| James Smith - 1869 - 470 páginas
...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,... | |
| Robert Johnston (F.R.G.S.) - 1869 - 178 páginas
...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
...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 - 1871 - 285 páginas
...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... | |
| Henry Major - 1873
...rectangle AB, BC, is equal to the rectangle AC, CB, together with the square of BC. -If a straiyht 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 "tarts. ca Let AB be divided... | |
| Edward Atkins - 1874
...11. If a straight line be divided into any number of parts, the square of the whole line is equal to **the sum of the squares of the parts, together with twice the** rectangles of the parts taken two and two together. 12. If ABC be an isosceles triangle, and DE be... | |
| Edward Atkins - 1876 - 119 páginas
...tho rectangle under the extreme segments. • 11. If a straight line be divided into any number of **parts, the square of the whole line is equal to the sum of the** squares of tho parts, together with twice the rectangles of the parts taken two and two together. 12.... | |
| Elias Loomis - 1877 - 458 páginas
...middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM. If a straight line is **divided into any two parts, the square of the whole line is** equivalent to the squares of the two parts, together with twice the rectangle contained by the parts.... | |
| Thomas Hunter - 1878 - 142 páginas
...because AB=BD. Therefore AB"=AB. AC+AB.CB. PROPOSITION XVI.—THEOREM. If a straight line be divided into **two parts, the square of the whole line is equal to the sum of the** squares of the parts and twice the rectangle contained by the parts. Let AB be a straight line divided... | |
| Isaac Sharpless - 1879 - 282 páginas
...AB.BE=AB.BC; AD-AC.CD = AC.CB, CE= CB\ AB.BC-AC.CB+CB\ Proposition 4. Theorem. — 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 two part*. Let the straight... | |
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