Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. Relation in degree or number between two similar things.
 n. The relative value of silver and gold in a currency system that is bimetallic.
 n. Mathematics A relationship between two quantities, normally expressed as the quotient of one divided by the other: The ratio of 7 to 4 is written 7:4 or 7/4.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A number representing a comparison between two things.
 n. The relative magnitudes of two quantities (usually expressed as a quotient).
 n. Short for ratio decidendi.
from the GNU version of the Collaborative International Dictionary of English
 adj.
 n. The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b by a/b; or (less commonly) the second term is made the dividend; as, a:b = b/a.
 n. Hence, fixed relation of number, quantity, or degree; rate; proportion.
from The Century Dictionary and Cyclopedia
 n. The relation between two similar magnitudes in respect to quantity; the relation between two similar quantities in respect to how many times one makes so many times the other.
 n. Proportion of relations or conditions; coincident agreement or variation; correspondence in rate; equivalence of relative movement or change.
 n. Reason; cause: often used as a Latin word in current Latin phrases.
 n. In musical acoustics, the relation between the vibrationnumbers of two tones. It is the physical or mathematical representation of the interval between them.
 n. In civil law. an account; a cause, or the giving of judgment therein.
 n. Loosely, a direct and simple ratio: as, the weights of bodies are in the direct ratio of their masses—that is, the weight of one is to that of another as the mass of the former is to that of the latter. Also direct proportion
 n. See progression.
 n. A ratio not compound.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the relation between things (or parts of things) with respect to their comparative quantity, magnitude, or degree
 n. the relative magnitudes of two quantities (usually expressed as a quotient)
Etymologies
Examples

These laws are often stated thus: the ratio of the octave to the fundamental is as two is to one; that of the major third as five is to four; that of the perfect fifth as three is to two, and so on through the entire series of pitches embraced within the octave, the _ratio_ being of course the same for all octaves.

When a ratio is duplicate of another ratio» the point/defcribes the difference of the terms in a double time*

Avoid confusion with actual numbers by using the word ratio or a phrase such as a 2to1 majority, rather than a 2to1 vote in the Senate or the like.

This ratio is also higher than 98% of all those taken during the past 12 months.

It issued new talking points approved by the legal departement, telling spokespeople to say that calcium and magnesium are not important in a sports drink — only tiny amounts of these minerals are lost through sweat, and the tinier amounts in ION4 (remember that the ratio is the same, not the content) provide no material benefit.

If you take out the illegals that should be getting health care in the first place and then the people making more than 75k a year that can afford it themselves the ratio is about the same.

If the ratio is at 85% to 90% then a Public Option or early medicare buyin is not necessary.

Mr. RAMSEY: The ratio you look at when you're trying to get anyone out of debt, whether it's a company, a country or an individual, is what we call the ratio of shovel to hole.

At Harvard and Stanford, the ratio is about 2: almost twice as many courses are social as mathematical.

Whether this ratio is appropriate obviously depends on just how many women authors there are versus men, a number nobody seems to have a good handle on.
frindley commented on the word ratio
@Logoswantingtochangename: since also associated with the concept of "reason"
August 23, 2008