| John Playfair - 1846 - 317 páginas
...(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...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 to... | |
| Harvey Goodwin - 1846 - 468 páginas
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of **the whole and one of the parts shall be equal to the square of** the other part. Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at): =... | |
| 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 either of the acute angles is... | |
| Great Britain. Committee on Education - 1847
...the angle contained by these two sides is a right angle. SECTION II. 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 either of the acute angles is... | |
| Euclides - 1848
...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...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 either... | |
| J. Goodall, W. Hammond - 1848
...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
...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 in... | |
| Euclides, Thomas Tate - 1849 - 108 páginas
...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...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
...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
...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,... | |
| |