 | Samuel Constable - Geometry - 1882 - 222 pages
...conditions, the maximum is that which is the greatest, the minimum is that which is the least. PROP. 68. To divide a given straight line into two parts, so that the sum of the squares of the segments (1) shall be given: (2) shall be a minimum. * Though the above definition... | |
 | Education - 1883 - 658 pages
...E ; show that OD = OE. 2. To divide a given straight line into two parts so that the difference of the squares on the whole line and on one of the parts may be equal to a given rectangle, which is not greater than the square on the whole line. 3. If a straight... | |
 | 1886 - 568 pages
...angles. 4. Straight lines which are parallel to the same straight line are parallel to each other. 5. 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.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...equal to the square on CD. PROPOSITION 7. THEOREM. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are ril to twice the rectangle contained by the whole and part, together with the square on the other... | |
 | Euclides - 1883 - 176 pages
...twice the rectangle contained by either side and the projection of the base upon it. PROP. 11. PROB. To divide a given straight line into two parts so that the square on one part shall be eqnal to the rectangle contained by the whole and the other part. F e GF... | |
 | Joseph Hughes - Education - 1883 - 578 pages
...squares on the two parts, together with twice the rectangle contained by the parts. Euclid II., 4. 3. 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.... | |
 | F. B. Stevens - Examinations - 1884 - 202 pages
...equal and pifrallel straight lines towards the same parts, are also themselves equal and parallel. 2. 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.... | |
 | Stewart W. and co - 1884 - 272 pages
...; but DG is equal to DB ; therefore the squares of AD, DB are twice the squares of AC, CD. XI. — 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.... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...equal and parallel straight **«9 towards the same parts are also themselves equal and parallel. 5. To divide a given straight line into two parts so that the rectangle contained by **« whol» and one of the parts may be equal to the square on the other part.... | |
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AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. 
