 IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.  Calendar of Dalhousie College and University - Page xby Dalhousie University - 1891Full view - About this book
 | Moffatt and Paige - 1879 - 506 pages
...added together in one straight line. Therefore, if a straight line, etc. QED Proposition IX. Theorem. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square... | |
 | Euclides - 1879 - 146 pages
...Now BC contains a — x units, hence the analogous result is established.] PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...14. Show how to describe a square that shall be equal to a given rectilineal figure. Deductions. 1. If a straight line be divided into two equal, and also into two unequal parts, the part between the points of section is •equal to half the difference of the unequal parts. 2. If the... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...joining the middle points the diagonals. From (II. 9) Add and apply (II. 4, Cor. 2) and (II. 9). 6. If a straight line be divided into two equal, and also into two unequal, parts, the rectangle contained by the unequal parts, together with the square of the line between the points of... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...the right angle. Give a geometrical construction for a square three times as great as a given square. 4. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...the line made of AB and BC together. Wherefore, if a, straight line &c. QED PROPOSITION 9. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...To combine these conclusions is the proof of the Proposition itself (as in 5). r PROP. IX. THEOREM. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts art together double of the square on half the line and of the square... | |
 | Moffatt and Paige - 1881 - 176 pages
...equal to the rectangles contained by the undivided line and the several parts of the divided line. 3. If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square... | |
 | Education, Higher - 1883 - 536 pages
...rectangle, the squares on PA and PC are together equal to the squares on PB and PD. 5. If a rectangle be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of... | |
 | Education, Higher - 1882 - 498 pages
...the bisecting lines a line be drawn to the opposite angle of the triangle it will bisect that angle. 4. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square... | |
| |
