Commentary on Aristotle's Ethics Book I, lecture 1, nos. 1-2 (On the Objective Division of Sciences):
1. As the Philosopher says in the beginning of the Metaphysics, it is the business of the wise man to order. The reason for this is that wisdom is the most powerful perfection of reason whose characteristic is to know order. Even if the sensitive powers know some things absolutely, nevertheless to know the order of one thing to another is exclusively the work of intellect or reason. Now a twofold order is found in things. One kind is that of parts of a totality, that is, a group, among themselves, as the parts of a house are mutually ordered to each other. The second order is that of things to an end. This order is of greater importance than the first. For, as the Philosopher says in the eleventh book of the Metaphysics, the order of the parts of an army among themselves exists because of the order of the whole army to the commander. Now order is related to reason in a fourfold way. There is one order that reason does not establish but only beholds, such is the order of things in nature. There is a second order that reason establishes in its own act of consideration, for example, when it arranges its concepts among themselves, and the signs of concepts as well, because words express the meanings of the concepts. There is a third order that reason in deliberating establishes in the operations of the will. There is a fourth order that reason in planning establishes in the external things which it causes, such as a chest and a house.
2. Because the operation of reason is perfected by habit, according to the different modes of order that reason considers in particular, a differentiation of sciences arises. The function of 1) natural philosophy is to consider the order of things that human reason considers but does not establish--understand that with natural philosophy here we also include metaphysics. The order that reason makes in its own act of consideration pertains to 2) rational philosophy [or logic], which properly considers the order of the parts of verbal expression with one another and the order of principles to one another and to their conclusions. The order of voluntary actions pertains to the consideration of 3) moral philosophy. The order that reason in planning establishes in external things arranged by human reason pertains to the 4) mechanical arts. Accordingly it is proper to moral philosophy, to which our attention is at present directed, to consider human operations insofar as they are ordered to one another and to an end.
Sicut philosophus dicit in principio metaphysicae, sapientis est ordinare. Cuius ratio est, quia sapientia est potissima perfectio rationis, cuius proprium est cognoscere ordinem. Nam etsi vires sensitivae cognoscant res aliquas absolute, ordinem tamen unius rei ad aliam cognoscere est solius intellectus aut rationis. Invenitur autem duplex ordo in rebus. Unus quidem partium alicuius totius seu alicuius multitudinis adinvicem, sicut partes domus ad invicem ordinantur; alius autem est ordo rerum in finem. Et hic ordo est principalior, quam primus. Nam, ut philosophus dicit in XI metaphysicae, ordo partium exercitus adinvicem, est propter ordinem totius exercitus ad ducem. Ordo autem quadrupliciter ad rationem comparatur. Est enim quidam ordo quem ratio non facit, sed solum considerat, sicut est ordo rerum naturalium. Alius autem est ordo, quem ratio considerando facit in proprio actu, puta cum ordinat conceptus suos adinvicem, et signa conceptuum, quae sunt voces significativae; tertius autem est ordo quem ratio considerando facit in operationibus voluntatis. Quartus autem est ordo quem ratio considerando facit in exterioribus rebus, quarum ipsa est causa, sicut in arca et domo.
Et quia consideratio rationis per habitum scientiae perficitur, secundum hos diversos ordines quos proprie ratio considerat, sunt diversae scientiae. Nam ad philosophiam naturalem pertinet considerare ordinem rerum quem ratio humana considerat sed non facit; ita quod sub naturali philosophia comprehendamus et mathematicam et metaphysicam. Ordo autem quem ratio considerando facit in proprio actu, pertinet ad rationalem philosophiam, cuius est considerare ordinem partium orationis adinvicem, et ordinem principiorum in conclusiones; ordo autem actionum voluntariarum pertinet ad considerationem moralis philosophiae. Ordo autem quem ratio considerando facit in rebus exterioribus constitutis per rationem humanam, pertinet ad artes mechanicas. Sic igitur moralis philosophiae, circa quam versatur praesens intentio, proprium est considerare operationes humanas, secundum quod sunt ordinatae adinvicem et ad finem.
From Aquinas' Commentary on Aristotle's Ethics, Book VI, lecture 7 (On the Order of Learning the Sciences):
So the proper order of learning will be the following. First, boys should be instructed in logical matters, because logic teaches the method of the whole of philosophy. Second, they are to be instructed in mathematics, which does not require experience and does not transcend the imagination. Third, they should be trained in the natural sciences which, thought not transcending sense and imagination, nevertheless require experience. Fourth, they are to be instructed in the moral sciences, which require experience and a soul free from passion, as is said in the first book [of Aristotle’s Ethics]. Fifth, they should be taught matters concerning wisdom and divine science, which go beyond the imagination and require a vigorous mind.
Erit ergo hic congruus ordo addiscendi, ut primo quidem pueri logicalibus instruantur, quia logica docet modum totius philosophiae. Secundo autem instruendi sunt in mathematicis quae nec experientia indigent, nec imaginationem transcendunt. Tertio autem in naturalibus, quae, etsi non excedant sensum et imaginationem, requirunt tamen experientiam; quarto autem in moralibus, quae requirunt et experientiam et animum a passionibus liberum, ut in primo habitum est. Quinto autem in sapientialibus et divinis quae transcendunt imaginationem et requirunt validum intellectum.
From Aquinas' Commentary on the Book of Causes, Lecture 1 (On the Order of Learning the Sciences):
The principal aim of the philosophers was that, through all their investigations of things, they might come to know the first causes. That is why they placed the science concerned with first causes last, and allotted the final period of their lives to its consideration. They began first of all with logic, which teaches the method of the sciences. Second, they went on to mathematics, which even boys are capable of learning. Third, they advanced to the philosophy of nature, which requires time because of the needed experience. Fourth, they proceeded to moral philosophy, of which a young person cannot be a suitable student. And finally they applied themselves to the divine science, whose object is the first causes of things.
Et inde est quod philosophorum intentio ad hoc principaliter erat ut, per omnia quae in rebus considerabant, ad cognitionem primarum causarum pervenirent. Unde scientiam de primis causis ultimo ordinabant, cuius considerationi ultimum tempus suae vitae deputarent: primo quidem incipientes a logica quae modum scientiarum tradit, secundo procedentes ad mathematicam cuius etiam pueri possunt esse capaces, tertio ad naturalem philosophiam quae propter experientiam tempore indiget, quarto autem ad moralem philosophiam cuius iuvenis esse conveniens auditor non potest, ultimo autem scientiae divinae insistebant quae considerat primas entium causas.