 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.  Euclid - Page 138by Euclid, Rupert Deakin - 1903 - 164 pagesFull view - About this book
 | 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. Let AB be the given straight... | |
 | 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 - 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. Let AB be the 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 - 446 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 - 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... | |
 | John Playfair - 1819 - 354 pages
...difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts, fouf times the rectangle contained by the whole line, and one of the parts, together with the square of the other fart, is equal to the square of the straight line which is made... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...AD, DB, 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. Let AB be the given straight... | |
 | Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...none of which lies within another, the tangents so drawn shall be equal to one another. LXXXI. PR. 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.... | |
 | Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...number of solutions. For example, if it be required to divide a given straight line into two such parts, that the rectangle contained by the whole line and one of the parts, shall be equal to the square of the other part; this problem is determinate. If on the other hand,... | |
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