 | Euclid - 1835 - 540 pages
...acute angles, is less than the squares of t 'fie 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 • 12. 1. fall the perpendicular* AD from the opposite angle: The square of AC, opposite to the angle... | |
 | Mathematics - 1835 - 684 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.... | |
 | Mathematics - 1836 - 488 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 perperdicular, let fall upon it from the opposite angle, and the acute angle. A. If one side of a triangle... | |
 | Euclides - Euclid's Elements - 1837 - 112 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...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 A.) 1. Prove... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...is greater than the squares of BC, CA, by twice the rectangle BC • CD. PROPOSITION XIII. THEOREM. of these sides, and the straight line intercepted...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 of the sides containing... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...acute angles is less than the squares of the sides containing the same angle, by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular, drawn to it from the opposite angle, and the acute angle. SUBSTANCE OF SECTION VII. 1. Squares are... | |
 | Euclides - 1838 - 264 pages
...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 the straight...and the angle at B one of its acute angles, and upon I3C, one of the sides containing it, ,j2 1 let fall the perpendicular* AD from the opposite angle:... | |
 | Robert Simson - Geometry - 1838 - 434 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...from the opposite angle and the acute angle.* Let BBC be any triangle, and the angle at B one of its acute angles, and upon BC one of the sides containing... | |
 | Euclid - Geometry - 1838 - 470 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...from the opposite angle and the acute angle.* Let BBC be any triangle, and the angle at B one of its acute angles, and upon BC one of the sides containing... | |
 | Euclides - Geometry - 1841 - 378 pages
...an acute angle, 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 angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,... | |
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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... 
