 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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 straight line ; it... | |
 | Euclides - 1846 - 292 pages
...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 the square ACDB ; bisect... | |
 | Euclides - 1848 - 52 pages
...of the line made up of the half and the part produced. PROP. XI. 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 the other part. PROP. XII. THEOREM. In obtuse-angled... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...the triangle between the perpendicular and the obtuse angle. Section 4. 1. 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. 2. Describe a square that shall be double... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...Wherefore, if a straight line, &c. QED Again, because EG F is EF 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 Tie equal to the square of the other part. Let AB be the given straight line; it... | |
 | University of Cambridge - 1849 - 560 pages
...homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. 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. Shew that in Euclid's figure four other... | |
 | Great Britain. Committee on Education - 1850 - 942 pages
...the same parallels, are equal to one another. 3. Solve Euc. II. 11. To divide a given finite straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the squire of the other part. 4. Prove Euc. III. 22. The opposite angles... | |
 | Francis James Jameson - Mathematics - 1851 - 144 pages
...+ AC2) + 4AE2 + 4AF2, = 4BC2 + AB2 + AC2, = 4BC2 + BC2, - 5BC8. 1849. (A). 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. (ii. 11.) (B). Shew that in Euclid's figure,... | |
 | 1867 - 336 pages
...of the line between the points of section. , Illustrate this by Algebra. 2. 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. Shew how to represent the square root... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. 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. Shew that in Euclid's figure four other... | |
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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 on the other part. 
