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" AB into two parts, so 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 - Σελίδα 548
των Daniel Cresswell - 1825 - 582 σελίδες
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 σελίδες
...because DG=DB; 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....

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 σελίδες
...AD, DB are double of the squares of AC, CD. \Vherefore, if a straight line, &c. QED PR6P. 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....

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 σελίδες
...double of the 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....

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

Daniel Cresswell - 1817 - 436 σελίδες
...tangents to the two circles, drawn from any point of the line, shall be equal to one another. (LXXV.) To divide a given straight line into two parts, so...contained by the other and a given straight line. (LXXVI.) If a given circle be cut by any number of circles, which all pass through the same two given...

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 σελίδες
...of the other part ; (m) being whole or fractional. 11. To divide a given line into two such parts, that the square of the one shall be equal to the rectangle contained by the other and a given line. 12. A straight line being given in magnitude aud position ; to draw to it, from a given point,...

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 σελίδες
...rectangle AB, AE is equal to (m) times the square of BE. (11.) To divide a given line into two such parts that the square of the one shall be equal to the rectangle contained by the other and a given line. Let AB be the given line to be divided, (see last Fig.) and BC the other given line. Let them...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 σελίδες
...DG=DB: Therefore, 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....

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...are double of the 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....

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...•3.1. « 46. 1. •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....

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...AD, DB are double 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....




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