Proposition IX.2 — If two numbers by multiplying one another make a square numb…

Proof

Converse of IX.1. If

mn

is square then

m : n

has a mean proportional in integers; by VIII.20 this means

m

n

are similar plane.

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Depends on (2)

VIII.20Proposition VIII.20If one mean proportional number fall between two numbers, the numbers will be similar plane numbers.
IX.1Proposition IX.1If two similar plane numbers by multiplying one another make some number, the product will be square.

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