• Metaphysics I (Alpha 1) – Aristotle observes that wisdom concerns the first principles and causes of things.  He writes that “all men suppose what is called Wisdom to deal with the first causes (αἰτίαι) and the principles (ἀρχαί) of things; … Wisdom, then, is knowledge about certain principles and causes” .  (Greek: τῶν πρῶτων αἰτίων καὶ τῶν ἀρχῶν.)  This establishes that archai (first principles) are the ultimate starting points or causes in metaphysics.  In context, Aristotle is explaining that natural human inquiry “desires to know” these principles (Met. A 1, 980a9–11).  The passage highlights that knowing the first principles is the goal of philosophical wisdom.
• Physics I.1 – In discussing scientific method, Aristotle states that knowledge requires knowing a thing’s first principles.  He says: “When the objects of an inquiry … have principles, conditions, or elements, it is through acquaintance with these that knowledge (that is to say, scientific knowledge) is attained.  For we do not think that we know a thing until we are acquainted with its primary conditions or first principles (καθ’ αὐτῶν ἀρχάς), and have carried our analysis as far as its simplest elements” .  Here Aristotle stresses that to truly know a subject one must reach its foundational principles.  This passage is from Physics I.1 (184a10–15) and shows that first principles (ἐστίαι or ἀρχαί) are the endpoints of analysis in natural science – the points beyond which knowledge rests.
• Posterior Analytics I.3 – Aristotle addresses how science depends on indemonstrable first principles.  He refutes the view that all knowledge can be demonstrated and states: “We hold that … the knowledge of ultimate principles is indemonstrable.  The necessity of this fact is obvious: if one must know the antecedent principles on which a demonstration rests, and if in this process we at last reach ultimates, these ultimates must necessarily be indemonstrable” .  (Literally: οὐκ ἔστιν αὖ οὐδὲν ἐπίστασθαι, εἰ μὴ ἀπαραδείδηλον γένηται ἐπιστήμη τῶν καθʼ ἀρχάς.)  The context (APo I.3, 72a) is a reply to objections, and Aristotle concludes that the archai (ἀρχαί) or first principles of each science cannot themselves be proved, but must be grasped prior to demonstration.  This is crucial to his epistemology: first principles (often associated with intuition, nous) are the starting points of scientific knowledge.
• Posterior Analytics I.13 – Discussing the search for definitions, Aristotle notes that even ordinary things must have first principles.  He says that “things which exist or come into existence ordinarily but not invariably must also possess certain ultimate starting points or first principles” .  (Greek: καὶ τὰ αὐτὰ ὄντα ποιούμενα ὁποιασδήποτε κατ’ ἐξοχήν· ἡμῖν δὲ διαγιγνώσκοντα, ὥσπερ ἐπὶ τὸ πάντα, ἀεὶ ἀναγκαιότατα πάντα.  Alternatively: ἀρχαὶ. ) This passage (APo I.13, ca. 77a) means that non-necessary (contingent) facts rely on archai just as permanent truths do.  It emphasizes that first principles are not limited to eternal truths but underlie all knowable phenomena.
• Nicomachean Ethics VI.7 – In explaining scientific knowledge (ἐπιστήμη) vs. wisdom (σοφία), Aristotle again speaks of principles.  He observes that “induction leads the learner up to universal principles, while syllogism starts from these.  There are principles, then, from which syllogism starts, which are not arrived at by syllogism, and which, therefore, must be arrived at by induction” .  (Greek: ἄρα οὖν ἀρχαί εἰσιν ἀφ’ ὧν ἡ σύλληψις ἄρχεται… οὐ διὰ συνθέσεως ἡ τοῦτο γιγνώσκειν γίνεται, ἀλλ’ ἐξ ἄτοπων διὰ τῆς ἔμμεσης ὁδείας.) Here (NE VI.7, around 1142a) Aristotle shows that archai of a science are first attained by an intuitive process (nous/induction), not by prior demonstration.  These are the principles “prior” (πρότεροι) to knowledge of conclusions.  The passage underscores the role of first principles in epistemology: they must be “better known” to us than the conclusions (i.e. grasped more firmly) for knowledge to be scientific.

Each of these passages explicitly centers on ἀρχαί (“first principles”) and illustrates their role as the foundational elements in Aristotle’s theory of knowledge.  In Metaphysics and the Organon he consistently treats archai as indemonstrable starting points of inquiry.  The English translations above (from Ross, Hardie–Gaye, and Bouchier) correspond to standard editions of Aristotle and are cited by book and Bekker section (e.g. Metaphysics A 1.982a).

Sources: Translations are from W. D. Ross (Metaphysics) , Hardie & Gaye (Physics) , and E. S. Bouchier (Posterior Analytics) , and F. H. Peters (Nicomachean Ethics) . (Greek phrases are indicated informally; full Greek texts are in the cited editions.)