 | Euclides - 1864 - 448 pages
...or o* = m* + 2mn + n'., That is, if a number be divided into any two parts, the square of the number is equal to the squares of the two parts together with twice the product of tile two parts. From Euc. n. 4, may be deduced a proof of Euc. I. 47. In the fig. take DL... | |
 | Euclides - 1865 - 402 pages
...the rectangle contained by the two parts, together with the square of the aforesaid part. Prop. 4. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Cor. The parallelograms about the diameter of a square are likewise squares. Prop. 5. If a straight... | |
 | Robert Potts - 1865 - 528 pages
...or o* ,= m* + 2mn + n*. That is, if a number be divided into any two parts, the square of the number is equal to the squares of the two parts together with twice the product of the two parts. From Euc. it. 4, may be deduced a proof of Euc. i. 47. In the fig. take DL... | |
 | John Playfair - Geometry - 1855 - 350 pages
...multiplying both members of this equality by c, we shall have oc=6c+c2. PROP. IV. THEOR. IJ a straight lint be divided into any two parts, the square of the whole line u equal to the squares of the two parts, together with twice the rectangle contained by the parts.... | |
 | Edinburgh univ - 1868 - 334 pages
...other ; the base of that which has the greater angle shall be greater than the base of the other. 3. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 4. The diameter is the greatest straight line in a circle ; and, of all others, that which is nearer... | |
 | Robert Potts - 1868 - 434 pages
...a* = i»s + 2m» + »*. That is, if a number be divided into any two parts, the square of the number is equal to the squares of the two parts together with twice the product of the two parts. From Euc. n. 4, may be deduced a proof of Eue. I. 47. In the fig. take DL... | |
 | Robert Johnston (F.R.G.S.) - Civil service - 1869 - 196 pages
...which it is proved that the three angles of a triangle are together equal to two right angles. 4. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 5. Divide a given straight line into two parts, so that the rectangle contained by the whole and one... | |
 | James Smith - Circle-squaring - 1869 - 459 pages
...equal to the area of a rectangle of which AD and AE are sides. By Euclid : Prop. 2 : Book 2 : " If a straight line be divided into any two parts •, the square of the whole line is equal to the sum of the rectangles contained by the whole line and each of its parts" Hence : (AD • AE + AD •... | |
 | James Smith - Mathematics - 1869 - 492 pages
...equal to the area of a rectangle of which AD and AE are sides. By Euclid : Prop. 2 : Book 2 : " IJ -a straight line be divided into any two parts, the square of the whole line is equal to the sum of the rectangles contained by the whole line and tach of its parts" Hence :(AD-AE + AD.ED) = AD',... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...If a line be divided into two parts, the square on the whole is equal to the sum of the squares on the two parts, together with twice the rectangle contained by the parts. Let AB (fig. 144) be divided in C ; then the square on AB = the sum of the squares on AC, CB, together... | |
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If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 
