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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. "
A Text-book of Geometrical Deductions: Book I [-II] Corresponding to Euclid ... - Page 181
by James Andrew Blaikie, William Thomson - 1892
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...therefore AD2+DB2=2AC2+ 2CD2. Wherefore, if a straight line, &c, QE D, 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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...of the squares of AC, CD. Wherefore, wr a straight line, &c. QED PROP. XI. PROB. TO clivjde 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 line...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...squares of AC, CD. Wherefore, if a straight line, £c. QED "46. 1 Ho. 1 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, shall be equal to the square of the other part. Let AB be the given straight...
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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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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 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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A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 616 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 - 1046 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 Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...the squares of AC, CD. Wherefore, " if a straight line," &c. QED 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, shall be equal to the square of the other part. Let AB be the given straight...
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