 | George Lees - 1826 - 276 σελίδες
...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... | |
 | John Playfair - 1829 - 210 σελίδες
...triangle the square of the side subtending an acute angle is less than the sum of the squares of the two sides containing that angle, by twice the rectangle contained by either of those sides and the distance between the acute angle and the perpendicular drawn from the opposite... | |
 | Pierce Morton - 1830 - 584 σελίδες
...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... | |
 | Euclides - 1834 - 518 σελίδες
...See N. THEOR. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that...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... | |
 | 1835 - 684 σελίδες
...13.) In every triangle, the square of the side which is opposite to any 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... | |
 | 1836 - 488 σελίδες
...obtuse angle. XIII. 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 perperdicular, let fall upon it from the opposite angle, and the acute angle. A. If one side of a triangle... | |
 | Euclides - 1837 - 112 σελίδες
...PROPOSITION XIII. Theorem. In every triangle, the square of the side -btending any of the acute angles is less than the squares of the sides containing that...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 - 1837 - 290 σελίδες
...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 - 1837 - 254 σελίδες
...the side subtending any of the acute angles is less than the squares of the sides containing the same angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular, drawn to it from the opposite angle, and the acute angle. SUBSTANCE OF SECTION VII. 1. Squares are... | |
 | Euclid - 1838 - 470 σελίδες
...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...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... | |
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In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the... 
