Proposition: 6.17: Rectangles Contained by Three Proportional Straight Lines
(Proposition 17 from Book 6 of Euclid's “Elements”)
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.
Modern Formulation
With $a:=A$, $b:=B$, $c:=C$, this proposition states that $\frac ab=\frac bc$ if and only if $ac=b^2.$
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016