For every construction, Émile Lemoine defines its "simplicity" and its "exactitude" to be the total cost of the performed operations, according to the following table:

operation |
simplicitycost | exactitudecost |

To place a compass end on a given point. | 1 | 1 |

To place a compass end on a given line. | 1 | 1 |

To draw a circle when the compass is placed. | 1 | 0 |

To place a ruler edge through a given point. | 1 | 1 |

To draw a line when the ruler is placed. | 1 | 0 |

On page 58 of [3], Coolidge notes:

*"Lemoine's criteria are, perhaps, the simplest and easiest to apply; it is hard to imagine anything rougher."*

He couldn't be more wrong: our complexity measure (number of lines + number of circles) is much simpler, easier and rougher!

**Note that our measure can be given in terms of Lemoine's: it is simply the simplicity minus the exactitude.**

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