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The numbers 18 and 8 are similar plane numbers.
When 18 is interpreted as a plane number with sides 6 and 3, and 8 has sides 4 and 2, then the sides are proportional. Proposition VIII.18 shows that the ratio of two similar plane numbers is the duplicate ratio of the corresponding sides. In this example, the ratio 18:8 is duplicate of the ratio 6:4. |
To illustrate similar solid numbers, consider the two numbers 240 and 810 when represented as 4 times 6 times 10 and 6 times 9 times 15, respectively.
Proposition VIII.19 shows that the ratio of two similar solid numbers is the triplicate ratio of the corresponding sides. In this example, the ratio 240:810 is triplicate of the ratio 4:6.