twice the rectangle contained by either of these sides, and the straight...angles, and upon BC, one of the sides containing it, let a 12. 1. fall the perpendicular" AD from the opposite angle: The square of AC, opposite to the angle... | |
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Therefore, in obtuse-angled triangles, &c. QED PROP. 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... 
