Proposition VIII.20 — If one mean proportional number fall between two numbers, th…

Proof

Converse of VIII.18: if

a : m = m : b

then

a

and

b

admit factorisations as similar plane numbers via VII.19.

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Depends on (2)

VII.19Proposition VII.19If four numbers be proportional, the number produced from the first and fourth will be equal to the number produced…
VIII.18Proposition VIII.18Between two similar plane numbers there is one mean proportional number, and the plane number has to the plane number…

Required by (dependents) (2)

VIII.21Proposition VIII.21If two mean proportional numbers fall between two numbers, the numbers are similar solid numbers.
IX.2Proposition IX.2If two numbers by multiplying one another make a square number, they are similar plane numbers.

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