 | Euclides - 1865 - 402 pages
...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 square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Cor. The parallelograms... | |
 | James Robert Christie - Mathematics - 1866 - 428 pages
...angle." 2. Parallelograms upon the same base, and between the same parallels, are &c. 3. If a straight line be divided into any two parts, the square of the whole line is equal to &c. 4. The opposite sides of a quadrilateral described about a circle are together equal to the other... | |
 | 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.... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...rectangle AD . AB is equal to the sum of all the other rectangles AD . AE, AD . EF, AD . FB. QE HCorol. If a right line be divided into any two parts, the square on the whole line is equal to both the rectangles of the whole line and each of the parts. CB THEOREM... | |
 | Edinburgh univ - 1868 - 334 pages
...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 square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 4. The diameter... | |
 | James Smith - Mathematics - 1869 - 492 pages
...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', that is,... | |
 | James Smith - Circle-squaring - 1869 - 459 pages
...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 • ED) = A D2,... | |
 | Robert Johnston (F.R.G.S.) - Civil service - 1869 - 196 pages
...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 square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 5. Divide a given... | |
 | James Smith - 1870 - 634 pages
...Now, by Euclid : Prop. 2 : Book 2 : '' If a straight line (AB) be divided into any two parts (AC, CB), the square of the whole line is equal to the sum of the rectangles contained by the whole line and each of its parts :" and I shall proceed to prove that this... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...equal to twice the rectangle of one of the lines and half the other line. PROPOSITION 12. If a straight line be divided into any two parts, the square of the whole line shall be equal to the sum of the squares of the two parts, together with twice the rectangle of those... | |
| |
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. 
