Proposition: 6.16: Rectangles Contained by Proportional Straight Lines
(Proposition 16 from Book 6 of Euclid's “Elements”)
If four straight lines are proportional then the rectangle contained by the (two) outermost is equal to the rectangle contained by the middle (two). And if the rectangle contained by the (two) outermost is equal to the rectangle contained by the middle (two) then the four straight lines will be proportional.
Modern Formulation
With $a:=\overline{AB},$ $b:=F,$ $c:={\overline{CD}}$, and $d:=E,$ this proposition states that $\frac ac=\frac db$ if and only if $ab=cd.$
Table of Contents
Proofs: 1
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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