Objection 1. It would seem that the miracles which Christ worked were not a sufficient proof of His Godhead. For it is proper to Christ to be both God and man. But the miracles which Christ worked have been done by others also. Therefore they were not a sufficient proof of His Godhead.
Objection 2. Further, no power surpasses that of the Godhead. But some have worked greater miracles than Christ, for it is written (John 14:12): "He that believeth in Me, the works that I do, he also shall do, and greater than these shall he do." Therefore it seems that the miracles which Christ worked are not sufficient proof of His Godhead.
Objection 3. Further, the particular is not a sufficient proof of the universal. But any one of Christ's miracles was one particular work. Therefore none of them was a sufficient proof of His Godhead, by reason of which He had universal power over all things.
On the contrary, our Lord said (John 5:36): "The works which the Father hath given Me to perfect... themselves... give testimony of Me."
I answer that, The miracles which Christ worked were a sufficient proof of His Godhead in three respects. First, as to the very nature of the works, which surpassed the entire capability of created power, and therefore could not be done save by Divine power. For this reason the blind man, after his sight had been restored, said (John 9:32-33): "From the beginning of the world it has not been heard, that any man hath opened the eyes of one born blind. Unless this man were of God, he could not do anything."
Secondly, as to the way in which He worked miracles--namely, because He worked miracles as though of His own power, and not by praying, as others do. Wherefore it is written (Luke 6:19) that "virtue went out from Him and healed all." Whereby it is proved, as Cyril says (Comment. in Lucam) that "He did not receive power from another, but, being God by nature, He showed His own power over the sick. And this is how He worked countless miracles." Hence on Matthew 8:16: "He cast out spirits with His word, and all that were sick He healed," Chrysostom says: "Mark how great a multitude of persons healed, the Evangelists pass quickly over, not mentioning one by one... but in one word traversing an unspeakable sea of miracles." And thus it was shown that His power was co-equal with that of God the Father, according to John 5:19: "What things soever" the Father "doth, these the Son doth also in like manner"; and, again (John 5:21): "As the Father raiseth up the dead and giveth life, so the Son also giveth life to whom He will."
Thirdly, from the very fact that He taught that He was God; for unless this were true it would not be confirmed by miracles worked by Divine power. Hence it was said (Mark 1:27): "What is this new doctrine? For with power He commandeth the unclean spirits, and they obey Him."
Reply to Objection 1. This was the argument of the Gentiles. Wherefore Augustine says (Ep. ad Volusian. cxxxvii): "No suitable wonders; say they, show forth the presence of so great majesty, for the ghostly cleansing" whereby He cast out demons, "the cure of the sick, the raising of the dead to life, if other miracles be taken into account, are small things before God." To this Augustine answers thus: "We own that the prophets did as much... But even Moses himself and the other prophets made Christ the Lord the object of their prophecy, and gave Him great glory... He, therefore, chose to do similar things to avoid the inconsistency of failing to do what He had done through others. Yet still He was bound to do something which no other had done: to be born of a virgin, to rise from the dead, and to ascend into heaven. If anyone deem this a slight thing for God to do, I know not what more he can expect. Having become man, ought He to have made another world, that we might believe Him to be Him by whom the world was made? But in this world neither a greater world could be made nor one equal to it: and if He had made a lesser world in comparison with this, that too would have been deemed a small thing."
As to the miracles worked by others, Christ did greater still. Hence on John 15:24: "If I had not done in [Douay: 'among'] them the works that no other men hath done," etc., Augustine says: "None of the works of Christ seem to be greater than the raising of the dead: which thing we know the ancient prophets also did... Yet Christ did some works 'which no other man hath done.' But we are told in answer that others did works which He did not, and which none other did... But to heal with so great a power so many defects and ailments and grievances of mortal men, this we read concerning none soever of the men of old. To say nothing of those, each of whom by His bidding, as they came in His way, He made whole... Mark saith (6:56): 'Whithersoever He entered, into towns or into villages or into cities, they laid the sick in the streets, and besought Him that they might touch but the hem of His garment: and as many as touched Him were made whole.' These things none other did in them; for when He saith 'In them,' it is not to be understood to mean 'Among them,' or 'In their presence,' but wholly 'In them,' because He healed them... Therefore whatever works He did in them are works that none ever did; since if ever any other man did any one of them, by His doing he did it; whereas these works He did, not by their doing, but by Himself."
Reply to Objection 2. Augustine explains this passage of John as follows (Tract. lxxi): "What are these 'greater works' which believers in Him would do? That, as they passed by, their very shadow healed the sick? For it is greater that a shadow should heal than the hem of a garment... When, however, He said these words, it was the deeds and works of His words that He spoke of: for when He said... 'The Father who abideth in Me, He doth the works,' what works did He mean, then, but the words He was speaking?... and the fruits of those same words was the faith of those (who believed): but when the disciples preached the Gospel, not some few like those, but the very nations believed... (Tract. lxxii). Did not that rich man go away from His presence sorrowful?... and yet afterwards, what one individual, having heard from Him, did not, that many did when He spake by the mouth of His disciples... Behold, He did greater works when spoken of by men believing than when speaking to men hearing. But there is yet this difficulty: that He did these 'greater works' by the apostles: whereas He saith as meaning not only them:... 'He that believeth in Me'... Listen!... 'He that believeth in Me, the works that I do, he also shall do': first, 'I do,' then 'he also shall do,' because I do that he may do. What works--but that from ungodly he should be made righteous?... Which thing Christ worketh in him, truly, but not without him. Yes, I may affirm this to be altogether greater than to create" [The words 'to create' are not in the text of St. Augustine] "heaven and earth... for 'heaven and earth shall pass away'; but the salvation and justification of the predestinate shall remain... But also in the heavens... the angels are the works of Christ: and does that man do greater works than these, who co-operates with Christ in the work of his justification?... let him, who can, judge whether it be greater to create a righteous being than to justify an ungodly one. Certainly if both are works of equal power, the latter is a work of greater mercy."
"But there is no need for us to understand all the works of Christ, where He saith 'Greater than these shall he do.' For by 'these' He meant, perhaps, those which He was doing at that hour: now at that time He was speaking words of faith:... and certainly it is less to preach words of righteousness, which thing He did without us, than to justify the ungodly, which thing He so doth in us that we also do it ourselves."
Reply to Objection 3. When some particular work is proper to some agent, then that particular work is a sufficient proof of the whole power of that agent: thus, since the act of reasoning is proper to man, the mere fact that someone reasons about any particular proposition proves him to be a man. In like manner, since it is proper to God to work miracles by His own power, any single miracle worked by Christ by His own power is a sufficient proof that He is God.
Source: Summa Theologica (New Advent)