Proposition Replicated
Proposition VIII.1
If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the numbers are the least of those which have the same ratio with them.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VIII.1
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
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Depends on (3)
- VII.14Proposition VII.14If there be as many numbers as we please, and others equal to them in multitude, which taken two and two are in the…
- 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.21Proposition VII.21Numbers prime to one another are the least of those which have the same ratio with them.
Required by (dependents) (5)
- VIII.2Proposition VIII.2To find numbers in continued proportion, as many as may be prescribed, and the least that are in a given ratio.
- VIII.3Proposition VIII.3If as many numbers as we please in continued proportion be the least of those which have the same ratio with them, the…
- VIII.6Proposition VIII.6If there be as many numbers as we please in continued proportion, and the first do not measure the second, neither will…
- VIII.9Proposition VIII.9If two numbers be prime to one another, and numbers fall between them in continued proportion, then, however many…
- IX.35Proposition IX.35If as many numbers as we please be in continued proportion, and there be subtracted from the second and the last…
Discussion
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