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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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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...given circle DPE. PROP. XXIV. 114. Problem. To divide a given finite straight line into two parts, such that the rectangle, contained by the whole line and one of the parts, shall most exceed the square of that part. Let AB be the given finite straight line ; it is required...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...of their squares may be equal to a given square, and their rectangle equal to a given rectangle. 9. To divide a straight line into two parts, so that the rectangle contained by the whole aud one of the parts may be equal to the square of a given line, which is less than the line to be...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...given rectangle. Also the squares of AD, DB are equal to the square of AB, ie to the given square. (9.) 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 of a given line, which is less than fhe line to be...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...AD3 +DB3=2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED . . 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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts, fouf times the rectangle contained by the whole line, and one of the parts, together with the square of the other fart, is equal to the square of the straight line which is made...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 582 pages
...produced, shall be to the square of the part produced, in a given ratio. VIII. PR. To divide a given finite straight line into two parts, so that the rectangle, contained by the whole line, and the difference of those two parts, shall be in a given ratio to the square of the less of the two parts....
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...squares of AC, CD. Wherefore, if a straight line, &c. QED Proposition Xf. Problem. 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 'o the square of the other part. Let AB be the given straight...
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The Principles of Analytical Geometry ...

Henry Parr Hamilton - Geometry, Analytic - 1826 - 326 pages
...number of solutions. For example, if it be required to divide a given straight line into two such parts, that the rectangle contained by the whole line and one of the parts, shall be equal to the square of the other part; this problem is determinate. If on the other hand,...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...•6.2. t Constr. • 47. 1. t 3 Ax. t 30 Def. t lAx. t 3 Ax. t 30 Def. PROP. XL PROB. 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. Let AB be the given straight...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...together equal to the square of the whole line. ..If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the rectangle contained by the two parts together with the square of the foresaid part....
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