| 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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