◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--7-elementary-number-theory / Definition: 7.18: Square Number

Definition: 7.18: Square Number

A square number is an equal times an equal, or (a plane number) contained by two equal numbers.

Modern Formulation

A square number (or a square) \(s\) is the product of some integer \(a\) with itself, formally

\[s=a\cdot a=a^2.\]

Notes

• A geometrical definition of a square was given in Def. 1.22.
• The following figure shows a geometrical interpretation of a square number

Mentioned in:

Corollaries: 1
Lemmas: 2 3
Proofs: 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
Propositions: 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Sections: 60
Solutions: 61 62 63 64 65 66

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References

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", https://proofwiki.org/wiki/Main_Page, 2016