CathInfo.com

Meanwhile, Scripture does offer some proofs/facts, which we must believe:
1.  Firmament
2.  4 corners of earth
3.  Earth's foundation/pillars
4.  Earth doesn't move.

These are just 4, simple facts which we must believe, as part of the infallibility of Scripture.  The only model which can answer these facts is FE.  There is no globe model which does, therefore it fails right out of the box.

This was taught by both St Augustine and St. Basil.  This was clearly accepted by all the medieval authors who wrote about the earth being a globe, since they would not have wanted to go against Scripture. Later, the St. Augustine passage was quoted by Leo XIII in the encylical Providentissimus Deus.  That makes it Church teaching. 

I'll provide the quotes later. 

It is also frequently asked what our belief must be about the form and shape of heaven according to Sacred Scripture. Many scholars engage in lengthy discussions on these matters, but the sacred writers with their deeper wisdom have omitted them.  Such subjects are of no profit for those who seek beatitude, and, what is worse, they take up very precious time that ought to be given to what is spiritually beneficial.

What concern is it of mine whether heaven is like a sphere and the earth is enclosed by it and suspended in the middle of the universe, [globe earth geocentric model] or whether heaven like a disk above the earth covers it over on one side? [flat earth model]...

Hence, I must say briefly that in the matter of the shape of heaven the sacred writers knew the truth, but that the Spirit of God, who spoke through them, did not wish to teach men these facts that would be of no avail for their salvation.

Those who have written about the nature of the universe have discussed at length the shape of the earth. If it be spherical or cylindrical, if it resemble a disc and is equally rounded in all parts, or if it has the forth of a winnowing basket and is hollow in the middle; all these conjectures have been suggested by cosmographers, each one upsetting that of his predecessor. It will not lead me to give less importance to the creation of the universe, that the servant of God, Moses, is silent as to shapes; he has not said that the earth is a hundred and eighty thousand furlongs in circuмference; he has not measured into what extent of air its shadow projects itself whilst the sun revolves around it, nor stated how this shadow, casting itself upon the moon, produces eclipses. He has passed over in silence, as useless, all that is unimportant for us. Shall I then prefer foolish wisdom to the oracles of the Holy Spirit? Shall I not rather exalt Him who, not wishing to fill our minds with these vanities, has regulated all the economy of Scripture in view of the edification and the making perfect of our souls? It is this which those seem to me not to have understood, who, giving themselves up to the distorted meaning of allegory, have undertaken to give a majesty of their own invention to Scripture. It is to believe themselves wiser than the Holy Spirit, and to bring forth their own ideas under a pretext of exegesis. Let us hear Scripture as it has been written.

..the sacred writers, or to speak more accurately, the Holy Ghost "Who spoke by them, did not intend to teach men these things (that is to say, the essential nature of the things of the visible universe), things in no way profitable unto salvation." Hence they did not seek to penetrate the secrets of nature, but rather described and dealt with things in more or less figurative language, or in terms which were commonly used at the time...