 | Euclides - 1864 - 448 Seiten
...double of the squares on AC, CD. Wherefore, if a straight line, &c. QED PROPOSITION XI. PROBLEM. To divide a given straight line into two parts, so that the rectangle cnntnined by the whole and one of the parts, shall be equal to the square oii the other part. Let AB... | |
 | Robert Potts - 1865 - 528 Seiten
...of the squares on AC, CD. Wherefore, if a straight liue, &c. QED PROPOSITION XI. PROBLEM. To divitfe 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 otlier part. Let AB be the given straight line. It is required... | |
 | Euclides - 1865 - 402 Seiten
...angle and the perpendicular let fall upon it from the opposite angle s. . . n. 13. Problems. 1. To divide a given straight line into two parts, so that the rectangle under the whole and one of the parts is equal to the square on the other part . . . . . . n. 11. 2.... | |
 | 1867 - 224 Seiten
...angle contained by those two sides is a right angle. 9. Define rectangle ; gnomon. '••/£: , 10. Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part, jj yi . 1 1. Give construction only for describing... | |
 | Euclid, Isaac Todhunter - 1867 - 424 Seiten
...shew that the square on BC is equal to the rectangle AB, BF, together with the rectangle AC, CE. 161. Divide a given straight line into two parts so that the rectangle contained by them may be equal to the square described on a given straight line which is less than half the straight... | |
 | Euclid, Isaac Todhunter - 1867 - 426 Seiten
...shew that the square on BC is equal to the rectangle AB, BF, together with the rectangle AC, CE. 161. Divide a given straight line into two parts so that the rectangle contained by them may bo equal to the square described on a given straight line which is less than half the straight... | |
 | Edinburgh univ - 1868 - 336 Seiten
...Equal triangles upon the same base, and upon the same side of it, are between the same parallels. 4. To divide a given straight line into two parts, so that...whole, and one of the parts, may be equal to the square of the other part. 5. The angles in the same segment of a circle are equal to one another. 6. If a... | |
 | Robert Potts - 1868 - 434 Seiten
...double of the squares on AC, CD ; but DG is equal to DB; BOOK II. PROP. XI. PROPOSITION XI. PROBLEM. To divide a given straight line into two parts* so that...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 is required to... | |
 | E. J. Brooksmith - 1889 - 356 Seiten
...are points in a straight line, taken in order, prove that the rectangle AC . BD = AB . CD + BC . AD. 4. Divide a given straight line into two parts, so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. 5. Equal straight lines in... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 Seiten
...of the complements, show that the complement is equal to half the other parallelogram. Ex. 652. — Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the rectangle contained by the other part and a given finite straight line. Ex.... | |
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AB be the given straight line ; it is required to divide it 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. 
