 | J. Goodall, W. Hammond - 1848 - 390 pages
...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 a given triangle.... | |
 | Euclides - 1848 - 52 pages
...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 triangles, if a perpendicular... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...line into two parts, such that the greater part may be a mean proportional between the whole line and the other part. Let AB be the given straight line; it is required to divide it into two parts at the point F, such that AB : AF:: AF:FB. At the extremity of the line AB, erect the perpendicular... | |
 | University of Cambridge - 1849 - 560 pages
...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 lines, beside the given... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...wherefore the angles CBD, DBE, and EBA are equal to one another. 2. To trisect a given straight line. Let AB be the given straight line: It is required to divide it into three equal parts. Upon AB describe (E. i. 1.) the equilateral triangle ABC; bisect (Ei 9.) the angles... | |
 | Great Britain. Committee on Education - 1850 - 942 pages
...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 of any quadrilateral... | |
 | Her MAjesty' Inspectors of schools - 1850 - 912 pages
...figures, and duplicate ratio. 3. Solve Euc. II. 11. To divide a given finite straight line into two part*, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other jjart. '2. Prove Kuc. 1. 36. Parallelograms upon equal bases,... | |
 | 1867 - 336 pages
...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 of any number by a geometrical... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...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 lines, beside the given... | |
 | 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, four other lines,... | |
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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. 
