In this section, you will find two passages. The first is from Augustine's Confessions. He frames his version of what it means to be curious. In the second passage, you will find a passage from Aquinas' Commentary on the Metaphysics of Aristotle. In that passage, he lays out his competing vision of what it means to be curious. 

Augstine

St. Augustine, Confessiones, X, 35 (54-55) 

54. At this point I mention another form of temptation, more various and dangerous. For over and above that lust of the flesh which lies in the delight of all our senses and pleasures—whoso slaves are wasted unto destruction as they go from You—there can also be in the mind itself, through those same bodily senses, a certain vain desire and curiosity, not of taking delight in the body, but of making experiments with the body’s aid, and cloaked under the name of learning and knowledge. Because this is in the appetite to know, and the eyes are the chief of the senses we use for attaining knowledge, it is called in Scripture the lust of the eyes. For “to see” belongs as a property to the eyes; yet we apply the word also to the other senses, when we use them for gaining knowledge. Thus we do not say: “Hear how it flashes,” or “Smell how bright it is,” or “Taste how it shines,” or “Touch how it glows”: because all these things are said to be seen. Yet we do not say only “See how it shines,” something that only the eye can perceive; but also “See how it sounds,” “See how it smells,” “See how it tastes,” “See how hot it is.” Thus the experience of the senses as a whole, as has been said, is called the lust of the eyes, yet we apply it to the other senses by analogy when they are in pursuit of the truth about anything.

55. In this it is easy to distinguish between the way in which the senses serve pleasure and the way in which they serve curiosity. Pleasure goes after objects that are beautiful to see, hear, smell, taste, touch, but curiosity for the sake of experiment can go after quite contrary things, not in order to experience their unpleasantness, but through the mere itch to experience and find out. What pleasure can there be in seeing a mangled corpse, which is only horrible? yet if there happens to be one anywhere about, people flock to it to be saddened and sickened: indeed they are in terror that they may dream about it. So that you would think that when they are awake they would not go to see it unless either they were dragged there by force, or some false report that the sight was beautiful had drawn them. It is the same with the other senses which it would be long to follow up. Because of this disease of curiosity you have the various freaks shown in the theatres. Thus men proceed to investigate the phenomena of nature—the part of nature external to us—though the knowledge is of no value to them: for they wish to know simply for the sake of knowing. We have a similar thing when for the sake of the same perverted learning inquiry is made by way of magic. And the same happens even in religion: God is tempted when signs and wonders are demanded, not for any purpose of salvation, but solely for the experience of seeing them.

Aquinas 

St. Thomas Aquinas, Commentary on the Metaphysics of Aristotle, Lesson 1

1. [Aristotle] says, first, that the desire to know belongs by nature to all men.

2. Three reasons can be given for this. The first is that each thing naturally desires its own perfection. Hence matter is also said to desire form as any imperfect thing desires its perfection. Therefore, since the intellect, by which man is what he is, considered in itself is all things potentially, and becomes them actually only through knowledge, because the intellect is none of the things that exist before it understands them, as is stated in Book III of The Soul; so each man naturally desires knowledge just as matter desires form.

3. The second reason is that each thing has a natural inclination to perform its proper operation, as something hot is naturally inclined to heat, and something heavy to be moved downwards. Now the proper operation of man as man is to understand, for by reason of this he differs from all other things. Hence the desire of man is naturally inclined to understand, and therefore to possess scientific knowledge.

4. The third reason is that it is desirable for each thing to be united to its source, since it is in this that the perfection of each thing consists. This is also the reason why circular motion is the most perfect motion, as is proved in Book VIII of the Physics, because its terminus is united to its starting-point. Now it is only by means of his intellect that man is united to the separate substances, which are the source of the human intellect and that to which the human intellect is related as something imperfect to something perfect. It is for this reason, too, that the ultimate happiness of man consists in this union. Therefore man naturally desires to know.