Although the authorship of Rhetorica ad Alexandrum was attributed to Aristotle up until the Renaissance, and it was in fact published in the 4th century BCE around the time Aristotle was lecturing on rhetoric, (Aristotle's Rhetoric wasn't published until 83 BCE), it is now considered the work of Anaximenes of Lampsacus, who like Aristotle was one of Alexander's tutors. He was also one of Isocrates' rivals. See the Wiki entry for more on Rhetoric ad Alexandrum and for more on Anaximenes
It's importance to the history of rhetoric is not its authorship, however, but the fact that it is the most complete rhetoric we have from Aristotle's era. Its similarities to Aristotle thus indicate Aristotle wasn't writing in a vacuum. There were others lecturing on the same subject in similar ways at the same time.
You can, if you want to, read the text online. If you aren't sure you want to read that much, below is James P Murphy's outline to give you a sense of what the text offers.
Part 1 Kinds of oratory
Speech genres and general arguments -- There are three speech genres: political, ceremonial, and forensic. They fall into seven species: exhortation and dissuasion, praise and blame, accusation and defense, and investigation. The main aspects of political speeches include justice, legality, expediency, honor, facility, pleasure, practicability, and necessity. Reasoning can be developed by analogy and the use of kinds of opposites.
Political speeches --
Political speeches must have as their main topic one of the seven: religious ritual, legislation, the constitution, alliances and treatises, war, peace or finance. Each of the seven can be developed with help of the seven aspects above and general stock arguments. Advice about just laws in different forms of government.
Ceremonial speeches --
Speeches of praise or blame must amplify virtues and marginalize vice or vice versa. Praiseworthy objects are what is just, lawful, expedient, noble, pleasant, or easy. Ways of amplification include presentation based on: the results, authoritative judgment, comparisons, the opposite, and the intentions of the person.
Forensic speeches --
In accusing, one must show that the act was breaking a law and caused harm. The former is crucial for laws with fixed punishments, the latter for flexible punishment. A defense of lack of intent can be anticipated. The defendant must show that either he did not commit the act, or that he was justified, or plead forgiveness based on error or misfortune.8
Investigations [cross examination] -- The aim of the investigation is to find inconsistencies and contradictions within the opponent's speech or between the speech and the orator's actions or intentions, or between any other aspect of the opponent's life and conduct.
Part 2- Rhetorical techniques as they apply to speech genres
The main aspects -- expedience, honor, etc.. are most important in political speeches. Amplification and minimization are especially useful for ceremonial speeches. Proofs
pisteis are central for forensic speeches. Additional techniques apply to all speech genres similarly.
Probabilities -- There are two groups of proof, direct and supplementary. Direct proofs include a probability
probability, eikos,
example, paradeigma,
cause, tekmerion,
induction, enthymeme,
maxim, gnome,
sign, semeion, and
irrefutable direct proof, elenchos.
Supplementary proofs consist of a opinion of the speaker,
witness evidence,
evidence under torture, and
oath.
Arguments based on probabilities can be derived from common emotions, customs, or motivation of profit. They can be employed by the accusing side and must be refuted by the defense. Arguments based on probability are also useful for other speech genres.
There are two types of examples, those illustrating the common expectations and those running against them. The former strengthen probable argumentation, the latter show that it is not fully reliable. Depending on the speaker's intention either can be a useful way of reminding the audience of the evidence provided by the past.
Indications of inconsistency are infallible signs that contradict the reasoning of the opponent and thus attack his credibility
Enthymemes are concise statements that point out an inconsistency or tension between the speech and actions, or motivations if one attacks the opponent. They can also be employed for one's own speech by showing that the speech is contrary to negative values. Enthymemes can be obtained with the techniques introduced in the chapter on investigations.
Maxims are memorable expressions about general matters of conduct. To construct such a point the orator should analyze the particular nature of the case, or use a hyperbole, or consider a parallel.
Signs A sign is an indication that something will happen, has happened, or is about to happen. Signs can also be used as indicators of varying strengths for the absence of something that would have brought about the sign in question.
Irrefutable direct proof A irrefutable direct proof is a non-defensible statement that points out an inconsistency in the opponent's claim or else demonstrates a necessary truth that requires no further argument.
Differences between various kinds of direct proof/supplementary proofs Probabilities are previously familiar to the audience, examples are newly introduced. Enthymemes can be produced from more sources than just word and deed. Signs produce clearer knowledge in the hearers than most other proofs, irrefutable direct proof teaches the judges the truth. The first form of supplementary proofs is the speaker's opinion. A speaker can use his own authority as a proof in personally supporting a claim and pointing out that he has experience in the topic and an incentive to speak the truth.
voluntary evidence
favorable evidence from voluntary testimony can be amplified by pointing out the plausibility of the statement and the credibility of the person. Unfavorable evidence can be attacked based on the content an don the person, by showing that the person might have ulterior motives or is otherwise untrustworthy
Evidence under torture
Topoi
i.e., common lines of argument in favor of the credibility of a statement made under torture include the argument, that people who are tortured tell the truth immediately to stop the pain. Topoi against include arguments based on the hostility of tortured slaves towards their masters and their willingness to confess anything to end the torture.
Evidence under oath The fourth kind of supplementary proofs is testimony with an appeal to the gods. A topos in favor of the credibility of testimony under oath is the fear of the witness to be punished by the gods for perjury. A topos against is the ruthlessness of a criminal mind that will fear neither gods nor men.
Anticipation -- rokatalepsis In political speeches the orator can reduce the resistance of the audience by offering reasons why he has the right and duty to offer counsel on the topic at hand. In speeches of defense the orator can use similar arguments and additionally point to the importance of hearing both sides in a fair trial. Anticipating the opponent's arguments before his speech takes away their novelty and some of their strengths and allows one to misrepresent them. In defense against anticipations the orator can clarify and must insist of giving an unaltered perspective.
Postulation -- aitenta The speaker can demand agreement from the audience on some basic premises if they are in accordance with the law or reasonable procedure. He must be attentive to his opponent if unjust postulates are presented and rebut them.
Recapitulation At the end of both a section of the speech and the entire speech the orator should remind his audience of the main points, by either calculating the results or enumerating his main arguments, or making a proposal, or posing a question.
Irony Irony can be used either in the form of pretending to pass over an aspect while thereby mentioning it" or by using one term while actually meaning its opposite.
Style and length of a speech Virtues of style include enthymemes in which the audience fills in part of the thought, maxims, and word variety. Adding divisions and internal summaries can lengthen speeches. They can be shortened with the help of a careful wording and concise grammatical structures.
Wort I arrangement Words can be simple, compound, or metaphorical. They can be linked in different ways, especially concerning the beginning and ending of words on a vowel or a consonant.
Twofold statements Statements can be brought into juxtapositions with each other to form twofold statements that are set parallel or in opposition to each other. There are six varieties of these combinations.
Clarity can be achieved by using the proper terms for all entities and by avoiding ambiguities on the word or sentence level. Introducing grammatical markers can help the audience to understand the speech more easily. If homonyms are unavoidable they must be accompanied by other expressions to make the intended meaning clear.
Sentences can be antithetical in wording or meaning or both. Antitheses consisting of terminological and content opposites are the strongest, but the single options are also useful.
Parisosis is a parallelism in sentence structure where two parts of the sentence are metrically equal to each other and thus produce a figure that is comparable but not as strong as antithesis.
Paromoeosis is a parallelism in sound produced by choosing similar syllables in different word. By not only providing a harmonic metric, but also elements of rhyme it is a stronger variety of parisosis. This concludes the explanation of the main aspects of the speech and their sources as well as general proofs and stylistic devices. The next section will be devoted to structure of speeches in the different rhetorical genres, starting with the introduction, which is similar in all genres.
Part III—Speech structure and specad considerations in each genre
Introduction --Prooimion in political speeches --
The main purpose of the introduction is to gain attention and good will from the audience. Attention is gained mainly through exposing the main topic in the light of an important aspect. Good will can be taken for granted with a favorable audience. In an indifferent audience it must be amplified by flattery and by reminding them of the importance of hearing advice. A hostile audience must be persuaded that the hostility toward the person or the proposition is unwarranted or has no bearing on the case at hand. Prejudices against the speaker based on his age or the frequency of his speeches can be reduced with reference to the importance of the topic.
Narrative -- The narrative of past events must be clear, concise, and convincing. This can be achieved by presenting the events in chronological order and by employing precise and adequate wording. Depending on the success or failure of a past activity the orator must emphasize or minimize the part he himself played in the event.
Depending on the size of the exposition and the knowledge of the audience, the narrative can be either included in the introduction or attached to it, or presented as an independent section of the speech.
The confirmation section in political speeches uses the kinds of proof already discussed, especially the customary course of events, examples, considerations, and speaker's opinion. If the individual facts do not need to be supported then the orator can directly proceed to showing that the proposal is just, lawful, expedient, honorable, pleasant, easy, practicable, and necessary—in that order.
In anticipating his opponent's arguments the orator makes use of amplification and matches one or more of his own arguments with the anticipated points such that they are outweighed.
If possible the orator should incite the audience to feel gratitude, compassion, friendship, or similar emotions toward the author of a proposal or the opposite to his opponent.
The introduction of speeches of praise or blame is similar to political introductions. The body of a praise contains a narrative of the person praised, outlining his or her external goods and virtues. Goods external to virtue include high birth, strength, beauty, and wealth. Virtues include wisdom, justice, courage, and temperance. Vituperations are constructed along the same topics but with a negative orientation. Ceremonial speeches should be delivered in a dignified style.
The structure of the introduction in speeches of accusation and defense is similar to political speeches. Beyond gaining the audience's attention a speaker should, depending on his side, arouse or diminish the prejudices against his client by anticipating the opponent and shifting the blame for the case on him. The narrative in an accusation also follows rules similar to political oratory. Next follows the confirmation employing the forms of proof outlined earlier, beginning with testimonies. The final sections are an anticipation of the defender's possible lines and a brief recapitulation including emotional appeals. The structure of speeches of defense is similar to accusations. A defense should end with an appeal to compassion for the accused and incite adverse feelings for the accuser.
Examinational oratory consists of an introduction, preparing for a benevolent reception by the audience; second, the examination of the words, life, or conduct of a person or administration; finally a brief conclusion. The tone of an examination should be mild for optimal oratorical effect.
Oratorical success is the consequence not only of adhering to the rhetorical rules, but also the result of proper conduct in one's personal and public life.