Aristotle's Prior Analytics (Greek: Ἀναλυτικὰ Πρότερα; Latin: Analytica Priora) is a central text of the traditional collection of logical works known as the Organon. it introduces the study of syllogisms, investigating how a given pair of premises can lead necessarily to a conclusion which is not contained in either premise.
If all A are B, and all B are C, then all A are C. This is an argument of a syllogism of the first figure, in which the middle term B is the subject of one premise and predicate of the other. In this example the premises are universal afffirmative propositions (all A are B). Aristotle also discusses universal negative propositions (no A are B), particular affirmative propositions (some A are B) and particular negative propositions (some A are not B).
After discussing the kinds of valid argument that can be made with syllogisms of the first figure, Aristotle goes on to consider syllogisms of the second figure, in which the middle term is the predicate of both premises, and of the third figure, in which the middle term is the subject of both premises.
All of this is, perhaps inevitably, rather dry reading. The historian of logic John Corcoran has described the Prior Analytics as 'dense, elliptical, succinct, unpolished, convoluted, and technical, unnecessarily so in the opinion of many.' However, he goes on to note:
It presupposes no previous logic on the part of the reader. There was none available to the audience for which it was written — even for today’s reader a month of beginning logic would be more than enough. However, it does require knowledge of basic plane geometry, including ability and experience in deducing non-evident theorems from intuitively evident premises such as those taken as axioms and postulates a generation or so later by Euclid (fl. 300 BCE). Especially important is familiarity with reductio ad absurdum or indirect deduction. Aristotle repeatedly refers to geometrical proofs, both direct and indirect. It also requires the readers to ask themselves what is demonstrative knowledge, how do humans acquire it, what is a proof, and how is a proof made?
If Corcoran regards the prose of the Prior Analytics as 'perversely reader-unfriendly', he nevertheless makes clear its importance, stating: 'The origin of logic is better marked than that of perhaps any other field of study—Prior Analytics marks the origin of logic. '
Free online and downloadable texts
Internet Archive: L 325 - The Categories and On Interpretation, translated by Harold P. Cook. Prior Analytics, translated by Hugh Tredennick. Greek and English Loeb edition. Multiple formats.
Internet Classics Archive: Prior Analytics, translated by A.J. Jenkinson. HTML and text formats.
University of Adelaide (Internet Archive): Prior Analytics, translated by A.J. Jenkinson. Multiple formats.
Wikisource: Prior Analytics, translated by Octavius Freire Owen.
Texts at Amazon US
Historyoflogic.com: Aristotle's Prior Analytics: the Theory of Categorical Syllogism.
History of Philosophy without any gaps: Aristotle's Logical Works - podcast by philosopher Peter Adamson.
Internet Encyclopedia of Philosophy: Aristotle: Logic, by Louis F. Groarke.
Librivox: Prior Analytics: public domain audiobook.
Stanford Encyclopedia of Philosophy: Aristotle's Logic, by Robin Smith.
Stanford Encyclopedia of Philosophy: The Traditional Square of Opposition, by Terence Parsons.
The First Science: Online Syllogism Solver.
University of Buffalo: John Corcoran, Aristotle’s Prior Analytics and Boole’s Laws of Thought, History and Philosophy of Logic, 2003.
Wikipedia: Prior Analytics.
The Great Conversation: Further reading at Tom's Learning Notes
Ancient Greek resources: Learn to read Greek classics in the original.