Proposition Replicated
Proposition VIII.3
If as many numbers as we please in continued proportion be the least of those which have the same ratio with them, the extremes of them are prime to one another.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VIII.3
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.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.
- VIII.1Proposition VIII.1If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the…
Required by (dependents) (3)
- VIII.7Proposition VIII.7If there be as many numbers as we please in continued proportion, and the first measure the last, it will measure the…
- IX.15Proposition IX.15If three numbers in continued proportion be the least of those which have the same ratio with them, any two whatever…
- IX.17Proposition IX.17If as many numbers as we please be in continued proportion, and the extremes of them be prime to one another, the last…
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