| John Playfair - Circle-squaring - 1819 - 333 pages
...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 is required to... | |
| Miles Bland - Euclid's Elements - 1819 - 377 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
...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 - 377 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
...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... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...sought. Ans. 1 1 , or 3] . Prob. 22. It is required to divide 20 into two such parts, that the product of **the whole and one of the parts, shall be equal to the square of the other.** Ans. lOv/5— 10, and 30— lOy/5. Prob. 23. A labourer dug two trenches, one of which was 6 yards... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...sought. Ans. II, or 3], Prob. 22. It is required to divide 20 into two such parts, that the product of **the whole and one of the parts, shall be equal to the square of the other.** Ans. lOv/5 — 10, and 30— 10^/5, Prob. 23. A labourer dug two trenches, one of which was 6 yards... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...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...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 to divide it into... | |
| John Bonnycastle - Algebra - 1825 - 312 pages
...is required to divide a line, of 20 inches in length, into two such parts that the rectangle of (he **whole and one of the parts shall be equal to the square of the other.** Ans. 10^5-10, and 30—10^/5 6. It is required to divide the number 60 into two such parts that their... | |
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