In every triangle, the square of the side subtending any of 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... A Supplement to the Elements of Euclid - Page 104by Daniel Cresswell - 1819 - 410 pagesFull view - About this book
| Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...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." (Eve. II. IS). Since the triangle may be either acute angled, or obtuse angled, or right... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...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, and the angle at B one of its acute angles, and upon BC, one... | |
| Pierce Morton - Geometry - 1830 - 584 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.... | |
| Euclides - 1834 - 518 pages
...twice the rectangle contained by either 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 any triangle, and the angle at B one of its acute angles ; and upon BC, one... | |
| Euclid - 1835 - 540 pages
...of t 'fie 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, and the angle at B one of its acute angles, and upon BC, one... | |
| 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 acute angle; greater if the given angle is greater than a right angle, and less if it is less . . .22... | |
| John Playfair - Geometry - 1836 - 148 pages
...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, and the angle at B one of its acute angles, and upon BC, one... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...squares of BC, CA, by twice the rectangle BC • CD. PROPOSITION XIII. THEOREM. 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 he any triangle, and the angle at B one of its acute angles, and upon BC, one... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...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. Fig. 1. Fig. 3. Steps of the Demonstration to Case 1st. (in which AD falls within the... | |
| Euclides - 1838 - 264 pages
...of the sides containing that angle, ly 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, and the angle at B one of its acute angles, and upon I3C, one... | |
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