 | 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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In every triangle, the square of the side subtending either 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... 
