If three straight lines are proportional then the rectangle contained by the (two) outermost is equal to the square on the middle (one). And if the rectangle contained by the (two) outermost is equal to the square on the middle (one) then the three straight lines will be proportional. * Let $A$, $B$ and $C$ be three proportional straight lines, (such that) as $A$ (is) to $B$, so $B$ (is) to $C$. * I say that the rectangle contained by $A$ and $C$ is equal to the square on $B$ (and conversely).
With $a:=|A|$, $b:=|B|$, $c:=|C|$, this proposition states that $\frac ab=\frac bc$ if and only if $ac=b^2.$
Proofs: 1
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