| Harvey Goodwin - Mathematics - 1846 - 500 pages
...(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):... | |
| Education - 1847 - 508 pages
...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... | |
| Great Britain. Committee on Education - School buildings - 1847 - 606 pages
...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... | |
| Euclides - 1848 - 52 pages
...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...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 pages
...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 pages
...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 pages
...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 - 942 pages
...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 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,... | |
| 582 pages
...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... | |
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