 | John Playfair - 1806 - Liczba stron: 320
...because DG=DB; therefore AD2+DB2=2AC2+ 2CD2. Wherefore, if a straight line, &c, QE D, 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... | |
 | Robert Simson - 1806 - Liczba stron: 546
...double of the squares of AC, CD. Wherefore, wr a straight line, &c. QED PROP. XI. PROB. TO clivjde 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... | |
 | Euclid - 1810 - Liczba stron: 554
...DB are double of the squares of AC, CD. \Vherefore, if a straight line, &c. QED PR6P. XI. PROB. 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... | |
 | Euclides - 1816 - Liczba stron: 588
...double of the squares of AC, CD. Wherefore, if a straight line, £c. QED "46. 1 Ho. 1 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, shall be equal to the square of the other part. Let AB be the given... | |
 | John Playfair - 1819 - Liczba stron: 350
...DG=DB: Therefore, AD3 +DB3=2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED . . 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... | |
 | Miles Bland - 1819 - Liczba stron: 444
...make with each other angles equal to given angles. 6. To divide a straight line into two parts such that the rectangle contained by them may be equal to the square of their difference. 7. If a straight line be divided into any two parts; -to produce it so that the... | |
 | Miles Bland - 1819 - Liczba stron: 442
...make with each other angles equal to given angles. 6. To divide a straight line into two parts such that the rectangle contained by them may be equal to the square of their difference. 7. If a straight line be divided into any two parts; to produce it so that the... | |
 | Peter Nicholson - 1825 - Liczba stron: 1046
...double of the squares of AC, CD. Wherefore, if a straight line, &c. QED Proposition Xf. 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 'o the square of the other part. Let AB be the given... | |
 | Euclid - 1826 - Liczba stron: 234
...being given A, B, с, a fourth proportional HF has been found. QEF Deductions. 1 . Divide a given right line into two parts, so that the rectangle contained by them may be equal to a given rectangle. 2. From a given point to draw a right line to cut a given circle, so that the distances... | |
 | Euclides - 1826 - Liczba stron: 226
...being given A, B, c, a fourth proportional HF has been found. QEF Deductions. 1. Divide a given right line into two parts, so that the rectangle contained by them may be equal to a given rectangle. 2. From a given point to draw a right line to cut a given circle, so that the distances... | |
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AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. 
