 | 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...parts shall be equal to the square of the other part. Shew that in Euclid's figure four other lines, beside the given line, are divided in the required manner.... | |
 | 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... | |
 | 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... | |
 | James Elliot - 1850 - 116 pages
...the half of its square by ยง ? 3. Divide 100 into two such parts, that the product of the whole by one of the parts shall be equal to the square of the other part. 4. A horse-dealer bought a number of young horses at a fair, all at the same price, for the sum of... | |
 | 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...parts shall be equal to the square of the other part. Shew how to represent the square root of any number by a geometrical figure. What is meant by magnitudes... | |
 | 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...parts shall be equal to the square of the other part. (ii. 11.) (B). Shew that in Euclid's figure, four other lines, beside the given line, are divided in... | |
 | 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...parts shall be equal to the square of the other part. Shew that in Euclid's figure four other lines, beside the given line, are divided in the required manner.... | |
 | University of Durham - Education, Higher - 1851 - 222 pages
...twice the rectangle contained by the parts. 5. To divide a given straight line into two parts, such that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 6. If two circles cut one another they cannot have the same centre. 7. Equal straight lines in a circle... | |
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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. 
