Pope Pius IX in his Letter to Archbishop Scherr of Munich in 1863:

"We desire to reassure ourselves that they did not mean to limit the obligation, which strictly binds Catholic teachers and writers, to those things only which are proposed by the infallible judgment of the Church as dogmas of faith to be believed by everybody. In a like manner, We are convinced that it was not their intention to state that the perfect adherence to revealed truths (which they regard as absolutely necessary for true progress in science and for refuting errors) can be maintained, if the submission of faith is given only to those dogmas expressly defined by the Church. The reason for this is the following: even supposing that we are treating of that subjection which is to be made by an explicit act of divine faith, this must not be limited to those things which have been defined in the express decrees of the ecumenical councils or of the Roman Pontiffs of this See; but it must also be extended to those things which, through the ordinary teaching of the whole Church throughout the world, are proposed as divinely revealed and, as a result, by universal and constant consent of Catholic theologians are held to be matters of faith."

Syllabus of Errors, 1864, Pope Pius IX (as a condemned assertion):

22. The obligation by which Catholic teachers and authors are strictly bound is confined to those things only which are proposed to universal belief as dogmas of faith by the infallible judgment of the Church. -- Letter to the Archbishop of Munich, "Tuas libenter," Dec. 21, 1863.

First Vatican Council, 1870:

"All those things are to be believed by divine and Catholic faith which are contained in the written Word of God or in Tradition, and which are proposed by the Church, either in solemn judgment or in its ordinary and universal teaching office, as divinely revealed truths which must be believed."

Pope Leo XIII, Sapientiae Christianae, Jan. 10, 1890:

"In settling how far the limits of obedience extend, let no one imagine that the authority of the sacred pastors, and above all of the Roman Pontiff, need be obeyed only in so far as it is concerned with dogmas, the obstinate denial of which en­tails the guilt of heresy. Again, it is not enough even to give a frank and firm assent to doctrines which are put forth in the ordinary and universal teaching of the Church as divinely revealed, although they have never been solemnly defined. Another point still must be reckoned amongst the duties of Christian men, and that is, they must be willing to be ruled and governed by the authority and direction of their bishops, and, in the first place, of the Apostolic See."

English Bishops in their joint Pastoral Letter of December, 1899, approved by a special letter of Pope Leo XIII:

"It may be well to insist, with the same [Vatican] Council, on the further truth—namely, that Catholics are bound to give their assent also to the decisions of the Church concerning matters appertaining to or affecting revelation, though these matters be not found, strictly speaking, within the deposit of faith. Such matters are, for instance, the interpretation of Scripture, the canonization of saints; the matter and form of sacraments in a given case, in which a dogmatic fact is under considera¬≠tion; other facts which are called dogmatic and the condemnation of false doctrines by the Holy See."

Pope Pius XII, Humani Generis, in 1950 (Denz. 2313):

"It is not to be thought that what is set down in Encyclical Letters does not demand assent in itself, because in this the popes do not exercise the supreme power of their magisterium. For these matters are taught by the ordinary magisterium, regarding which the following is pertinent: "He who heareth you, heareth me." [Luke 10:16]; and usually what is set forth and inculcated in the Encyclical Letters, already pertains to Catholic doctrine. But if the Supreme Pontiffs in their acts, after due consideration, express an opinion on a hitherto controversial matter, it is clear to all that this matter, according to the mind and will of the same Pontiffs, cannot any longer be considered a question of free discussion among the theologians."

Definition of "Infallibility" from "A Catholic Dictionary", 1951:

"This infallibility resides (A) in the pope personally and alone; (B) in an ecumenical Council subject to papal confirmation (these infallibilities are distinct but correlative); (C) in the bishops of the Church, dispersed throughout the world, teaching definitively in union with the pope. This is not a different infallibility from (B) but is the ordinary exercise of a prerogative (hence called the "ordinary magisterium") which is manifested in a striking manner in an ecumenical Council. This ordinary magisterium is exercised by pastoral letters, preaching, catechisms, the censorship of publications dealing with faith and morals, the reprobation of doctrines and books: it is thus in continuous function and embraces the whole deposit of faith."