| 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 - 444 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 - 442 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... | |
| Euclid, John Playfair - Circle-squaring - 1819 - 348 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 - 740 pages
...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 - 540 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 - Geometry - 1837 - 410 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;... | |
| |