| 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): = o2 - Zax + a?2, x- -... | |
| John Playfair - Euclid's Elements - 1847 - 340 pages
...6)2; hence, (2a-t-6)2+62=2a2+2(a+6)2, and the proposition is evident from this algebraical equality. **PROP. XI. PROS. To divide a given straight line into...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... | |
| 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...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 less than the... | |
| 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...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 less than the... | |
| Euclides - 1848 - 52 pages
...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...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 of the acute... | |
| 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...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 of a parallelogram... | |
| 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...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.... | |
| 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... | |
| James Elliot - 1850 - 116 pages
...the half of its square by § ? 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... | |
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