 | Robert Simson - 1806 - 546 pàgines
...PROP. XIII. THEOR. See N. IN every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that...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,... | |
 | John Playfair - 1806 - 320 pàgines
...acute angles is less than the squares of the sides containing that angle, by twice the rect. angle 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,... | |
 | John Mason Good - 1813 - 714 pàgines
...angle. Prop. XIII. Theor. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Prop. XIV. Prob. To describe... | |
 | Euclides - 1814 - 560 pàgines
...t. PKOP. XIII. THEOR. IN every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...contained by either of these sides, and the straight line intercopted between the perpendicular let fall upon it from the opposite angle, and the acute angle.... | |
 | John Playfair - 1819 - 350 pàgines
...PROP. XIII. THEOR. In every triangle, the square of the side subtending any of the acute angles, i$ less than the squares of the sides containing that...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,... | |
 | Peter Nicholson - 1825 - 1046 pàgines
...Proposition XIII. Theorem. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...contained by either of these sides, and the straight line inteicepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.... | |
 | Henry Parr Hamilton - 1826 - 354 pàgines
...following Proposition : " In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that...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... | |
 | Robert Simson - 1827 - 546 pàgines
...XIII. THEOR. In every triangle, the square of the side subtending either SeeN. of the acute angles, is less than the squares of the sides containing that...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,... | |
 | Pierce Morton - 1830 - 584 pàgines
...21 (б) In every triangle, the square of the side which is opposite to a given angle is greater or less than the squares of the sides containing that...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... | |
 | John Playfair - 1832 - 358 pàgines
...QED B PROP. XIII. THEOR. In every triangle the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...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,... | |
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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... 
