| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...G, so that FG may be equal to FB; then join AG, and AG will intersect CD at the required point. 40. **To divide a given straight line into two parts such that the** difference of the squares on the parts may be equal to a given square. Let AB be the given straight... | |
| James Maurice Wilson - 1869 - 260 pages
...therefore remembering that AD = DC, we obtain by addition that AB* + BC* = 2AD* + 2DB*. Ex. 3. To divide a **straight line into two parts such that the rectangle contained by the whole line and one of** the parts is equal to the square of the other part. Let AB be the given line. Construction. Draw a... | |
| Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...squares on ABlt _B02, CAS together, is equal to the sum of those on A Ci, BAt, CB3 together. n. 11. **Divide a given straight line into two parts, such that the rectangle contained by the whole** and one part may be equal to that contained by the other part and a given straight line. 1863. in.... | |
| Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...velocity of the river and the speed of the boats in still water. (25.) Section B.—Geometry. 27. Show how **to divide a given straight line into two parts, such that the rectangle** under the whole line and one of the parts may be equal to the square on the other part. Given, a straight... | |
| Edward Harri Mathews - 1879 - 94 pages
...other. What is the greatest value which these complements, for a given parallelogram, can have ? 3. **Divide a given straight line into two parts, such that the rectangle contained by the whole** and one of the parts shall be equal to the square on the other part. Divide a given straight line into... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...?arts is equal to the sum of the squares described on the parts, the straight line is bisected. 135. **Divide a given straight line into two parts such that the rectangle contained by** them shall be the greatest possible. 136. Construct a rectangle equal to the difference of two given... | |
| College of preceptors - 1882 - 528 pages
...the two parts increased by twice the rectangle contained by the two parts. 6. Show how to divide a **straight line into two parts such that the rectangle contained by the whole line and one** part shall be equal to the square described upon the other part. Prove the construction. 7. Define... | |
| John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...sides shall be equal each to each, and the third angle of the one to the third angle of the other. 5. **Divide a given straight line into two parts such that the rectangle contained by the whole** and one part may be equal to the square on the other part. 6. In an isosceles triangle ABC, prove that... | |
| University of Glasgow - 1883 - 438 pages
...in reference to human action. HIGHER MATHEMATICS. Uth Oc'ober, 1882. 1. Divide a given straight lino **into two parts, such that the rectangle contained by the whole line and one of** the parts shall be equal to the square on the other part. Where does Euclid afterwards make use of... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...parts is equal to the sum of the squares described on the parts, the straight line is bisected. 135. **Divide a given straight line into two parts such that the rectangle contained by** them shall be the greatest possible. 136. Construct a rectangle equal to the difference of two given... | |
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