This is a short research into FAITH as determined by four well known Christian public domain reference sources:

1. Webster (Webster’s 1820 Dictionary)
2. Fausset (Fausset’s Biblical Dictionary)
3. Easton (Easton’s Bible Dictionary)
4. The ISBE (International Standard Bible Encyclopedia)

Webster says of Faith:

FAITH, n. [L. fides, fido, to trust; Gr. to persuade, to draw towards anything, to conciliate; to believe, to obey. In the Greek Lexicon of Hederic it is said, the primitive signification of the verb is to bind and draw or lead, as signifies a rope or cable. But this remark is a little incorrect. The sense of the verb, from which that of rope and binding is derived, is to strain, to draw, and thus to bind or make fast. A rope or cable is that which makes fast. Heb.]

1. Belief; the assent of the mind to the truth of what is declared by another, resting on his authority and veracity, without other evidence; the judgment that what another states or testifies is the truth. I have strong faith or no faith in the testimony of a witness, or in what a historian narrates.

2. The assent of the mind to the truth of a proposition advanced by another; belief, or probable evidence of any kind.

3. In theology, the assent of the mind or understanding to the truth of what God has revealed. Simple belief of the scriptures, of the being and perfections of God, and of the existence, character and doctrines of Christ, founded on the testimony of the sacred writers, is called historical or speculative faith; a faith little distinguished from the belief of the existence and achievements of Alexander or of Cesar.

4. Evangelical, justifying, or saving faith, is the assent of the mind to the truth of divine revelation, on the authority of God’s testimony, accompanied with a cordial assent of the will or approbation of the heart; an entire confidence or trust in God’s character and declarations, and in the character and doctrines of Christ, with an unreserved surrender of the will to his guidance, and dependence on his merits for salvation. In other words, that firm belief of God’s testimony, and of the truth of the gospel, which influences the will, and leads to an entire reliance on Christ for salvation.

Being justified by faith. (Romans 5)

Without faith it is impossible to please God. (Hebrews 11)

For we walk by faith, and not by sight. (2 Corinthians 5)

With the heart man believeth to righteousness. (Romans 10)

The faith of the gospel is that emotion of the mind, which is called trust or confidence, exercised towards the moral character of God, and particularly of the Saviour.

Faith is an affectionate practical confidence in the testimony of God.

Faith is an affectionate practical confidence in the testimony of God.

Faith is a firm, cordial belief in the veracity of God, in all the declarations of his word; or a full and affectionate confidence in the certainty of those things which God has declared, and because he has declared them.

5. The object of belief; a doctrine or system of doctrines believed; a system of revealed truths received by Christians.

They heard only, that he who persecuted us in times past, now preacheth the faith which once he destroyed. (Galatians 1)

6. The promises of God, or his truth and faithfulness.

… shall their unbelief make the faith of God without effect? (Romans 3)

7. An open profession of gospel truth.

Your faith is spoken of throughout the whole world. (Romans 1)

8. A persuasion or belief of the lawfulness of things indifferent.

Hast thou faith? Have it to thyself before God. (Romans 14)

9. Faithfulness; fidelity; a strict adherence to duty and fulfilment of promises.

Her failing, while her faith to me remains, I would conceal. Children in whom is no faith. (Deuteronomy 32)

10. Word or honour pledged; promise given; fidelity. He violated his plighted faith.

For you alone I broke my faith with injured Palamon.

11. Sincerity; honesty; veracity; faithfulness. We ought in good faith, to fulfill all our engagements.

12. Credibility or truth. [Unusual.]

The faith of the foregoing narrative.

Fausset says of Faith:

Faith:

Hebrews 11:1, “the substance of things hoped for (i.e., it substantiates God’s promises, the fulfilment of which we hope, it makes them present realities), the evidence (elengchos, the ‘convincing proof’ or ‘demonstration’) of things not seen.” Faith accepts the truths revealed on the testimony of God (not merely on their intrinsic reasonableness), that testimony being to us given in Holy Scripture. Where sight is, there faith ceases (John 20:29; 1 Peter 1:8). We are justified (i.e. counted just before God) judicially by God (Romans 8:33), meritoriously by Christ (Isaiah 53:11; Romans 5:19), mediately or instrumentally by faith (Romans 5:1), evidentially by works. Loving trust. James 2:14-26, “though a man say he hath faith, and have not works, can (such a) faith save him?” the emphasis is on “say,” it will be a mere saying, and can no more save the soul than saying to a “naked and destitute brother, be warmed and filled” would warm and fill him.

“Yea, a man (holding right views) may say, Thou hast faith and I have works, show (exhibit to) me (if thou canst, but it is impossible) thy (alleged) faith without thy works, and I will show thee my faith by my works.” Abraham believed, and was justified before God on the ground of believing (Genesis 15:6). Forty years afterward, when God did” tempt,” i.e. put him to the test, his justification was demonstrated before the world by his offering Isaac (Genesis 22). “As the body apart from (chooris) the spirit is dead, so faith without the works (which ought to evidence it) is dead also.” We might have expected faith to answer to the spirit, works to the body. As James reverses this, he must mean by “faith” here the FORM of faith, by “works” the working reality. Living faith does not derive its life from works, as the body does from its animating spirit.

But faith, apart from the spirit of faith, which is LOVE (whose evidence is works), is dead, as the body is dead without the spirit; thus James exactly agrees with Paul, 1 Corinthians 13:2, “though I have all faith … and have not charity (love), I am nothing.” In its barest primary form, faith is simply crediting or accepting God’s testimony (1 John 5:9-13). Not to credit it is to make God a “liar”! a consequence which unbelievers may well start back from. The necessary consequence of crediting God’s testimony (pisteuoo Theoo) is believing in (pisteuoo eis ton huion, i.e. “trusting in”) the Son of God; for He, and salvation in Him alone, form the grand subject of God’s testimony. The Holy Spirit alone enables any man to accept God’s testimony and accept Jesus Christ, as his divine Savoir, and so to “have the witness in himself” (1 Corinthians 12:3). Faith is receptive of God’s gratuitous gift of eternal life in Christ.

Faith is also an obedience to God’s command to believe (1 John 3:23); from whence it is called the “obedience of faith” (Romans 1:5; Romans 16:26; Acts 6:7), the highest obedience, without which works seemingly good are disobediences to God (Hebrews 11:6). Faith justifies not by its own merit, but by the merit of Him in whom we believe (Romans 4:3; Galatians 3:6). Faith makes the interchange, whereby our sin is imputed to Him and His righteousness is imputed to us (2 Corinthians 5:19; 2 Corinthians 5:21; Jeremiah 23:6; 1 Corinthians 1:30). “Such are we in the sight of God the Father, as is the very Son of God Himself” (Hooker) (2 Peter 1:1; Romans 3:22; Romans 4:6; Romans 10:4; Isaiah 42:21; Isaiah 45:21-24; Isaiah 45:25).

Easton says of Faith:

Faith is in general the persuasion of the mind that a certain statement is true (Philippians 1:27; 2 Thessalonians 2:13). Its primary idea is trust. A thing is true, and therefore worthy of trust. It admits of many degrees up to full assurance of faith, in accordance with the evidence on which it rests.

Faith is the result of teaching (Romans 10:14-17). Knowledge is an essential element in all faith, and is sometimes spoken of as an equivalent to faith (John 10:38; 1 John 2:3). Yet the two are distinguished in this respect, that faith includes in it assent, which is an act of the will in addition to the act of the understanding Assent to the truth is of the essence of faith, and the ultimate ground on which our assent to any revealed truth rests is the veracity of God.

Historical faith is the apprehension of and assent to certain statements which are regarded as mere facts of history.

Temporary faith is that state of mind which is awakened in men (e.g., Felix) by the exhibition of the truth and by the influence of religious sympathy, or by what is sometimes styled the common operation of the Holy Spirit.

Saving faith is so called because it has eternal life inseparably connected with it. It cannot be better defined than in the words of the Assembly’s Shorter Catechism: “Faith in Jesus Christ is a saving grace, whereby we receive and rest upon him alone for salvation, as he is offered to us in the gospel.”

The object of saving faith is the whole revealed Word of God. Faith accepts and believes it as the very truth most sure. But the special act of faith which unites to Christ has as its object the person and the work of the Lord Jesus Christ (John 7:38; Acts 16:31). This is the specific act of faith by which a sinner is justified before God (Romans 3:22, Romans 3:25; Galatian 2:16; Philippians 3:9; John 3:16-36; Acts 10:43; Acts 16:31). In this act of faith the believer appropriates and rests on Christ alone as Mediator in all his offices.

This assent to or belief in the truth received upon the divine testimony has always associated with it a deep sense of sin, a distinct view of Christ, a consenting will, and a loving heart, together with a reliance on, a trusting in, or resting in Christ. It is that state of mind in which a poor sinner, conscious of his sin, flees from his guilty self to Christ his Saviour, and rolls over the burden of all his sins on him. It consists chiefly, not in the assent given to the testimony of God in his Word, but in embracing with fiducial reliance and trust the one and only Saviour whom God reveals. This trust and reliance is of the essence of faith. By faith the believer directly and immediately appropriates Christ as his own. Faith in its direct act makes Christ ours . It is not a work which God graciously accepts instead of perfect obedience, but is only the hand by which we take hold of the person and work of our Redeemer as the only ground of our salvation.

Saving faith is a moral act, as it proceeds from a renewed will, and a renewed will is necessary to believing assent to the truth of God (1 Corinthians 2:14; 2 Corinthians 4:4). Faith, therefore, has its seat in the moral part of our nature fully as much as in the intellectual. The mind must first be enlightened by divine teaching (John 6:44; Acts 13:48; 2 Corinthians 4:6; Ephesians 1:17, Ephesians 1:18) before it can discern the things of the Spirit.

Faith is necessary to our salvation (Mark 16:16), not because there is any merit in it, but simply because it is the sinner’s taking the place assigned him by God, his falling in with what God is doing.

The warrant or ground of faith is the divine testimony, not the reasonableness of what God says, but the simple fact that he says it. Faith rests immediately on, “Thus saith the Lord.” But in order to this faith the veracity, sincerity, and truth of God must be owned and appreciated, together with his unchangeableness. God’s word encourages and emboldens the sinner personally to transact with Christ as God’s gift, to close with him, embrace him, give himself to Christ, and take Christ as his. That word comes with power, for it is the word of God who has revealed himself in his works, and especially in the cross. God is to be believed for his word’s sake, but also for his name’s sake.

Faith in Christ secures for the believer freedom from condemnation, or justification before God; a participation in the life that is in Christ, the divine life (John 14:19; Romans 6:4-10; Ephesians 4:15, Ephesians 4:16, etc.); “peace with God” (Romans 5:1); and sanctification (Acts 26:18; Galatians 5:6; Acts 15:9).
All who thus believe in Christ will certainly be saved (John 6:37, John 6:40; John 10:27, John 10:28; Romans 8:1).
The faith = the gospel (Acts 6:7; Romans 1:5; Galatians 1:23; 1 Timothy 3:9; Jude 1:3).

The ISBE says of Faith:

Faith

1. Etymology
2. Meaning: A Divergency
3. Faith in the Sense of Creed
4. A Leading Passage Explained
5. Remarks
6. Conclusion

In the Old Testament (the King James Version) the word occurs only twice: Deuteronomy 32:20 (אמוּן, ‘ēmūn); Habakkuk 2:4 (אמוּנה, ‘ĕmūnāh). In the latter the Revised Version (British and American) places in the margin the alternative rendering, “faithfulness.” In the New Testament it is of very frequent occurrence, always representing πιστις, pistis, with one exception in the King James Version (not the Revised Version (British and American)), Hebrews 10:23, where it represents ἐλπίς, elpı́s, “hope.”

1. Etymology

The history of the English word is rather interesting than important; use and contexts, alike for it and its Hebrew and Greek parallels, are the surest guides to meaning. But we may note that it occurs in the form “feyth,” in Havelok the Dane (13th century); that it is akin to fides and this again to the Sanskrit root bhidh, “to unite,” “to bind.” It is worthwhile to recall this primeval suggestion of the spiritual work of faith, as that which, on man’s side, unites him to God for salvation.

2. Meaning: A Divergency

Studying the word “faith” in the light of use and contexts, we find a bifurcation of significance in the Bible. We may distinguish the two senses as the passive and the active; on the one side, “fidelity,” “trustworthiness”; and “faith,” “trust,” on the other. In Galatians 5:22, e.g. context makes it clear that “fidelity” is in view, as a quality congruous with the associated graces. (the Revised Version (British and American) accordingly renders pistis there by “faithfulness.”) Again, Romans 3:3 the King James Version, “the faith of God,” by the nature of the case, means His fidelity to promise. But in the overwhelming majority of cases, “faith,” as rendering pistis, means “reliance,” “trust.” To illustrate would be to quote many scores of passages. It may be enough here to call attention to the recorded use of the word by our Lord. Of about twenty passages in the Gospels where pistis occurs as coming from His lips, only one (Matthew 23:23) presents it in the apparent sense of “fidelity.” All the others conspicuously demand the sense of “reliance,” “trust.” The same is true of the apostolic writings . In them, with rarest exceptions, the words “reliance,” “trust,” precisely fit the context as alternatives to “faith.”

3. Faith in the Sense of Creed

Another line of meaning is traceable in a very few passages, where pistis, “faith,” appears in the sense of “creed,” the truth, or body of truth, which is trusted, or which justifies trust. The most important of such places is the paragraph James 2:14-26, where an apparent contradiction to some great Pauline dicta perplexes many readers. The riddle is solved by observing that the writer uses “faith” in the sense of creed, orthodox “belief.” This is clear from James 2:19, where the “faith.” in question is illustrated: “Thou believest that God is one.” This is the credal confession of the orthodox Jew (the shema‛; see Deuteronomy 6:4), taken as a passport to salvation. Briefly, James presses the futility of creed without life, Paul the necessity of reliance in order to receive “life and peace.”

4. A Leading Passage Explained

It is important to notice that Hebrews 11:1 is no exception to the rule that “faith” normally means “reliance,” “trust.” There “Faith is the substance (or possibly, in the light of recent inquiries into the type of Greek used by New Testament writers, “the guaranty”) of things hoped for, the evidence (or “convincing proof”) of things not seen.” This is sometimes interpreted as if faith, in the writer’s view, were, so to speak, a faculty of second sight, a mysterious intuition into the spiritual world. But the chapter amply shows that the faith illustrated, e.g. by Abraham, Moses, Rahab, was simply reliance upon a God known to be trustworthy. Such reliance enabled the believer to treat the future as present and the invisible as seen. In short, the phrase here, “faith is the evidence,” etc., is parallel in form to our familiar saying, “Knowledge is power.”

5. Remarks

A few detached remarks may be added: (a) The history of the use of the Greek pistis is instructive. In the Septuagint it normally, if not always, bears the “passive” sense “fidelity,” “good faith,” while in classical Greek it not rarely bears the active sense, “trust.” In the koinē, the type of Greek universally common at the Christian era, it seems to have adopted the active meaning as the ruling one only just in time, so to speak, to provide it for the utterance of Him whose supreme message was “reliance,” and who passed that message on to His apostles. Through their lips and pens “faith,” in that sense, became the supreme watchword of Christianity.

6. Conclusion

In conclusion, without trespassing on the ground of other articles, we call the reader’s attention, for his Scriptural studies, to the central place of faith in Christianity, and its significance. As being, in its true idea, a reliance as simple as possible upon the word, power, love, of Another, it is precisely that which, on man’s side, adjusts him to the living and merciful presence and action of a trusted God. In its nature, not by any mere arbitrary arrangement, it is his one possible receptive attitude, that in which he brings nothing, so that he may receive all. Thus “faith” is our side of union with Christ. And thus it is our means of possessing all His benefits, pardon, justification, purification, life, peace, glory.

As a comment on our exposition of the ruling meaning of “faith” in Scripture, we may note that this precisely corresponds to its meaning in common life, where, for once that the word means anything else, it means “reliance” a hundred times. Such correspondence between religious terms (in Scripture) and the meaning of the same words in common life, will be found to be invariable.