 | Euclides - 1883 - 176 pages
...twice the rectangle contained by either side and the projection of the base upon it. PROP. 11. PROB. To divide a given straight line into two parts so that the square on one part shall be eqnal to the rectangle contained by the whole and the other part. F e GF Let AB... | |
 | 1886 - 568 pages
...angles. 4. Straight lines which are parallel to the same straight line are parallel to each other. 5. 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.... | |
 | Joseph Hughes - Education - 1883 - 568 pages
...squares on the two parts, together with twice the rectangle contained by the parts. Euclid II., 4. 3. 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.... | |
 | F. B. Stevens - Examinations - 1884 - 202 pages
...equal and pifrallel straight lines towards the same parts, are also themselves equal and parallel. 2. 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 on the other part.... | |
 | Stewart W. and co - 1884 - 272 pages
...; but DG is equal 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.... | |
 | Euclides - 1884 - 434 pages
...— If two chords of a circle when produced cut one another, the rectangle contained by the segments of the one shall be equal to the rectangle contained by the segments of the other ; and conversely. Let AC, BD, two chords of the O ABC, cut one another when produced... | |
 | 1885 - 608 pages
...double of the square on half the line and of the square on the line between the points of section. 4. 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.... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...equal and parallel straight **«9 towards the same parts are also themselves equal and parallel. 5. To divide a given straight line into two parts so that the rectangle contained by **« whol» and one of the parts may be equal to the square on the other part.... | |
 | Richard Anthony Proctor - Geometry - 1887 - 202 pages
...rectangles AC, CD, and AC, D B. Prop. 11 is an important one. It may be enunciated also thus : — To divide a given straight line into two parts so that the squares on the whole line and on one of the parts may be together equal to three times the square on... | |
 | Euclid - Geometry - 1890 - 442 pages
...each side, we get sq. on AX + sq. on BX = 2 (sq. on AM + sq. on MX). 95 Proposition 11. PROBLEM — To divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. Let AB... | |
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AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. 
