◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Corollary: Cor. 10.023: Segment Commensurable with Medial Area is Medial

Corollary: Cor. 10.023: Segment Commensurable with Medial Area is Medial

(related to Proposition: Prop. 10.023: Segment Commensurable with Medial Segment is Medial)

(Corollary to Proposition 23 from Book 10 of Euclid's “Elements”)

And (it is) clear, from this, that an (area) commensurable with a medial area is medial.

Modern Formulation

A medial area is equal to the square on some medial straight line. Hence, a medial area is expressible as \[\left(\frac pq\right)^{1/2},\] for some rational number $p/q$. And an area, which is commensurable with a medial area is itself medial.

Table of Contents

Proofs: 1

Mentioned in:

Corollaries: 1
Proofs: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Propositions: 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

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References

Adapted from (subject to copyright, with kind permission)

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