The following is as given in Sir Thomas L. Heath's translation, which can be found in the book The Thirteen Books of The Elements, Vol. 1.

Book I | Book II | Book IX |
---|---|---|

Definitions, Postulates, and Common Notions | Definitions | Proposition 20 |

Proposition 1, Proposition 3, | Proposition 14 | Proposition 36 |

Proposition 5, Proposition 6, | ||

Proposition 29, Proposition 47 |

*Given two unequal straight lines, to cut off from the greater a straight line equal to the less.*

Let `AB`, `C` be the two given unequal straight lines, and let `AB` be the greater of them.

Thus it is required to cut off from `AB` the greater a straight line equal to `C` the less.

At the point `A` let `AD` be placed equal to the straight line `C`; [I. 2]

and with centre `A` and distance `AD` let the circle
`DEF` be described. [Post. 3]

Now, since the point `A` is the centre of the circle `DEF`,

But `C` is also equal to `AD`.

Therefore ach of the straight lines `AE`, `C` is equal to `AD`; so that `AE` is also equal to `C`. [C. N. 1]

Therefore, given the two straight lines `AB`, `C`, from `AB` the greater `AE` has been cut off equal to `C` the less.

(Being) what it was required to do.