Proposition IX.10 — If as many numbers as we please beginning from a unit be in …

Proof

Squares in

1, r, r^{2}, \dots

occur exactly at even powers; if

r

is not square, only

r^{2 k}

terms are square.

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Depends on (2)

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…
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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