 | Euclides - 1848 - 52 Seiten
...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 parts, so that...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 be drawn from... | |
 | J. Goodall, W. Hammond - 1848 - 390 Seiten
...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...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. 3. Prove that the diagonals... | |
 | University of Cambridge - 1849 - 560 Seiten
...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...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 line, are divided... | |
 | Euclid, Thomas Tate - 1849 - 120 Seiten
...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...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 to divide... | |
 | Great Britain. Committee on Education - 1850 - 942 Seiten
...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 of any quadrilateral... | |
 | Her MAjesty' Inspectors of schools - 1850 - 912 Seiten
...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,... | |
 | 582 Seiten
...every respect." Enumerate tlie cases proved in Book 1 and state what ease is omitted. SECTION IT. 1. Divide a given straight line into two parts, so that...and one of the parts, shall be equal to the square of the other part. 2. If a straight line be divided into any two parts, the square of the whole line... | |
 | Harvey Goodwin - 1851 - 196 Seiten
...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...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 line, are divided... | |
 | Francis James Jameson - 1851 - 144 Seiten
.../. 4 (BE2 + CF2) = 4 (ABa + AC2) + 4AE2 + 4AF2, = 4BC2 + AB2 + AC2, = 4BC2 + BC2, - 5BC8. 1849. (A). Divide a given straight line into two parts, so that...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, beside the given... | |
 | University of Durham - 1851 - 222 Seiten
...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 of the 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... | |
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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, may be equal to the square of the other part. 
