Webster's Dictionary 
(1): (n.) A resemblance of relations; an agreement or likeness between things in some circumstances or effects, when the things are otherwise entirely different. Thus, learning enlightens the mind, because it is to the mind what light is to the eye, enabling it to discover things before hidden.
(2): (n.) A relation or correspondence in function, between organs or parts which are decidedly different.
(3): (n.) Proportion; equality of ratios.
(4): (n.) Conformity of words to the genius, structure, or general rules of a language; similarity of origin, inflection, or principle of pronunciation, and the like, as opposed to anomaly.
Cyclopedia of Biblical, Theological and Ecclesiastical Literature 
( Ἀναλογία ) , Proportion.
1. As applied to the works of God generally, it leads to the conclusion that since He is the chief of intelligent agents, a part of any system of which He is the author must, in respect of its leading principles, be similar to the whole of that system; and, farther, that the work of an intelligent and moral being must bear in all its lineaments the traces of the character of its author. In accordance with these principles of analogy, it is maintained that the revelation of God in the Holy Scriptures is in all respects agreeable to what we know of God, from the works of nature and the order of the world, and that such agreement amounts to a strong evidence that the book professing to contain this revelation of God's mind and purposes is really and truly indited by Him. The best exposition of this argument is to be found in Bishop Butler's immortal Analogy of Religion to the Constitution and Course of Nature. (best ed. by Crooks, N. Y. 12mo). (See Butler).
2. The Analogy Of Faith is the correspondence of the several parts of divine revelation in one consistent whole. Its use is pointed out by the apostle in his direction ( Romans 12:6) that "prophecy" — that is, preaching — be according to "the proportion of faith." His rule, of course, extends to all interpretation and exposition of Scripture. The parts of Scripture must be explained according to the tenor of the whole; and, in order to his doing this, the reader must understand the design of the whole. If he do not, he will be continually liable to fall into error. Prejudices and leanings of our own will dispose us to interpret particular parts of the word of God according to the analogy of our own system, rather than according to the total sense of the divine word. Almost every sect and school of divinity has fallen into this error. A prerequisite for following the analogy of faith is the simple love of truth for its own sake. This, more than any thing else, will protect the mind of a student of Scripture from destroying the proportions of sacred truth. The course necessary to avoid these errors is well stated by Dr. Campbell, as follows: "In vain do we search the Scriptures for their testimony concern, ing Christ, if, independently of these Scriptures, we have received a testimony from another quarter, and are determined to admit nothing as the testimony of Scripture which will not perfectly quadrate with that formerly received. This was the very source of the blindness of the Jews in our Savior's time.
They searched the Scriptures as much as we do; but, in the disposition they were in, they would never have discovered what that sacred volume testifies of Christ. Why? Because their great rule of interpretation was the analogy of the faith; or, in other words, the system of the Pharisaean scribe, the doctrine then in vogue, and in the profound veneration of which they had been educated. This is that veil by which the understandings of that people were darkened, even in reading the law, and of which the apostle observed that it remained unremoved in his day, and of which we ourselves have occasion to observe that it remains unremoved in ours. Is it not precisely in the same way that the phrase is used by every sect of Christians for the particular system or digest of tenets for which they themselves have the greatest reverence? The Latin Church, and even the Greek, are explicit in their declarations on this article. With each, the analogy of the faith is their own system alone. That different parties of Protestants, though more reserved in their manner of speaking, aim at the same thing, is undeniable; the same, I mean, considered relatively to the speakers; for, absolutely considered, every party means a different thing." But Chalmers remarks on this, "I think Dr. Campbell sets too little value on the analogy of faith as a principle of interpretation. He seems never to speak of a system of divinity without the lurking imagination that there must be human invention in it, whereas such a system may be as well grounded as Scripture criticism" (Chalmers, Institutes of Theology, 1, 370; and see further at that place).
There has just appeared (1864) a work entitled Analoqy considered as a Guide to Truth, and applied as an Aid to Faith, by J. Buchanan, D.D., professor of theology, New College, Edinburgh. The following notice of it is from the Bibliotheca Sacra, January, 1865: "Archbishop King, and after him Dr. Copleston and Archbishop Whately, define analogy as ‘ a resemblance of relations or ratios,' so that there may be an analogy between things that have no direct resemblance at all. Between the seed and the plant, the egg and the bird, there is a resemblance of ‘ relations,' although no external likeness. ‘ A sweet taste gratifies the palate,' says Dr. Whately, ‘ so does a sweet sound gratify the ear, and hence the same word
"sweet" is applied to both, though no flavor can resemble a sound in itself.' This limitation Dr. Buchanan thinks is too narrow. While it is true to a certain extent, it omits the use which we make of analogy in connection with concrete objects and substantive realities. It is liable also, he thinks, to the objection that is founded on a comparatively small part of human knowledge, viz. the sciences of number and quantity. Without attempting a logical definition, the author of this volume seems to apply the term to all cases where a resemblance exists." — Campbell, Prelim. Dissert. 4, § 13; Home. Introd. 2, 342; Knapp, Theol. Introd. § 5; Ansgus, Bible Handbook, § 304-307; Home, Introd. 2, 243. (See Faith).