 | Miles Bland - 1819 - 442 Seiten
...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...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... | |
 | John Playfair - 1819 - 350 Seiten
...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... | |
 | John Playfair - 1819 - 354 Seiten
...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 Seiten
...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... | |
 | Miles Bland - 1819 - 444 Seiten
...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... | |
 | Daniel Cresswell - 1819 - 486 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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...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 Seiten
...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... | |
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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. 
