 | John Playfair - Mathematics - 1806 - 320 pages
...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.... | |
 | Euclid - Geometry - 1810 - 554 pages
...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.... | |
 | Euclides - 1816 - 588 pages
...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.... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...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... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...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,... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...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... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...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.... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...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.... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...•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.... | |
 | Euclid - 1835 - 540 pages
...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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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. 
