 | Daniel Cresswell - 1817 - 454 pàgines
...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.... | |
 | Miles Bland - 1819 - 442 pàgines
...Also the squares of AD, DB are equal to the square of AB, ie to the given square. (9.) To divide a straight line into two parts, so that the rectangle...to the square of a given line, which is less than fhe line to be divided. Let AB he tlie given line to be divided. Upon it describe a semicircle, in... | |
 | John Playfair - 1819 - 350 pàgines
...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 the square of the other part. Upon AB describe (46. 1.) the square ABDC ; bisect... | |
 | John Playfair - 1819 - 354 pàgines
...AD3+DB==2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED PROP. XI, PROB. To divide a given straight line into too parts, so that the rectangle contained by the whole, and one of the parts, niay be equal to the square of the other part. Let AB be the given straight line ; it is required to... | |
 | John Mason Good - 1819 - 800 pàgines
...made up of the half and the part produced. Prop. XI. Prob. To divide a given straight lint into tu'o parts, so that the rectangle contained by the whole, and one of the parts, shall be equal tu the fquare of the other part. Prop. XII. Theor. In obtuse angled triangles, if a... | |
 | Miles Bland - 1819 - 444 pàgines
...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 - 1819 - 486 pàgines
...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 - 1821 - 898 pàgines
...that the sum of their squares may be equal to a given square, and their rectangle equal to a given rectangle. contained by the whole and one of the parts...the square of a given line, which is less than the Hue to be divided. 10. To divide a given line iuto two such parts, that the rectangle contained by... | |
 | Euclid, Robert Simson - 1821 - 514 pàgines
...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 dne of the parts shall be equal to the square of the other part. Upon AB describe (46. 1.) the square... | |
 | Peter Nicholson - 1825 - 1046 pàgines
...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...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 line ; it is required... | |
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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 the square of the other part. 
