Proposition VIII.23 — If four numbers be in continued proportion, and the first be…

Proof

Same scheme as VIII.22 with two means; the fourth term is the cube of the ratio's denominator scaled appropriately.

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Depends on (2)

VIII.12Proposition VIII.12Between two cube numbers there are two mean proportional numbers, and the cube has to the cube the ratio triplicate of…
VIII.22Proposition VIII.22If three numbers be in continued proportion, and the first be square, the third will also be square.

Required by (dependents) (2)

VIII.25Proposition VIII.25If two numbers have to one another the ratio which a cube number has to a cube number, and the first be cube, the…
IX.9Proposition IX.9If as many numbers as we please beginning from a unit be in continued proportion, and the number after the unit be…

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