| Euclides - 1883 - 172 pages
...(ie, AB2) = AB . AC + AB . CB. QED PROP. 3. THEOR. If a straight line be divided into any two parts, **the rectangle contained by the whole line and one of the parts** will be equal to the square on that part together with the rectangle contained by the two parts. Let... | |
| Mathematical association - 1883 - 86 pages
...several parts into which the other is divided. COR. 1. If a straight line is divided into two parts, **the rectangle contained by the whole line and one of the parts** is equal to the sum of the square on that part and the rectangle contained by the two parts. COR. 2.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...EUCLID'S ELEMENTS. PROPOSITION 8. THEOREM. If a straight line lie divided into any two parts, four times **the rectangle contained by the whole line and one of the parts,** together with the square on the other part, is equal to the square on the straight line which is made... | |
| F. B. Stevens - Examinations - 1884 - 202 pages
...sum of the two interior angles on the same side of the secant line is equal to two right angles. 3. **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 on the other part. 4. To divide a given line into two... | |
| Alexander Knox (B.A.) - 1884 - 214 pages
...j - — - z - - — =$ (by question) rate of variation of angle «fc!=4, COS X=9, angle = 60°. 4. **Divide a straight line into two parts, so that the rectangle contained by the** parts may be the greatest possible. Let a = the line, DIFFERENTIAL CALCULUS. then rectangle = (a —... | |
| 1884
...intersection will be bisected at right angles by the straight line joining their centres. 3. 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. 4. The angles in the same segment... | |
| Stewart W. and co - 1884 - 266 pages
...to DB ; therefore the squares of AD, DB are twice the squares of AC, CD. XI. — 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. It is required to divide AB into... | |
| University of Cambridge - 1884 - 622 pages
...the whole and each of the parte are together equal to the square on the whole line. 5. 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 on the other part. Prove that the rectangle contained... | |
| Mathematical association - 1884 - 146 pages
...contained by AB and CE, AB and EF, AB and FD. QED COR. 1. If a straight line is divided into two parts, **the rectangle contained by the whole line and one of the parts** is equal to the sum of the square on that part and the rectangle contained by the two parts. This follows... | |
| Euclides - 1884 - 434 pages
...segments ; for AB = AD - BD, or BD - AD. 6. When a straight line is divided into two segments, such **that the rectangle contained by the whole line and one of the** segments is equal to the square on the other segment, the straight line is said to be divided in medial... | |
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