Proof
Run the anthyphairesis (Euclidean algorithm). Since the numbers are
not prime to one another, the procedure terminates at a non-unit
remainder ; that measures both inputs, and any other common
measure also divides by the same persistence argument as VII.1.
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Depends on (2)
Required by (dependents) (5)
- VII.3Proposition VII.3Given three numbers not prime to one another, to find their greatest common measure.
- VII.4Proposition VII.4Any number is either a part or parts of any number, the less of the greater.
- VII.20Proposition VII.20The least numbers of those which have the same ratio with them measure those which have the same ratio the same number…
- VII.23Proposition VII.23If two numbers be prime to one another, the number which measures the one of them will be prime to the remaining number.
- VII.34Proposition VII.34Given two numbers, to find the least number which they measure.
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