 | John Playfair - 1819 - 350 sider
...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 (46. 1.) the square ABDC ; bisect... | |
 | Miles Bland - 1819 - 444 sider
...their squares may be equal to a given 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 aud one of the parts may be equal to the square of a given line, which is less than the line to be... | |
 | John Playfair - 1819 - 354 sider
...AD3+DB==2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED PROP. XI, PROB. To divide a given straight line into too parts, so that the rectangle contained by the whole, and one of the parts, niay be equal to the square of the other part. Let AB be the given straight line ; it is required to... | |
 | John Mason Good - 1819 - 800 sider
...made up of 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... | |
 | Daniel Cresswell - 1819 - 486 sider
...manifest from this proposition, and from E. 1O. 4., that if the semi-diameter of a circle be divided into two parts, so that the rectangle contained by the whole and the lesser part may be equal to the square of the greater part, the greater segment shall be equal... | |
 | Miles Bland - 1821 - 898 sider
...given rectangle. Also the squares of AD, DB are equal to the square of AB, г. e. to the given square. 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. Let AB be the given line to be divided.... | |
 | Euclid, Robert Simson - 1821 - 514 sider
...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 dne of the parts shall be equal to the square of the other part. Upon AB describe (46. 1.) the square... | |
 | Peter Nicholson - 1825 - 1046 sider
...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 straight line ; it is required... | |
 | Daniel Cresswell - 1825 - 616 sider
...produced, shall be to the square of the part produced, in a given ratio. VIII. PR. To divide a given finite straight line into two parts, so that the rectangle, contained by the whole line, and the difference of those two parts, shall be in a given ratio to the square of the less of... | |
 | Miles Bland - 1827 - 462 sider
...rectangle contained by the whole line produced and the part produced may be equal to a given square. 9. To divide a straight line into two parts, so that 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 a given line into two such... | |
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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. 
