I answer that, As stated above (Articles [1],3), fasting is directed to two things, the deletion of sin, and the raising of the mind to heavenly things. Wherefore fasting ought to be appointed specially for those times, when it behooves man to be cleansed from sin, and the minds of the faithful to be raised to God by devotion: and these things are particularly requisite before the feast of Easter, when sins are loosed by baptism, which is solemnly conferred on Easter-eve, on which day our Lord's burial is commemorated, because "we are buried together with Christ by baptism unto death" (Rm. 6:4). Moreover at the Easter festival the mind of man ought to be devoutly raised to the glory of eternity, which Christ restored by rising from the dead, and so the Church ordered a fast to be observed immediately before the Paschal feast; and for the same reason, on the eve of the chief festivals, because it is then that one ought to make ready to keep the coming feast devoutly. Again it is the custom in the Church for Holy orders to be conferred every quarter of the year (in sign whereof our Lord fed four thousand men with seven loaves, which signify the New Testament year as Jerome says [*Comment. in Marc. viii]): and then both the ordainer, and the candidates for ordination, and even the whole people, for whose good they are ordained, need to fast in order to make themselves ready for the ordination. Hence it is related (Lk. 6:12) that before choosing His disciples our Lord "went out into a mountain to pray": and Ambrose [*Exposit. in Luc.] commenting on these words says: "What shouldst thou do, when thou desirest to undertake some pious work, since Christ prayed before sending His apostles?"
With regard to the forty day's fast, according to Gregory (Hom. xvi in Evang.) there are three reasons for the number. First, "because the power of the Decalogue is accomplished in the four books of the Holy Gospels: since forty is the product of ten multiplied by four." Or "because we are composed of four elements in this mortal body through whose lusts we transgress the Lord's commandments which are delivered to us in the Decalogue. Wherefore it is fitting we should punish that same body forty times. or, because, just as under the Law it was commanded that tithes should be paid of things, so we strive to pay God a tithe of days, for since a year is composed of three hundred and sixty-six days, by punishing ourselves for thirty-six days" (namely, the fasting days during the six weeks of Lent) "we pay God a tithe of our year." According to Augustine (De Doctr. Christ. ii, 16) a fourth reason may be added. For the Creator is the "Trinity," Father, Son, and Holy Ghost: while the number "three" refers to the invisible creature, since we are commanded to love God, with our whole heart, with our whole soul, and with our whole mind: and the number "four" refers to the visible creature, by reason of heat, cold, wet and dry. Thus the number "ten" [*Ten is the sum of three, three, and four] signifies all things, and if this be multiplied by four which refers to the body whereby we make use of things, we have the number forty.
Each fast of the Ember days is composed of three days, on account of the number of months in each season: or on account of the number of Holy orders which are conferred at these times.