What is "extreme and mean ratio"

Extreme \Ex*treme"\, a. [L. extremus, superl. of exter, extrus, on the outside, outward: cf. F. extr[^e]me. See Exterior.]

1. At the utmost point, edge, or border; outermost; utmost; farthest; most remote; at the widest limit.

2. Last; final; conclusive; -- said of time; as, the extreme hour of life.

3. The best of worst; most urgent; greatest; highest; immoderate; excessive; most violent; as, an extreme case; extreme folly. ``The extremest remedy.''
   --Dryden. ``Extreme rapidity.''
   --Sir W. Scott.

   Yet extreme gusts will blow out fire.
   --Shak.

4. Radical; ultra; as, extreme opinions.

   The Puritans or extreme Protestants.
   --Gladstone.

5. (Mus.) Extended or contracted as much as possible; -- said of intervals; as, an extreme sharp second; an extreme flat forth.

   Extreme and mean ratio (Geom.), the relation of a line and its segments when the line is so divided that the whole is to the greater segment is to the less.

   Extreme distance. (Paint.) See Distance., n.,

6. Extreme unction. See under Unction.

   Note: Although this adjective, being superlative in signification, is not properly subject to comparison, the superlative form not unfrequently occurs, especially in the older writers. ``Tried in his extremest state.''
   --Spenser. ``Extremest hardships.''
   --Sharp. ``Extremest of evils.''
   --Bacon. ``Extremest verge of the swift brook.''
   --Shak. ``The sea's extremest borders.''
   --Addison.