 | Euclides - 1816 - 588 pages
...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,... | |
 | John Bonnycastle - Algebra - 1818 - 326 pages
...It is required to divide a line, of 20 inches in length, into two such jiarts that the rectangle of the whole and one of the parts shall be equal to the square of the other. Ans. lOv/6-10 5. It is required to divide the number 60 into two such parts, that their product shall... | |
 | John Mason Good - 1819 - 800 pages
...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 perpendicular be... | |
 | Daniel Cresswell - Geometry - 1819 - 486 pages
...such, that the rectangle contained by the whole line and one of its parts, shall have a given ratio to the square of the other part. Let AB be the given straight line : It is reAB % quired to divide it into two parts, such that the rectangle contained by AB and one of the parts... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...DB are equal to the square of AB, ie to the given square. (9.) To divide a straight line into ttvo 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. L,etAB be the... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...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 contained by the whole and one of the parts may be equal to the square of a given line, which is less than fhe line to be divided. Let AB he tlie... | |
 | John Playfair - 1819 - 354 pages
...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... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...DAH > the L HAG ; and so on. . PROP. XXXIII. 47. PROBLEM. To trisect av given finite straight line. Let AB be the given straight line: It is required to divide it into three equal parts. Upon AB describe (E. 1.1.) the equilateral A CAB ; bisect (E. 9. 1.) the two equal... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...has^ieen inscribed. Which was to be done. x Otherwise. •' Divide the radius of the given circle, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other (11. 2.). Apply in the circle, on each side of a given point,... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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 ABDC; bisect (10. 1.) AC in E, and join BE; produce CA to F, and... | |
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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, may be equal to the square of the other part. 
