 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...the other, as the remaining side of this other is to the remaining side of the first. 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. PROPOSITION 1. THEOREM. Triangles... | |
 | Euclides - 1884 - 434 pages
...drawn from any point in one of its sides to the opposite side, or that side produced. 7. A straight line is said to be cut in extreme and mean ratio when the whole line is to one segment as that segment is to the other. As in the case of medial section, a straight line might... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...by a square ( BM ) . For the solution use II. 14, //. 6, and I. 47. See Ex. 504. DBF.— A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. PROPOSITION 30. PROBLEM. To cut a... | |
 | David Sands Wright - Geometry - 1906 - 104 pages
...harmonically in the ratio of 3 to 1. The proportion may be written AC : CB=AC' : BC'. 4. A line is divided in Extreme and Mean Ratio when the whole line is to the longer segment as the longer segment is to the shorter segment. ACB ! ! I " ~ I If the line .4/2 is... | |
 | Edson Homer Taylor, Fiske Allen - Mathematics - 1922 - 176 pages
...problems he must learn how to solve a quadratic equation. Dividing a line into two segments such that the whole line is to the greater segment as the greater segment is to the smaller segment is said to be dividing the line into extreme and mean ratio, or finding the golden... | |
 | Morris Kline - Mathematics - 1990 - 434 pages
...corresponding angles equal and the sides about the equal angles proportional. Definition 3. A straight line is cut in extreme and mean ratio when the whole line is to the greater segment as the greater to the less. Definition 4. The height of any figure is the perpendicular drawn from the vertex to the... | |
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A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. 
