Proposition Replicated

Proposition VIII.11

Between two square numbers there is one mean proportional number, and the square has to the square the ratio duplicate of that which the side has to the side.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VIII.11

Euclid's Elements, encoded as an rrxiv paper

Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT

Neighborhood at a glance

Incoming (2)

VII.17 VII.18

PropositionProposition VIII.11

Outgoing (4)

VIII.14 VIII.22 VIII.24 IX.8

Full neighborhood

Depends on (2)

VII.17Proposition VII.17If a number by multiplying two numbers make certain numbers, the numbers so produced will have the same ratio as the…
VII.18Proposition VII.18If two numbers by multiplying any number make certain numbers, the numbers so produced will have the same ratio as the…

Required by (dependents) (4)

VIII.14Proposition VIII.14If a square measure a square, the side will also measure the side; and if the side measure the side, the square will…
VIII.22Proposition VIII.22If three numbers be in continued proportion, and the first be square, the third will also be square.
VIII.24Proposition VIII.24If two numbers have to one another the ratio which a square number has to a square number, and the first be square, the…
IX.8Proposition IX.8If as many numbers as we please beginning from a unit be in continued proportion, the third from the unit will be…

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