 | Robert Simson - 1762 - 488 σελίδες
...the other part. Let AB be the given ftraight line ; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fnall be equal to the fquare of the other part. Upon AB defcribc " the fquare ABDC, bifect b AC in... | |
 | Robert Simson - 1775 - 534 σελίδες
...the other part. Let AB be the given ftraight line ; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB deferibe * the fquare ABDC ; bifect b AC in... | |
 | Euclid - 1781 - 552 σελίδες
...look II, k 10 i. e SI 46.".. *47-IPRO P. XI. PRO B. TO divide a given ftraight line into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight line ; it is required... | |
 | Alexander Ingram - 1799 - 374 σελίδες
...*• 11 B Let AB be the given ftraight line ; it is required to divide CoIK II. it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB defcribe » the fquare ABDC ; bifea b AC in... | |
 | Robert Simson - 1804 - 528 σελίδες
...of the other part. Let AB be the given ftraight line; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB defcribe » the fquare ABDC, bifect b AC in... | |
 | John Playfair - 1806 - 320 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...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 ; it is required to... | |
 | Euclides - 1816 - 592 σελίδες
...equal to the square of the other part. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by...the whole, and one of the parts, shall be equal to thcsquare of the other part. Upon AB describe* the square ABDC ; bisect b AC in E, and join BE ; produce,... | |
 | Daniel Cresswell - 1817 - 454 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 that the square of the one shall be equal to the rectangle contained by the other and a given straight line.... | |
 | John Playfair - 1819 - 348 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...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 ; it is required to... | |
 | Miles Bland - 1819 - 442 σελίδες
...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 and one of the parts may be equal to the square of a given line, which is less than the line to be divided. 10. To divide... | |
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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. 
