 | Euclides - 1816 - 528 pages
...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 straight line; it is required to... | |
 | Miles Bland - Euclid's Elements - 1819 - 377 pages
...equal to the square of AB, ie to the given square. (9.) To divide a straight line into ttvo 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. L,etAB be the... | |
 | Miles Bland - Euclid's Elements - 1819 - 377 pages
...square, and their rectangle equal to a given rectangle. 9. To divide a 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. 10. To divide... | |
 | John Playfair - Circle-squaring - 1819 - 333 pages
...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 (46. 1.) the square ABDC ; bisect... | |
 | John Mason Good - 1819
...the half and the part produced. Prop. XI. Prob. To divide a given straight lint into tu'o parts, so that the rectangle contained by the whole, and one of the parts, shall be equal tu the fquare of the other part. Prop. XII. Theor. In obtuse angled triangles, if a... | |
 | Peter Nicholson - Mathematics - 1825 - 372 pages
...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 (46. I.) the square ABDC; bisect (10.... | |
 | Robert Simson - Trigonometry - 1827 - 513 pages
...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 in E,... | |
 | Euclid - 1835 - 513 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. e 47. 1. Upon AB describe » the square ABDC ; bisect5... | |
 | John Playfair - Geometry - 1836 - 114 pages
...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 (8.... | |
 | Euclid, James Thomson - Geometry - 1837 - 390 pages
...the given lines are equal. PROP. XXIII. PROB. To divide a given straight line into two parts, such. that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the given line;... | |
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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. 
