| Alfred Wrigley - 1845
...diameter drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 a given line, which is less than the line to be divided. (Euclid, iii.... | |
| Euclides - 1846
...equal to the square of the other part. Let AB be the given straight line : it is required to divide it **into two parts, so that the rectangle contained by...parts shall be equal to the square of the other part.** Upon AB describe the square ACDB ; bisect AC in E, and join BE ; produce CA to F, and make EF equal... | |
| Harvey Goodwin - 1846 - 468 Seiten
...(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- -... | |
| Euclid, John Playfair - 1846 - 317 Seiten
...the proposition is evident from this algebraical equality. PROP. XI. PROB. 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. Let AB be the given straight line ; it is required to... | |
| 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...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... | |
| 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...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... | |
| John Playfair - 1847 - 317 Seiten
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. **Let AB be the given straight line ; it is required to divide** if into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the... | |
| Euclides - 1848
...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 the rectangle contained...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
...the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight **line into two parts, so that the rectangle contained...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
...homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight **line into two parts, so that the rectangle contained...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.... | |
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