Definition: 7.15: Multiplication of Numbers

(Definition 15 from Book 7 of Euclid's “Elements”)

A number is said to multiply a(nother) number when the (number being) multiplied is added (to itself) as many times as there are units in the former (number), and (thereby) some (other number) is produced.

Modern Formulation

See integer multiplication of two positive integers.

Notes

Definitions: 1 2 3 4
Proofs: 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 46 47 48 49 50
Propositions: 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69


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References

Adapted from (subject to copyright, with kind permission)

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