| Euclid, James Thomson - Geometry - 1845 - 382 pages
...expression, the first and third partu of whioh are, by the same curolla'y, tli» 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... | |
| Great Britain. Council on Education - 1845 - 696 pages
...the rectangle contained by the whole and that part, together with the square of the other part. 62. 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. 63. Show that if — B he substracted... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...(2a+i)2+J2=2o2+2(a+4)2, and 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... | |
| Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...segments whose rectangle is invariable. 5. Divide algebraically a given line (a) into two parts such that the rectangle contained by the whole and one part may be equal to the square of the other. Deduce Euclid's construction from one solution, and explain the other, 6. Find a straight... | |
| Euclides - 1848 - 52 pages
...the line bisected, and of the square of the line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two...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
...line intercepted without 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
...squares of AC, CD: 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
...upon the necessary 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
...between 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... | |
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