 | Edward Atkins - 1874 - 426 pages
...on AC and CD. Therefore, if a straight line, &c. QED Proposition 11. — Problem. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square on the other part. Let AB be the given straight line. It... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...sides, the sums of the squares on the alternate segments of the sides are equal to one another. 12. Divide a straight line into two parts, so that the rectangle contained by the two parts shall be equal to the square on a given line. How many solutions are there? When is the problem... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...sides which are not parallel and twice the rectangle contained by the sides which are parallel. 11. Divide a straight line into two parts so that the rectangle contained by them may be equal to a given rectangle. 1 2. Describe a rectangle equal to a given square, and having... | |
 | Edward Atkins - 1874 - 428 pages
...equal to the square on the other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square on the other part. CONSTRUCTION. — Upon AB describe the... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...double of the square on half ithe line and of the square on the line between the points of section. 8. Divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 9. In the Algebraic solution of the preceding... | |
 | Edward Atkins - 1876 - 130 pages
...on AC and CD. Therefore, if a straight line, &c. QED Proposition 11. — Problem. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square on the other part. Let AB be the given straight line. It... | |
 | Henry Major - 1876 - 784 pages
...squares on the two parts, together with twice the rectangle contained by the parts. 2. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part. 3. If the diagonals of a quadrilateral... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pages
...EF = twice sq. on AC together with twice sq. on CD. QED PROPOSITION XI. PROBLEM. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square on the other part. jD K I"' Let AB be the given st. line.... | |
 | University of Madras - 1876 - 580 pages
...isosceles triangle is less than that of any other equal triangle upon the same base. III. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. IV. (a) If from any point without a circle... | |
 | 1880 - 160 pages
...two parts, together with twice' *the rectangle contained by the two parts. (viii.) To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 5. If the distances of a point from two... | |
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To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part. 
