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" Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. "
A Supplement to the Elements of Euclid - Page 349
by Daniel Cresswell - 1819 - 410 pages
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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884 - 148 pages
...parallels, are equal to one another. 5. Describe a square that shall be equal to a given rectilineal figure. Divide a given straight line into two parts, such that the rectangle contained by them shall be equal to the square of their difference. 6. If two circles touch one another internally,...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...external segments ; for AB = AD - BD, or BD - AD. 6. When a straight line is divided into two segments, such that the rectangle contained by the whole line and one of the segments is equal to the square on the other segment, the straight line is said to be divided in...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 356 pages
...triangle has the least perimeter. 5. Describe a square that shall be equal to a given rectilineal figure. Divide a given straight line into two parts, such that the rectangle contained by them shall be equal to the square of their difference. 6. If two circles touch one another internally,...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...angle between two given straight lines without producing the given straight lines to meet. Ex. 127. — To divide a given straight line into two parts such that the square on one part shall be double of the square on the other part. Remembering how to obtain a square...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 486 pages
...perpendicular to CA, AB respectively, then the rectangle BA, AE is equal to the rectangle CA, AD. 3. Shew how to divide a given straight line into two parts such that the difference of the squares described on them may be equal to a given rectangle. Is a solution always...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...straight lines. 239. Problem. To find the mean proportional between two given straight lines. 240. Problem. To divide a given straight line into two parts such that the greater part is a mean proportional between the whole line and the smaller part. 241. Problem. To divide...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...perpendicular to CA, AB respectively, then the rectangle BA, AE is equal to the rectangle CA, AD. 3. Shew how to divide a given straight line into two parts such that the difference of the squares described on them may be equal to a given rectangle. Is a solution always...
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Examinations Papers

1898 - 870 pages
...contained by the sum and difference of the hypotenuse and the other side. 5. Divide a given finite straight line into two parts such that the rectangle contained by the whole line and one part is equal to the square on the other. Prove that the sum of the squares on the whole and the smaller...
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Examination Papers

University of Toronto - 1900 - 1164 pages
...square on the line between the points of section, is equal to the square on half the line. (II. 5.) Divide a given straight line into two parts such that the rectangle contained by them shall be the greatest possible. 2. To describe a square which shall be equal to a given rectilineal...
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Annual Report of the Commissioners ..., Volume 68

1902 - 482 pages
...which shall be similar to one given rectilineal figure, and equal to another. SECTION B. 7. Divide a straight line into two parts such that the rectangle contained by the whole line and one part shall be equal to twice the square on the other part. 8. Show how to describe a right-angled'...
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