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For example, a ratio of 3:2 is the same as 12:8. It is usual either to reduce terms to the lowest common denominator, or to express them in parts per hundred . If a mixture contains substances A, B, C and D in the ratio 5:9:4:2 then there are 5 parts of A for every 9 parts of B, 4 parts of C and 2 parts of D.
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The exhibited homothety has a positive ratio, so its ratio equals the ratio of the similarity: 1/ √ 2. And the angle of the rotation is + 135 degrees modulo 360 degrees: the angle of the similarity. We can construct the center S of this similarity solely because of its oriented angle + 135 degrees.
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cross ratio metrology example: Image title: Use of cross ratios to measure real-world dimensions of features shown in a rectilinear image (pinhole camera model) by CMG Lee. In (1), the width of the side street, W is computed from the known widths of the adjacent shops. In (2), the width of only one shop is needed because a vanishing point, V is ...