 | Robert Simson - 1827 - عدد الصفحات: 546
...« 46. 1. •6.2. t Constr. • 47. 1. t 3 Ax. t 30 Def. t lAx. t 3 Ax. t 30 Def. PROP. XL 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... | |
 | Euclid - 1835 - عدد الصفحات: 540
...AD, DB are double the squares of AC, CD. Wherefore, " if a straight line," &c. QED 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... | |
 | Euclid, James Thomson - 1837 - عدد الصفحات: 410
...HB, AD are equal. Then c B (II. 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... | |
 | Euclides - 1837 - عدد الصفحات: 112
...that this = AC* + CE* + EF! + 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... | |
 | Euclides - 1838 - عدد الصفحات: 264
...AD, DB are double of the 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... | |
 | Euclides - 1841 - عدد الصفحات: 378
...DB are double of the squares 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... | |
 | Adrien Marie Legendre - 1841 - عدد الصفحات: 288
...from the given points. (215.) Fig. 364. Q. LXXVIII. To divide a straight line AB into two parts such that the rectangle contained by them may be equal to the square of their difference. Upon AB describe a semicircle ADB. From B draw BC at right angles, and equal to... | |
 | John Playfair - 1842 - عدد الصفحات: 332
...(2a-f*)2+*2=2a2+2(a+i)2, and the 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... | |
 | Euclides - 1842 - عدد الصفحات: 316
...equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED 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 equivalent to the square of the other part. Let AB be the... | |
 | 1844 - عدد الصفحات: 688
...contained by the whole and 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... | |
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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. 
