| John Playfair - Euclid's Elements - 1806 - 311 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. Let AB be the given straight line ; it is... | |
| Robert Simson - Trigonometry - 1806 - 518 pages
...double 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 ; it... | |
| Euclid - Geometry - 1810 - 518 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. Let AB be the given straight line ; it... | |
| Euclides - 1816 - 528 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. Let AB be the given straight line; it... | |
| 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 that the** square of the one shall be equal to the rectangle contained by the other and a given straight line.... | |
| John Playfair - Euclid's Elements - 1819 - 333 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. Let AB be the given straight line ; it... | |
| Miles Bland - Euclid's Elements - 1819 - 442 pages
...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.... | |
| Daniel Cresswell - Geometry - 1819 - 410 pages
...them without the circles, shall (E. 36. 3. and S. 80. 3.) be equal to one another. PROP. LXXXI. 106. **PROBLEM. 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.... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
...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... | |
| Daniel Cresswell - Geometry - 1819 - 486 pages
...manifest from this proposition, and from E. 1O. 4., that if the semi-diameter of a circle be divided **into two parts, so that the rectangle contained by the whole and** the lesser part may be equal to the square of the greater part, the greater segment shall be equal... | |
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