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. Introduction and books 1,2 - Page 402by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| Euclides - 1845
...square of the other part. Let AB be the given straight line. It is required to divide AB 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. H KD Upon AB describe the square ACDB; (i. 46.)... | |
| Great Britain. Council on Education - 1845
...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 from A,... | |
| Euclides - Geometry - 1845 - 199 pages
...a straight line, &c. QED PROPOSITION 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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...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 is required... | |
| Euclides - 1846
...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 AC... | |
| George Moody - 1847
...angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, **so that the rectangle contained by the whole and one of the** parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending... | |
| Euclides - 1848
...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 triangles,... | |
| J. Goodall, W. Hammond - 1848
...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 a given... | |
| University of Cambridge, Sir Thomas Gery Cullum - 1849
...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 lines,... | |
| Euclides - 1849
...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 is required... | |
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