 | Alfred Wrigley - 1845 - 222 pages
...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 - 382 pages
...the first and third partu of whioh are, by the same curolla'y, tli» 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 - 292 pages
...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 - 334 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 - 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- -... | |
 | 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
...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 - 390 pages
...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 - 560 pages
...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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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. 
