| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...given circle DPE. PROP. XXIV. 114. Problem. To divide a given finite straight line into two parts, such **that the rectangle, contained by the whole line and one of the parts,** shall most exceed the square of that part. Let AB be the given finite straight line ; it is required... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
...of their 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... | |
| Miles Bland - Euclid's Elements - 1819 - 442 pages
...given rectangle. 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 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... | |
| John Playfair - Euclid's Elements - 1819 - 333 pages
...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... | |
| John Playfair - 1819 - 317 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... | |
| Daniel Cresswell - Euclid's Elements - 1825 - 582 pages
...produced, shall be to the square of the part produced, in a given ratio. VIII. PR. To divide a given finite **straight line into two parts, so that the rectangle, contained by the whole line, and** the difference of those two parts, shall be in a given ratio to the square of the less of the two parts.... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...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... | |
| Henry Parr Hamilton - Geometry, Analytic - 1826 - 326 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,... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...•6.2. t Constr. • 47. 1. t 3 Ax. t 30 Def. t lAx. t 3 Ax. t 30 Def. PROP. XL 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... | |
| John Playfair - Geometry - 1829 - 186 pages
...together equal to the square of the whole line. ..If a straight line be divided into any two parts, **the rectangle contained by the whole line and one of the parts** is equal to the rectangle contained by the two parts together with the square of the foresaid part.... | |
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