 | Euclides - 1883 - 176 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 - 428 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 - 210 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 - 266 pages
...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 - 272 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 - 624 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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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 on the other part. 
