Proposition IX.19 — Given three numbers, to investigate when it is possible to f…

Proof

A fourth proportional to

a

b

c

exists iff

b c / a

is an integer; otherwise no integer extends the proportion.

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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…
IX.18Proposition IX.18Given two numbers, to investigate whether it is possible to find a third proportional to them.

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