Proposition: Prop. 10.027: Construction of Components of First Bimedial

(Proposition 27 from Book 10 of Euclid's “Elements”)

To find (two) medial (straight lines), containing a rational (area), (which are) commensurable in square only. * Let the two rational (straight lines) $A$ and $B$, (which are) commensurable in square only, be laid down. * And let $C$ - in mean proportion3 (straight line) to $A$ and $B$ - have been taken [Prop. 6.13]. * And let it be contrived that as $A$ (is) to $B$, so $C$ (is) to $D$ [Prop. 6.12]. fig027e

Modern Formulation

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Proofs: 1

Proofs: 1
Propositions: 2

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Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016