| Euclides - 1816 - 528 pages
...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 - 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 Bonnycastle - Algebra - 1818 - 260 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... | |
| Euclid, John Playfair - Circle-squaring - 1819 - 348 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...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 - 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. 10. To divide... | |
| John Mason Good - 1819 - 740 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... | |
| John Playfair - 1819 - 317 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... | |
| 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 - 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.... | |
| 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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