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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, shall be equal to the square on the other part. "
Elements of Euclid [selections from book 1-6] adapted to modern methods in ... - Page 89
by Euclides - 1874
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 172 pages
...(ie, AB2) = AB . AC + AB . CB. QED PROP. 3. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts will be equal to the square on that part together with the rectangle contained by the two parts. Let...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...several parts into which the other is divided. COR. 1. If a straight line is divided into two parts, the rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the rectangle contained by the two parts. COR. 2....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...EUCLID'S ELEMENTS. PROPOSITION 8. THEOREM. If a straight line lie divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made...
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Yale Examination Papers

F. B. Stevens - Examinations - 1884 - 202 pages
...sum of the two interior angles on the same side of the secant line is equal to two right angles. 3. To divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 4. To divide a given line into two...
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Differential calculus for beginners

Alexander Knox (B.A.) - 1884 - 214 pages
...j - — - z - - — =$ (by question) rate of variation of angle «fc!=4, COS X=9, angle = 60°. 4. Divide a straight line into two parts, so that the rectangle contained by the parts may be the greatest possible. Let a = the line, DIFFERENTIAL CALCULUS. then rectangle = (a —...
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The Civil service year book and official calendar

1884
...intersection will be bisected at right angles by the straight line joining their centres. 3. Divide a given straight line into two parts so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 4. The angles in the same segment...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 266 pages
...to DB ; therefore the squares of AD, DB are twice the squares of AC, CD. XI. — To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. It is required to divide AB into...
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Cambridge University Examination Papers

University of Cambridge - 1884 - 622 pages
...the whole and each of the parte are together equal to the square on the whole line. 5. 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 on the other part. Prove that the rectangle contained...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...contained by AB and CE, AB and EF, AB and FD. QED COR. 1. If a straight line is divided into two parts, the rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the rectangle contained by the two parts. This follows...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...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 medial...
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