 | John Playfair - 1829 - 210 σελίδες
...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 angle to that side.... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...PROP. XIII. THEOR. IN any triangle, the square of the side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle...perpendicular drawn to that side from the opposite angle. Let ABC (see this figure and that of the foregoing proposition,) be any triangle, having the angle... | |
 | Euclides - 1840 - 82 σελίδες
...subtending the obtuse angle exceeds the sum of the squares of the sides containing the obtuse angle, by twice the rectangle contained by either of those sides and the produced part of it intercepted between the perpendicular let fall on it from the opposite angle and... | |
 | Euclides - 1841 - 378 σελίδες
...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, and the angle at B one of its acute... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...PROP. XIII. THEOR. — In any triangle, the square of a side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle...perpendicular drawn to that side from the opposite angle. Let ABC (see this figure and that of the foregoing proposition) be any triangle, having the angle B... | |
 | Euclides - 1845 - 546 σελίδες
...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, and the angle at B one of its acute... | |
 | Home and colonial school society - 1848 - 412 σελίδες
...adds, with reference to Greek, — angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of those...intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. " Investigate the polar equation to a parabola. " Investigate... | |
 | Euclides - 1848 - 52 σελίδες
...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. PROP. XIV. PROBLEM. BOOK III. DEFINITIONS. I. EQUAL circles... | |
 | Great Britain. Council on Education - 1848 - 596 σελίδες
...less than tbe 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 this proposition need be demonstrated.)... | |
 | J. Goodall, W. Hammond - 1848 - 390 σελίδες
...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 this proposition need be demonstrated.)... | |
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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 acute... 
