 | John Playfair - 1836 - 148 σελίδες
...equal to the 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 (16. 2.) the square... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...9.) HB2 + BD*, 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 ;... | |
 | Euclides - 1837 - 112 σελίδες
...FG", and that 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.... | |
 | Euclides - 1838 - 264 σελίδες
...squares of AC, CD. 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:... | |
 | Euclides - 1841 - 378 σελίδες
...of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 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;... | |
 | John Playfair - 1842 - 332 σελίδες
...proposition is evident from this algebraical equality. 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 ;... | |
 | Euclides - 1842 - 316 σελίδες
...equivalent to the 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 equivalent to the square of the other part. Upon AB describe (46. 1.) the... | |
 | 1844 - 688 σελίδες
...each of the parts 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... | |
 | Great Britain. Council on Education - 1845 - 696 σελίδες
...whole and that part, together with the square of the other part. 62. 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. 63. Show that if — B he substracted... | |
 | Euclides - 1845 - 546 σελίδες
...equal to the square of the other part. Let AB be the given straight line. It is required to divide AB 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. H KD Upon AB describe the square... | |
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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. 
