| Alfred Wrigley - 1845
...contact, and the 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.... | |
| Euclid, James Thomson - Geometry - 1845 - 352 pages
...the first and third partu of whioh are, by the same curolla'y, tliť 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... | |
| 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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...(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 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... | |
| Harvey Goodwin - Mathematics - 1846 - 468 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- -... | |
| Great Britain. Committee on Education - School buildings - 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... | |
| Education - 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... | |
| Euclides - 1848
...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 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 of the acute... | |
| J. Goodall, W. Hammond - 1848
...intercepted without the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide **a given straight line into two parts, so that 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 of a parallelogram... | |
| University of Cambridge - 1849
...necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide **a given straight line into two parts, so that 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 the required manner.... | |
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