 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...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 sides and the... | |
 | 1900 - 650 pages
...lines cannot be drawu from the given point to the circumference. 4. In any triangle the square on any 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 them and the intercept... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...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 these sides, and... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...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 sides and the... | |
 | George Bruce Halsted - Geometry - 1904 - 324 pages
...equilateral triangle. _Proof. AB\ 305. Theorem. In any triangle, the square of a side opposite any acute angle is less than the sum of the squares of the other two sides by twice the product of either of those sides cand a sect from the foot of that ...... | |
 | George Bruce Halsted - Geometry - 1904 - 313 pages
...+ FG 2 = (±ABr + (i3(AB) 2 = AB\ 305. Theorem. In any triangle, the square of a side opposite any acute angle is less than the sum of the squares of the other two sides by twice the product of either of those sides c ~ ___ and a sect from the foot of that... | |
 | Trinity College (Dublin, Ireland) - 1911 - 614 pages
...and between the same parallels are equal in area. 2. Prove that the square of a side of a triangle subtending an acute angle is less than the sum of the squares of the sides containing the angle by twice a certain rectangle. 3. Prove that chords nearer to the centre of a circle are longer... | |
 | Alberta. Department of Education - Education - 1912 - 244 pages
...produced. 6 — II. 3 (b) Express the theorem in (o) algebraically. 9 10. In every triangle the square on the side subtending an acute angle is less than the sum of the squares on the sides containing the acute angle, by twice the rectangle contained by either of these sides,... | |
 | University of South Africa - Universities and colleges - 1913 - 768 pages
...(a — b)a — a.. — 2 ah + bi. 14) 0z _ bz = (a -fb) (a — b). 1n 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 these sides, and... | |
 | Trinity College (Dublin, Ireland) - 1917 - 560 pages
...given triangle, and have an angle equal to a given angle. 4. Prove that in any triangle the square of a side subtending an acute angle is less than the sum of the squares of the other sides by twice the rectangle contained by either of those sides, and the straight line intercepted... | |
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In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the... 
