| Mathematics - 1835 - 684 pages
...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 angle, by twice...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... | |
| Mathematics - 1836 - 488 pages
...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 angle, by twice...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... | |
| John Playfair - Euclid's Elements - 1836 - 488 pages
...In every triangle, the square of the side sub- . tending 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** tides, and the straight line intercepted between the perpendicular, let fall upon it from the opposite... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...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 angle, by twice...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 - Euclid's Elements - 1837 - 290 pages
...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 - Geometry - 1837 - 254 pages
...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... | |
| Robert Simson - Geometry - 1838 - 434 pages
...THEOR. Iir 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...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... | |
| Euclides - 1840 - 82 pages
...THEOR. In any triangle, the square of a side subtending an acute angle is less than the sum of the **squares of the sides containing that angle, by twice the rectangle contained by either of** those sides and the part of it intercepted between the perpendicular let fall on it from the opposite... | |
| Euclides - Geometry - 1841 - 378 pages
...XIII. THEOR. In every triangle, the square of the side subtending an acute angle, is less than the **squares of the sides containing that angle, by twice...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,... | |
| Euclides - 1842 - 316 pages
...сл, by twice the rectangle вc, CD. Therefore, in obtuseangled triangles, &c. QED PROP. XIII. THEOR. **the sides containing that angle, by twice the rectangle...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... | |
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