| 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 - 358 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 - 336 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 - 1869 - 490 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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