| Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...definition of the projection of a straight line given on p. 153, we may enunciate Prop. 13 as follows ; **In every triangle, the square on the side subtending an acute angle is less than the** sum of the squares on the sides containing that angle, by twice the rectangle contained by one of these... | |
| Education - 1900 - 898 pages
...the side subtending the obtuse angle is greater than the sum of the squares on the other two sides **by twice the rectangle contained by either of these sides, and the** part of it produced beyond the obtuse angle to meet a perpendicular from the opposite vertex. 16. 7.... | |
| Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...rectangle contained by the whole and that part, together with the square on the other part. 5- Prove that **in every triangle the square on the side subtending an acute angle is less than the** sum of the squares on the sides containing that angle, by twice the rectangle contained by either of... | |
| Education - 1901 - 548 pages
...straight line to cut Ihe sides AB, AC, DB, DC, in the points E, F, G, H, such that EK equals KG or GH. (4) **In every triangle the square on the side subtending an acute angle is less** ihan the squares on the sides containing that angle, by twice the rectangle contained by either of... | |
| James McMahon - Geometry, Plane - 1903 - 380 pages
...THEOREM 22. In any triangle the square on the side opposite an acute angle is less than the sum of **the squares on the sides containing that angle by twice the rectangle** of either of these sides and the projection of the other upon it. Let ABC be a triangle having the... | |
| Euclid - Euclid's Elements - 1904 - 488 pages
...definition of the projection of a straight line given on p. 153, we may enunciate Prop. 13 as follows ; **In every triangle, the square on the side subtending an acute angle is less than the** sum of the squares on the sides containing that angle, by twice the rectangle contained by one of these... | |
| 1906 - 818 pages
...the rectangle contained by the whole and that part, together with the square on the other part. 4. **In every triangle the square on the side subtending...containing that angle by twice the rectangle contained by** cither of these sides, and the straight line intercepted between the perpendicular let fall upon it... | |
| Henry Sinclair Hall - 1908 - 286 pages
...by one of those sides and the projection of the other side upon it. . 226 THEOREM 55. [Euc. II. 13.] **In every triangle the square on the side subtending an acute angle is** equal to the sum of the squares on the sides containing that angle diminished by twice the rectangle... | |
| Alexander H. McDougall - Geometry - 1910 - 316 pages
...the obtuse angle equals the sum of the squares on the sides that contain the obtuse angle increased **by twice the rectangle contained by either of these sides and the** projection on that side of the other. Hypothesis. — ABC is a A in which LC is obtuse, and CD is the... | |
| Education - 1911 - 1330 pages
...described on the hypotenuse is equal to the sum of the squares described on the other two sides. 2. **In every triangle the square on the side subtending an acute angle is** equal to the sum of the squares on the sides containing that angle, diminished by twice the rectangle... | |
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