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. Introduction and books 1,2 - Page 402by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| John Playfair - Geometry - 1836 - 114 pages
...of the other part. Let 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. Upon AB describe (16. 2.) the square ABDC; bisect... | |
| Euclid - 1837 - 390 pages
...or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. 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 of the other part. Let AB be the given straight line ; it is required... | |
| Euclides - 1837
...these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ 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 of c KT~i the other part. Steps of the Demonstration. 1. Prove that... | |
| Euclides - 1838
...Wherefore, if a straight line, &c. QED PROP. XI. PROS. 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. Let AB be the given straight line: it is required... | |
| Euclides - 1841
...square of the other part. Let 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. Upon AB describe* the square ABDC; bisect* AC... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...equilateral and equiangular pentagon has been inscribed. Otherwise. " Divide the radius of the given circle, **so that the rectangle contained " by the whole and one of the** parts may be equal to the square of the other " (11. 2.). . Apply in the circle, on each side of a... | |
| Euclides - 1842
...of the other part. Let 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 equivalent to the square of the other part. Upon AB describe (46. 1.) the square ABDC... | |
| Education - 1844
...are together equal to the square of the whole line. 7. 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. 8. If in a circle two straight lines cut one... | |
| 1845
...these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 of a given line, which is less than the line to be divided. (Euclid,... | |
| James Thomson - Geometry - 1845 - 358 pages
...are, by the same curolla'y, tliť PROP. XI. PROB. — 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 of the other part. Let AB be the given straight line ; it is required... | |
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