 | John Playfair - Euclid's Elements - 1842 - 332 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...B one of its acute angles, and upon BC, one of the side's containing it, let fall the perpendicular (12. 1.) AD from the opposite angle : The square of... | |
 | Euclides - 1842 - 316 pages
...obtuseangled triangles, &c. QED PROP. XIII. THEOR. the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight...acute angle. Let ABC be any triangle, and the angle at в one of its acute angles, and upon в c, one of the sides containing it, let fall the perpendicular... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...the acute angles, is less than the sum of the squares of the other two sides, by twice the rectangle contained by either of these sides and the straight...upon it from the opposite angle, and the acute angle. PROPOSITION XIII. THEOREM. In a triangle ABC, if the angle C is obtuse, the square of the opposite... | |
 | John Playfair - Euclid's Elements - 1844 - 338 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 perpendicular,let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle,... | |
 | Euclides - 1845 - 546 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 acute angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 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. Prop. 46. Prop. 39. Prop. is. P J, 47 Fig. 1. A BDC 1st. When GEOMETRY. Fig. 2. A Fig. 3. A BC D BC... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...than the squares of the sides containing that angle, by twice the rectangle contained by either oj these sides, and the straight line intercepted between...the opposite angle, and the acute angle. Let ^\ ABC have the acute L ABC, upon BC one of the sides containing it, draw AD J_ BC ; then AC 8 < CB« + BA... | |
 | Great Britain. Council on Education - Education - 1848 - 532 pages
...any 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...upon it from the opposite angle and the acute angle ; prove only the first case of this proposition. Section 4. 1. Construct a triangle whose area shall... | |
 | Great Britain. Committee on Education - Education - 1848 - 514 pages
...any 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...upon it from the opposite angle and the acute angle ; prove only the first case of this proposition. Section 4. 1. Construct a triangle whose area shall... | |
 | Great Britain. Committee on Education - 1848 - 606 pages
...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... | |
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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... 
