Levels 101 to 200

Grammar Rhetoric

Seminar

• Homer, Iliad: Books 1-2

Tutorial: Language

Greek: the alphabet, breathings and accents, a second and slower pass, reading aloud. Read the opening lines of the Iliad aloud from a printed Greek text each day for ten days, and copy one line by hand each day.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Reconstruct the quarrel of Book 1 as each side would argue it, give the strongest objection to Achilles' position, and answer it from the text in 400 words. Read the poem's first line aloud in Greek without help. You pass when your account of both sides survives a second reading of Book 1.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard

Geometry Logic

Seminar

• Homer, Iliad: Books 3-4

Tutorial: Mathematics

Euclid: circles, chords and centres. Work through Book 3, propositions 1-15, and redraw each figure with compass and straightedge, writing each step as one sentence with its reason.

• Euclid, Elements: Book 3, propositions 1-15

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main action of Iliad Books 3-4 in 200 words, then state the strongest objection to one character's choice there and answer it from the text. Then choose one proposition from Book 3, propositions 1-15, state each step and its reason, and measure in your redrawn figure the lengths or angles the proposition says are equal. You pass when your objection is answered from the text and your summary matches the books on a second reading and the measured lengths or angles agree with the proposition.

On the site: Construct and justify: Geometry, Round 1, Geometry, Euclid and Trigonometry

Grammar Logic

Seminar

• Homer, Iliad: Books 5-6

Tutorial: Laboratory

Observing plants: draw, measure and record one plant over a week, separating observation from inference. Each day write one observation and, on a separate line, one inference, and mark each inference as a guess until a test supports it.

Acts

Understand exactly, Check it against evidence

Pass when: Summarise the main action of Iliad Books 5-6 in 200 words, then state the strongest objection to one character's choice there and answer it from the text. Then produce a table of your week of plant records, at least seven rows, with observations and inferences in separate columns. You pass when your objection is answered from the text and every inference in your table is marked as an inference and a reader can check each observation against your drawings and measurements.

On the site: Observe, Define, Represent: The First Three Moves

Grammar Rhetoric

Seminar

• Homer, Iliad: Books 7-8

Tutorial: Language

Greek: first-declension nouns and the definite article. Decline three first-declension nouns in full, singular and plural, with the article, then translate ten short phrases from the books that use them.

Acts

Understand exactly, Express it truly

Pass when: Decline three first-declension nouns in full, with the definite article, from memory. Translate ten short phrases from Iliad Books 7-8 that contain first-declension nouns, then write 200 words in English on the main action of those books and state the strongest objection to one character's choice there, answered from the text. You pass when your objection is answered from the text and every form matches a printed table, or is noted as a Homeric variant, when you reopen it and each phrase reads correctly against the Greek.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Geometry Logic

Seminar

• Homer, Iliad: Books 9-10

Tutorial: Mathematics

Euclid: tangents and the angles in circles. Work through Book 3, propositions 16-37, and for each proposition state what it claims in one sentence, then draw it and measure one angle.

• Euclid, Elements: Book 3, propositions 16-37

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main action of Iliad Books 9-10 in 200 words, and give the strongest objection to one choice a leader makes there, answered from the text. Then draw one proposition on tangents from Book 3 and measure the angle it names. You pass when your objection is answered from the text and the measured angle agrees with the proposition within the error of your drawing.

On the site: What each step rests on: Geometry, Round 1

Grammar Logic

Seminar

• Homer, Iliad: Books 11-12

Tutorial: Laboratory

Observing animals: structure and function in one animal you can watch. Watch the animal in three sessions of twenty minutes, and write one sentence for each visible part saying what it does, marking each sentence as seen or assumed.

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Describe the main action of Iliad Books 11-12 in 200 words, then answer one objection to a reading of those books from the text. Write up your three observation sessions with one sentence for each part of the animal, each marked seen or assumed. You pass when a reader can tell from your write-up which claims you saw and which you assumed, and the summary matches the books when you reopen them.

On the site: Observe, Define, Represent: The First Three Moves

Grammar Rhetoric

Seminar

• Homer, Iliad: Books 13-14

Tutorial: Language

Greek: adjectives of the first and second declensions, agreeing with nouns in gender, number and case. Make a table of one adjective in all its forms, then write ten short phrases that pair nouns and adjectives correctly.

Acts

Understand exactly, Express it truly

Pass when: Build the table of one first-and-second-declension adjective in all its forms, and translate ten short phrases from Iliad Books 13-14 that agree it with a noun. Then write 200 words in English on one scene from those books and why it matters to the action, and state the strongest objection to one character's choice in it, answered from the text. You pass when your objection is answered from the text and every phrase agrees in gender, number and case, and your scene account matches the text when you reopen the books, with any Homeric variant of an ending noted.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Geometry Logic

Seminar

• Homer, Iliad: Books 15-16

Tutorial: Mathematics

Euclid: inscribed and circumscribed figures, to the regular pentagon and the fifteen-sided figure. Work through Book 4 step by step, and draw each figure with compass and straightedge, labelling every point.

• Euclid, Elements: Book 4

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main action of Iliad Books 15-16 in 200 words, then state the strongest objection to one turning point in those books and answer it from the text. Draw the regular pentagon from Book 4 with compass and straightedge, label it, and measure its sides. You pass when your objection is answered from the books and the measured sides agree within your drawing error.

On the site: Construct and justify: Geometry, Round 1

Grammar Logic

Seminar

• Homer, Iliad: Books 17-18

Tutorial: Laboratory

Aristotle on how to study animals. Read the method chapters of Book 1 slowly, then list in at most six numbered points what Aristotle says about how to study animals.

• Aristotle, Parts of Animals: Book 1, on method

Acts

Understand exactly, Examine the reasons

Pass when: Reconstruct the main action of Iliad Books 17-18 in 200 words, and state the strongest objection to one character's action there, answered from the text. Then set out, as a numbered list of at most six points, what Aristotle says in the method chapters of Book 1 about how to study animals, and state one objection to it with your answer. You pass when each point in your list can be tied to something Aristotle says in the method chapters and your objection is answered from the book when you reopen it.

On the site: Observe, Define, Represent: The First Three Moves

Grammar

Seminar

• Homer, Iliad: Books 19-20

Tutorial: Language

Greek: the present indicative active of omega verbs. Conjugate two verbs in full, then translate ten short sentences from the books that use them, naming the person and number each time.

Acts

Understand exactly, Express it truly

Pass when: Conjugate two omega verbs in the present indicative active and translate ten sentences from Iliad Books 19-20 that contain present indicative active omega verbs, giving the person and number of each verb. Then write 200 words in English on the main action of those books and state the strongest objection to one character's choice there, answered from the text. You pass when your objection is answered from the text and every verb form matches the printed table, or is noted as a Homeric variant, and every translation reads correctly against the Greek when you reopen the books.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Geometry

Seminar

• Homer, Iliad: Books 21-22

Tutorial: Mathematics

Euclid: what a ratio is, and when two ratios are the same. Learn the definitions of Book 5 and, for each one, write a plain sentence and, where the definition can be tried on numbers, an example with two pairs of numbers.

• Euclid, Elements: Book 5, definitions

Acts

Understand exactly, Examine the reasons

Pass when: Summarise the main action of Iliad Books 21-22 in 200 words, and answer one objection to Achilles' conduct there from the text. Then state the definitions of ratio and of equal ratios from Book 5 in your own words, and test the definition of equal ratios with two pairs of numbers. You pass when both definitions are stated without the book and your pairs of numbers show the definition of equal ratios working.

On the site: Ratio and common measure: Arithmetic, Round 1

Grammar Logic

Seminar

• Homer, Iliad: Books 23-24

Tutorial: Laboratory

Aristotle on the parts of animals and what they are for. Read the selections slowly and write, for three parts of an animal, what the part does and what Aristotle says it is for, each in two sentences.

• Aristotle, Parts of Animals: Books 2-4, selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Summarise the main action of Iliad Books 23-24 in 200 words and answer one objection to how the books end, from the text. Then, for three parts of an animal, write what each part does and what Aristotle says it is for, and give one objection to his reason for one part with your answer. You pass when each function you state matches the selections when you reopen them and your objection is answered from the text.

On the site: Observe, Define, Represent: The First Three Moves

Grammar Music

Seminar

• Homer, Odyssey: Books 1-3

Tutorial: Music

Sight-singing: major and minor scales and simple melodies. Sing each major and minor scale from the tonic up and down, then sight-sing ten simple melodies a day, slowly, with a drone or a piano.

Acts

Understand exactly, Express it truly

Pass when: Summarise the main action of Odyssey Books 1-3 in 200 words, then state the strongest objection to one character's choice there and answer it from the text. Then sing every major and minor scale from its tonic and sight-sing ten simple melodies with a drone, slowly, naming the key of each. You pass when your objection is answered from the text and your summary matches the books when you reopen them and each melody is sung in tune in the key you named, checked against the printed score.

On the site: Intervals as ratios of string length: Music, Round 1

Grammar

Seminar

• Homer, Odyssey: Books 4-6

Tutorial: Language

Greek: third-declension nouns with consonant stems. Decline four such nouns in full, with their gender, then translate ten short phrases from the books that use them.

Acts

Understand exactly, Express it truly

Pass when: Decline four third-declension nouns with consonant stems in full, giving the gender of each, and translate ten phrases from Odyssey Books 4-6 that contain such nouns. Write 200 words in English on the main action of those books and state the strongest objection to one character's choice there, answered from the text. You pass when your objection is answered from the text and every declension matches a printed table, or is noted as a Homeric variant, and each translation reads correctly against the Greek when you reopen the text.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Geometry

Seminar

• Homer, Odyssey: Books 7-9

Tutorial: Mathematics

Euclid: the theory of proportion. Work through Book 5, propositions 1-13, and for each, give the claim in one sentence and check it with a numerical example.

• Euclid, Elements: Book 5, propositions 1-13

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main action of Odyssey Books 7-9 in 200 words and state one objection to a choice one character makes there, answered from the text. Then state three propositions from Book 5, propositions 1-13, in your own words and test each with a numerical example. You pass when the objection is answered from the books and each proposition holds for your examples when you recalculate them.

On the site: Ratio and common measure: Arithmetic, Round 1

Grammar Logic

Seminar

• Homer, Odyssey: Books 10-12

Tutorial: Laboratory

Anatomy by dissection or with an anatomical atlas: a fish or a heart, drawn and labelled. Draw the organ, label each part, and write one sentence on what each part does, checking every label against the atlas.

Acts

Understand exactly, Check it against evidence

Pass when: Summarise the main action of Odyssey Books 10-12 in 200 words, then state the strongest objection to one character's choice there and answer it from the text. Then draw one fish or one heart, label every part, and write one sentence on each part's function. You pass when your objection is answered from the text and every label matches an anatomical atlas when you reopen it and the summary matches the books.

On the site: Hypotheses, Predictions and Tests

Grammar

Seminar

• Homer, Odyssey: Books 13-15

Tutorial: Language

Greek: third-declension nouns with vowel stems, and third-declension adjectives. Decline two vowel-stem nouns and one adjective in full, then translate ten phrases from the books that use them.

Acts

Understand exactly, Express it truly

Pass when: Decline two vowel-stem nouns and one third-declension adjective in full, then translate ten phrases from Odyssey Books 13-15 that contain such nouns or adjectives. Write 200 words in English on one turning point of those books and what it changes, and state the strongest objection to one character's choice at it, answered from the text. You pass when your objection is answered from the text and each declension matches the printed table, or is noted as a Homeric variant, and each translation reads correctly against the Greek.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Geometry

Seminar

• Homer, Odyssey: Books 16-18

Tutorial: Mathematics

Euclid: the theory of proportion, completed. Work through Book 5, propositions 14-25, and for each, state the claim in one sentence and test it with a numerical example.

• Euclid, Elements: Book 5, propositions 14-25

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main action of Odyssey Books 16-18 in 200 words and answer one objection to a scene in which a character is recognised, from the text. Then state four propositions from Book 5, propositions 14-25, in your own words and test each with numbers. You pass when the objection is answered and each proposition holds for your examples when you recalculate them.

On the site: Ratio and common measure: Arithmetic, Round 1

Grammar Arithmetic

Seminar

• Homer, Odyssey: Books 19-21

Tutorial: Laboratory

Harvey: watching the heart move. Watch a published film of a beating heart, count the beats in one minute three times, and then read the opening chapters and write what Harvey says the heart does, in your own words.

• Harvey, On the Motion of the Heart and Blood in Animals: the opening chapters

Acts

Understand exactly, Check it against evidence

Pass when: Summarise the main action of Odyssey Books 19-21 in 200 words, then state the strongest objection to one character's choice there and answer it from the text. Then state in your own words what Harvey says the heart does in the opening chapters, and give a table of your three one-minute beat counts with their average. You pass when your objection is answered from the text and your account of Harvey matches the chapters when you reopen them and the average follows from the three counts.

On the site: Hypotheses, Predictions and Tests

Grammar

Seminar

• Homer, Odyssey: Books 22-24

Tutorial: Language

Greek: personal, demonstrative and relative pronouns. Learn the forms of each kind in a table, then translate ten sentences from the books that use one pronoun of each kind, naming the kind each time.

Acts

Understand exactly, Express it truly

Pass when: Build a table of the personal, demonstrative and relative pronouns and translate ten sentences from Odyssey Books 22-24, naming the kind of each pronoun. Then write 200 words in English on how the books end and state the strongest objection to one character's conduct in the ending, answered from the text. You pass when your objection is answered from the text and each pronoun is named correctly and each translation reads correctly against the Greek when you reopen the books.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Geometry

Seminar

• Aeschylus, Agamemnon: the whole play

Tutorial: Mathematics

Euclid: similar figures and the mean proportional. Work through Book 6, propositions 1-13, and for two similar triangles you draw, measure the sides and compare their ratios.

• Euclid, Elements: Book 6, propositions 1-13

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the argument of Agamemnon as the chorus and the principal speakers would each argue it, in 300 words, and state the strongest objection to one speaker's case, answered from the play. Then draw two similar triangles, measure their sides and show that the ratios agree. You pass when your reconstruction survives a second reading of the play and the measured ratios agree within your drawing error.

On the site: Construct and justify: Geometry, Round 1

Grammar Rhetoric

Seminar

• Aeschylus, Libation Bearers: the whole play

Tutorial: Language

Greek: the imperfect and the future active. Conjugate one verb in each tense, then translate ten sentences from the play that use them.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Conjugate one verb in the imperfect active and one in the future active, then translate ten sentences from Libation Bearers that use them. Write 200 words on the main action of the play in English, and state the strongest objection to one character's choice there. You pass when each form matches the printed table, each translation reads correctly against the Greek, and your objection is answered from the play.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Aeschylus, Eumenides: the whole play

Tutorial: Laboratory

Harvey: the argument from quantity, recalculated with your own numbers. Read the argument from quantity and redo its calculation with numbers you choose and can defend, showing each step.

• Harvey, On the Motion of the Heart and Blood in Animals: the argument from quantity

Acts

Examine the reasons, Check it against evidence

Pass when: Reconstruct the main action of Eumenides in 300 words, and state one objection to the outcome of the court scene, answered from the play. Then reconstruct Harvey's argument from quantity in five numbered steps, and redo its calculation with numbers you choose, showing each step and the result. You pass when your reconstruction matches the play when you reopen it and your recalculated result follows from the steps you wrote.

On the site: Hypotheses, Predictions and Tests

Grammar Geometry Logic

Seminar

• Aeschylus, Prometheus Bound: the whole play

Tutorial: Mathematics

Euclid: similar figures, completed. Work through Book 6, propositions 14-33, and for each, state the claim in one sentence and check it with one drawing and its measurements.

• Euclid, Elements: Book 6, propositions 14-33

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the argument of Prometheus Bound as a defence of Prometheus would argue it, in 300 words, and give the strongest reply to that defence with your answer to it. Then draw two similar figures from Book 6, propositions 14-33, measure them and show that their ratios match. You pass when your reconstruction survives a second reading of the play and the measurements match the proposition.

On the site: Construct and justify: Geometry, Round 1

Grammar Rhetoric

Seminar

• Sophocles, Oedipus Rex: the whole play

Tutorial: Language

Greek: the first and second aorist active. Learn the endings of both, conjugate one verb in each, and translate ten sentences from the play that use them, naming the aorist each time.

Acts

Understand exactly, Express it truly

Pass when: Conjugate one verb in the first aorist active and one in the second aorist active, then translate ten sentences from Oedipus the King that use them. Write 200 words in English on one step in the play's investigation and what it reveals, and state the strongest objection to one character's choice in it, answered from the play. You pass when your objection is answered from the text and every form matches the printed table and each translation reads correctly against the Greek when you reopen the play.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Arithmetic Logic

Seminar

• Sophocles, Oedipus at Colonus: the whole play

Tutorial: Mathematics

Euclid: number, measure and the unit. Work through Book 7, selections, and for each definition or proposition you choose, state it in one sentence and test it with three examples of whole numbers.

• Euclid, Elements: Book 7, selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the argument of Oedipus at Colonus in 300 words, and answer one objection to the play's closing movement from the text. Then state three definitions or propositions from Book 7 selections in your own words, and test each with three whole-number examples. You pass when the objection is answered from the play and each statement holds for your examples when you recalculate them.

On the site: Patterns, recurrence and induction: Arithmetic, Round 1

Grammar Logic

Seminar

• Sophocles, Antigone: the whole play

Tutorial: Laboratory

Classification: build a key that sorts twenty organisms, and test it on someone else. Choose twenty organisms from a field guide, write each key step as a yes-or-no question, and give the key to a second reader to test.

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the central conflict of Antigone as each main character would argue it, in 300 words, and state the strongest objection to one character's position, answered from the play. Then build a dichotomous key that sorts twenty organisms from a field guide, and record how many of the twenty a second reader places correctly. You pass when your reconstruction survives a second reading of the play and the second reader places at least eighteen of the twenty correctly.

On the site: Observe, Define, Represent: The First Three Moves

Grammar Rhetoric

Seminar

• Sophocles, Philoctetes: the whole play

Tutorial: Language

Greek: the middle and passive voices in the present system. Conjugate one verb in the middle and one in the passive, then translate ten sentences from the play that use them.

Acts

Understand exactly, Express it truly

Pass when: Conjugate one verb in the present middle and one in the present passive, then translate ten sentences from Philoctetes that use them, marking each voice. Write 200 words in English on the central choice the play presents and what each side gains from it, and state the strongest objection to one side's case, answered from the play. You pass when your objection is answered from the text and each voice is marked correctly against the printed table and each translation reads correctly against the Greek when you reopen the play.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Arithmetic

Seminar

• Sophocles, Ajax: the whole play, a variable selection

Tutorial: Mathematics

Euclid: numbers in continued proportion. Work through Book 8, selections, and for each proposition you choose, state the claim in one sentence and test it with a short sequence of numbers.

• Euclid, Elements: Book 8, selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the main action of Ajax in 300 words, and answer one objection to a decision a character takes there, from the play. Then state three propositions from Book 8 selections in your own words and test each with a short sequence of numbers. You pass when the objection is answered from the text and each proposition holds for your sequences when you recalculate them.

On the site: Patterns, recurrence and induction: Arithmetic, Round 1

Grammar Logic

Seminar

• Euripides, Bacchae: the whole play

Tutorial: Laboratory

Aristotle on generation. Read the selections slowly and write, for one kind of animal, what Aristotle says its generation requires, in three sentences with the reason for each.

• Aristotle, Generation of Animals: selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Reconstruct the central conflict of Bacchae in 300 words, and give the strongest objection to one character's position, answered from the play. Then write what Aristotle's selections say generation requires for one kind of animal, in three sentences with a reason for each. You pass when your reconstruction survives a second reading of the play and each sentence about generation matches the selections when you reopen them.

On the site: Observe, Define, Represent: The First Three Moves

Grammar Rhetoric

Seminar

• Euripides, Hippolytus: the whole play, a variable selection

Tutorial: Language

Greek: the aorist and future passive. Conjugate one verb in the aorist passive and one in the future passive, then translate ten sentences from the play that use them.

Acts

Understand exactly, Express it truly

Pass when: Conjugate one verb in the aorist passive and one in the future passive, then translate ten sentences from Hippolytus that use them. Write 200 words in English on one speech in the play and what it asks the audience to judge, and state the strongest objection to what the speaker claims, answered from the play. You pass when your objection is answered from the text and each form matches the printed table, each translation reads correctly against the Greek, and your account of the speech matches the text when you reopen it.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Rhetoric Arithmetic

Seminar

• Aristophanes, Clouds: the whole play

Tutorial: Mathematics

Euclid: primes, even and odd, and perfect numbers. Work through Book 9, selections, and for each proposition you choose, state the claim in one sentence and test it with at least five examples.

• Euclid, Elements: Book 9, selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Reconstruct the main argument of Clouds as its two opposing speakers would each argue it, in 300 words, and answer the strongest objection to the play's conclusion from the text. Then state three propositions from Book 9 selections in your own words and test each with at least five numerical examples. You pass when your reconstruction survives a second reading and each proposition holds for all your examples when you recalculate them.

On the site: Primes and Euclid's proof: Arithmetic, Round 1

Grammar Arithmetic

Seminar

• Herodotus, Histories: Book 1

Tutorial: Laboratory

Cells: observe cells with a microscope, or in published micrographs, and draw what you see at three scales. Draw each view, label it with its magnification, and write one sentence on what each scale shows.

Acts

Understand exactly, Check it against evidence

Pass when: Summarise the main account in Herodotus, Histories, Book 1, in 200 words, and state one claim in it that you would check against another source. Then draw cells at three scales, label each drawing with its magnification, and write one sentence per scale on what it shows. You pass when your drawings match the magnifications you label and the summary matches the book when you reopen it.

On the site: Observe, Define, Represent: The First Three Moves

Grammar Rhetoric

Seminar

• Herodotus, Histories: Books 2-3, selections

Tutorial: Language

Greek: the perfect system. Conjugate one verb in the perfect active, and one in the perfect middle or passive, then translate ten sentences from the selections that use them.

Acts

Understand exactly, Express it truly

Pass when: Conjugate one verb in the perfect active and one in the perfect middle or passive, then translate ten sentences from the Herodotus selections that use them. Write 200 words in English on one account in those selections and how its author presents the evidence for it, and state the strongest objection to the account, answered from the selections. You pass when your objection is answered from the text and each form matches the printed table, or is noted as an Ionic variant, and each translation reads correctly against the Greek when you reopen the selections.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Arithmetic

Seminar

• Herodotus, Histories: Books 4-5, selections

Tutorial: Mathematics

Nicomachus: figured numbers and the means. Work through Book 2, selections, and for each figured number you meet, write its definition and build five examples with counters or squares.

• Nicomachus, Arithmetic: Book 2, selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main account in the Herodotus selections from Books 4-5 in 200 words, and state one claim there that rests on a number or a distance. Then define three figured numbers from Nicomachus Book 2 selections and build five examples of each with counters or squares. You pass when your summary matches the selections and each example fits its definition when you check it by counting.

On the site: Patterns, recurrence and induction: Arithmetic, Round 1

Grammar Logic

Seminar

• Herodotus, Histories: Books 6-7, selections

Tutorial: Laboratory

Virchow: cells from cells. Read the selections and write, in three sentences, what Virchow says a new cell comes from, and then state what observation would count against his claim.

• Rudolf Virchow, Cellular Pathology: selections

Acts

Understand exactly, Examine the reasons

Pass when: Summarise the Herodotus selections from Books 6-7 in 200 words, and state the strongest objection to one account there, answered from the text. Then write in three sentences what Virchow's selections say a new cell comes from, and state one observation that would count against his claim. You pass when your summary matches the selections and your observation would really test the claim when you reopen Virchow.

On the site: Hypotheses, Predictions and Tests

Grammar

Seminar

• Herodotus, Histories: Books 8-9, selections

Tutorial: Language

Greek: forming participles. Form the present, aorist and perfect participles of two verbs, then translate ten sentences from the selections that contain participles.

Acts

Understand exactly, Express it truly

Pass when: Form the present, aorist and perfect participles of two verbs in a table, and translate ten sentences from the Herodotus selections from Books 8-9 that contain participles. Write 200 words in English on the main action of those selections and state the strongest objection to one account in them, answered from the selections. You pass when your objection is answered from the text and every participle matches the printed table, or is noted as an Ionic variant, and each translation reads correctly against the Greek when you reopen the selections.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Music

Seminar

• Plutarch, Lycurgus: the whole life

Tutorial: Music

Singing in parts: a round, or a simple hymn in four parts. Learn your line alone, then sing it with a partner or a recording until you can hold your part against the others for a full verse.

Acts

Understand exactly, Express it truly

Pass when: Summarise the life of Lycurgus as Plutarch tells it in 200 words, and state one claim about it that you would test against a second source. Then sing your line of a round or a four-part hymn against a recording until you can hold your part for a full verse. You pass when your summary matches the life when you reopen it, and a listener can hear that you held your part through the verse without losing the pitch.

On the site: Intervals as ratios of string length: Music, Round 1

Grammar Geometry

Seminar

• Plutarch, Solon: the whole life

Tutorial: Mathematics

Euclid: commensurable and incommensurable magnitudes. Work through Book 10, definitions and the first propositions, and for each, state the claim in one sentence and give one pair of lengths that illustrates it, using the side and diagonal of a square for incommensurable magnitudes.

• Euclid, Elements: Book 10, definitions and the first propositions

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the life of Solon as Plutarch tells it in 200 words, and answer one objection to Solon's reforms from the text. Then state the definitions of commensurable and incommensurable magnitudes from Book 10 in your own words, and illustrate each: draw a pair of lengths with a common measure you can name, and for the second use the side and diagonal of a square, explaining from the Book 10 definition why measuring cannot settle it. You pass when the objection is answered from the life, the first pair's common measure checks by measuring, and your explanation for the second does not rely on a measurement.

On the site: Squares, diagonals and the incommensurable: Geometry, Round 1

Grammar Logic

Seminar

• Thucydides, History of the Peloponnesian War: Book 1

Tutorial: Laboratory

Driesch: the divided embryo, and what it seemed to show. Read the selections and write what Driesch took the experiment to show, in three sentences, then state one other explanation the same result could support.

• Hans Driesch, The Science and Philosophy of the Organism: selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Reconstruct the main argument of Thucydides, Book 1, in 300 words, and state the strongest objection to one claim the historian makes there, answered from the text. Then write in three sentences what Driesch took his divided embryo experiment to show, and state one rival explanation that the same result could support. You pass when your reconstruction survives a second reading of Book 1 and your rival explanation fits the same result when you check it against the selections.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard

Grammar Rhetoric

Seminar

• Thucydides, History of the Peloponnesian War: Book 2

Tutorial: Language

Greek: using participles: attributive, circumstantial and supplementary. Translate ten sentences from Book 2 that contain participles, and name the use of each participle in every sentence.

Acts

Understand exactly, Express it truly

Pass when: Translate ten sentences from Thucydides, Book 2, that contain participles, naming the use of each. Then write 300 words in English on how the speech or narrative of one passage makes its case, and state the strongest objection to it. You pass when each use is named correctly against the Greek, and your objection is answered from the text when you reopen Book 2.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Geometry

Seminar

• Thucydides, History of the Peloponnesian War: Book 3

Tutorial: Mathematics

Euclid: the classification of irrational lines, in outline. Work through the outline of Book 10, selections, and write the classes in a table with one example of a line in each class.

• Euclid, Elements: Book 10, selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main argument of Thucydides, Book 3, in 300 words, and state the strongest objection to one decision recorded there, answered from the text. Then write the classes of irrational lines from Book 10 selections in a table, with one example in each class. You pass when your summary matches the book on a second reading and each example in your table fits its class when you check it against the selections.

On the site: Squares, diagonals and the incommensurable: Geometry, Round 1

Grammar Logic

Seminar

• Thucydides, History of the Peloponnesian War: Books 4-5, selections

Tutorial: Language

Greek: infinitives and indirect statement. Translate ten sentences from the selections that use infinitives, and mark each indirect statement with its subject and its verb.

Acts

Understand exactly, Examine the reasons

Pass when: Translate ten sentences from the Thucydides selections from Books 4-5 that use infinitives, and mark each indirect statement with its subject and verb. Then state, in 200 words, one claim a speaker makes in those selections and what evidence he gives for it. You pass when each indirect statement is marked correctly against the Greek and your account of the claim matches the selections when you reopen them.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Logic

Seminar

• Thucydides, History of the Peloponnesian War: Book 6

Tutorial: Laboratory

Spemann: the organiser experiment. Read the paper and write its design as four numbered steps, then state what each step was meant to show.

• Hans Spemann, The Organizer-Effect in Embryonic Development: the paper

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the main argument of Thucydides, Book 6, in 200 words, and answer one objection to the expedition's reasoning from the text. Then write Spemann's experiment as four numbered steps, and state for each step what it was meant to show. You pass when your summary matches the book when you reopen it and each step of your design matches the paper when you check it against the text.

On the site: Hypotheses, Predictions and Tests

Grammar Geometry

Seminar

• Thucydides, History of the Peloponnesian War: Books 7-8, selections

Tutorial: Mathematics

Euclid: solid geometry, lines and planes. Work through Book 11, selections, and for each definition or proposition you choose, state it in one sentence and draw it as a simple model.

• Euclid, Elements: Book 11, selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the Thucydides selections from Books 7-8 in 200 words, and answer one objection to a military judgment there from the text. Then state three definitions or propositions from Book 11 selections in your own words and draw a simple model of each from paper or card. You pass when the objection is answered from the selections and each model matches its statement when you check it against the book.

On the site: What each step rests on: Geometry, Round 1

Grammar Rhetoric

Seminar

• Plutarch, Alexander: the whole life

Tutorial: Language

Greek: the subjunctive mood. Learn the forms of the present and aorist subjunctive for one verb, then translate ten sentences from the Life that use the subjunctive, naming the use each time.

Acts

Understand exactly, Express it truly

Pass when: Write out the present and aorist subjunctive of one verb and translate ten sentences from Plutarch's Life of Alexander that use the subjunctive, naming its use in each. Then write 200 words in English on one decision the life presents as decisive and what it cost, and state the strongest objection to that decision, answered from the life. You pass when your objection is answered from the text and each form matches the printed table, each translation reads correctly against the Greek, and your account of the decision matches the life when you reopen it.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Logic

Seminar

• Plato, Gorgias: first half

Tutorial: Laboratory

Spemann: development and induction. Read the selections and write, in three sentences, what Spemann says induction is, and which experiment he used to show it.

• Hans Spemann, Embryonic Development and Induction: selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Reconstruct the argument of the first half of Gorgias as Socrates and his chief interlocutor would each argue it, in 300 words, and state the strongest objection to one of Socrates' claims, answered from the dialogue. Then write in three sentences what Spemann says induction is and the experiment he used to show it. You pass when your reconstruction survives a second reading of the half and your sentences about induction match the selections when you reopen them.

On the site: Test a definition: Logic, Round 1

Grammar Geometry Logic

Seminar

• Plato, Gorgias: second half

Tutorial: Mathematics

Euclid: circles are to one another as the squares on their diameters, by the method of exhaustion. Work through Book 12, proposition 2, state each step of the argument in one sentence, and test the claim with two circles drawn on a grid, counting squares.

• Euclid, Elements: Book 12, proposition 2

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the argument of the second half of Gorgias in 300 words, and state the strongest objection to Socrates' conclusion, answered from the dialogue. Then state each step of Book 12, proposition 2 in one sentence, and test the claim with two circles drawn on a grid, counting squares. You pass when the objection is answered from the dialogue and your counts show the ratio the proposition claims within the error of the grid.

On the site: Test a definition: Logic, Round 1

Grammar Rhetoric

Seminar

• Plato, Phaedo: first half

Tutorial: Language

Greek: the optative mood. Learn the optative forms of the verbs met so far, then translate twenty sentences from the first half of Phaedo that use the optative, naming the use (wish, potential, or indirect speech) each time.

Acts

Understand exactly, Express it truly

Pass when: Write out the optative forms of the verbs you have met so far, and translate twenty sentences from the first half of Phaedo that use the optative, naming the use each time. Then write 300 words in English on the first half of Phaedo, stating the strongest objection to one argument there and answering it from the dialogue. You pass when each form matches the printed table, each use is named correctly against the Greek, and your objection is answered from the text.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Geometry Logic

Seminar

• Plato, Phaedo: second half

Tutorial: Mathematics

Euclid: the five regular solids. Work through Book 13, the regular solids, and build each of the five solids from card or paper, counting faces, edges and vertices for each.

• Euclid, Elements: Book 13, the regular solids

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the argument of the second half of Phaedo in 300 words, and answer one objection to its final proof from the dialogue. Then build the five regular solids from card or paper and count the faces, edges and vertices of each in a table. You pass when the objection is answered from the dialogue and each solid in your table is the one Book 13 constructs, and your counts for it agree when you count a second time and match a published table of the regular solids.

On the site: Construct and justify: Geometry, Round 1

Grammar Logic

Seminar

• Plato, Republic: Book 1

Tutorial: Laboratory

Parts and wholes: 600 words on what distinguishes living from non-living things, using this year's laboratory readings. Reread your observation notes from the year and write the 600 words with at least three examples, labelling any claim you cannot test.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Reconstruct the argument of Republic, Book 1, in 300 words, and state the strongest objection to one definition offered there, answered from the book. Then write 600 words on what distinguishes living from non-living things, with three examples and a label on each claim you cannot test. You pass when your reconstruction survives a second reading of Book 1 and a reader can see which of your claims you tested and which you did not.

On the site: Observe, Define, Represent: The First Three Moves

Grammar Rhetoric

Seminar

• Plato, Republic: Book 2

Tutorial: Language

Greek: contract verbs. Conjugate one alpha, one epsilon and one omicron contract verb in the present indicative, then translate ten sentences from Book 2 that use them.

Acts

Understand exactly, Express it truly

Pass when: Conjugate one alpha, one epsilon and one omicron contract verb in the present indicative, and translate ten sentences from Republic, Book 2, that use them. Write 200 words in English on one argument of the book and the objection it meets there. You pass when each form matches the printed table, each translation reads correctly against the Greek, and your account of the argument matches the book when you reopen it.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Logic Geometry

Seminar

• Plato, Republic: Book 3

Tutorial: Mathematics

The role of diagrams in reasoning: what a figure proves and what it only suggests. Take one diagram from Euclid, state what it proves by its construction, and write 300 words on what it only suggests.

Acts

Examine the reasons, Express it truly

Pass when: Reconstruct the argument of Republic, Book 3, in 300 words, and state the strongest objection to one of its claims, answered from the text. Then take one diagram from Euclid, state in two sentences what it proves by its construction, and write 300 words on what it only suggests. You pass when your reconstruction survives a second reading of the book and a reader can see the line between what your diagram proves and what it suggests.

On the site: Proof and Precise Reasoning: From Arguments to Theorems

Arithmetic Geometry

Seminar

• Plato, Republic: Book 4

Tutorial: Laboratory

Archimedes: the law of the lever, demonstrated. Read Book 1 of On the Equilibrium of Planes, write each postulate and proposition in one sentence, then test the law with a ruler, a pivot and coins.

• Archimedes, On the Equilibrium of Planes: Book 1

Acts

Understand exactly, Check it against evidence

Pass when: Reconstruct the argument of Republic, Book 4, in 200 words, and answer one objection to its account of the soul from the text. Then write the postulates and propositions of Archimedes, Book 1, in one sentence each, and test the law of the lever with a ruler, a pivot and coins, recording the distances and weights in a table. You pass when your table shows the balance predicted by the proposition within the error of your measurements.

On the site: Quantitative Reasoning with Stated Assumptions

Grammar Rhetoric

Seminar

• Plato, Republic: Book 5

Tutorial: Language

Greek: verbs in -mi. Conjugate one -mi verb in the present active indicative, then translate ten sentences from Book 5 that use -mi verbs.

Acts

Understand exactly, Express it truly

Pass when: Conjugate one -mi verb in the present active indicative and translate ten sentences from Republic, Book 5, that use -mi verbs. Write 200 words in English on the proposal Book 5 defends and the strongest objection to it. You pass when each form matches the printed table, each translation reads correctly against the Greek, and your objection is answered from the book when you reopen it.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Geometry

Seminar

• Plato, Republic: Book 6

Tutorial: Mathematics

Number and magnitude: why Euclid keeps them apart, and what that costs. Write 300 words comparing Euclid's treatment of number and magnitude in two books, then give one case where the separation makes a proof harder.

Acts

Examine the reasons, Express it truly

Pass when: Reconstruct the argument of Republic, Book 6, in 300 words, and answer one objection to its account of knowledge from the text. Then write 300 words comparing Euclid's treatment of number and magnitude in two books, and give one case where keeping them apart makes a proof harder. You pass when your reconstruction survives a second reading and the comparison matches both books when you reopen them.

On the site: Proof and Precise Reasoning: From Arguments to Theorems

Grammar Arithmetic

Seminar

• Plato, Republic: Book 7, a second reading

Tutorial: Laboratory

Archimedes: floating bodies. Read Book 1 of On Floating Bodies and state each proposition in one sentence; then float a block in water and measure how far it sinks against a stated prediction.

• Archimedes, On Floating Bodies: Book 1

Acts

Understand exactly, Check it against evidence

Pass when: Reconstruct the argument of Republic, Book 7, including the cave, in 300 words, and state the strongest objection to the cave's reading of education, answered from the text. Then state the propositions of Archimedes, Book 1, in one sentence each, predict how far a block will sink, float it, and record the measured depth against your prediction. You pass when your reconstruction survives a second reading of Book 7 and your measured depth agrees with the prediction within the error you state.

On the site: What Does It Take to Know Something?

Grammar Logic

Seminar

• Plato, Republic: Book 8

Tutorial: Language

Greek: particles and connectives, and what they do to an argument. Find ten particles in Book 8, state what each does in its sentence, then translate two paragraphs and mark the connectives.

Acts

Understand exactly, Examine the reasons

Pass when: Find ten particles in Republic, Book 8, and state in one sentence what each does in its sentence. Translate two paragraphs and mark each connective, then write 200 words on how the connectives shape the argument of those paragraphs. You pass when each particle is named against the Greek and your account of the argument matches the two paragraphs when you reopen them.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Logic Geometry

Seminar

• Plato, Republic: Book 9

Tutorial: Mathematics

Oral examination on the Elements: one proposition from each of three books. Choose one proposition from each of three books of the Elements, state it aloud from memory with its proof, and time yourself at five minutes per proposition.

Acts

Examine the reasons, Express it truly

Pass when: Reconstruct the argument of Republic, Book 9, in 300 words, and answer one objection to its account of the tyrant from the text. Then state aloud one proposition from each of three books of the Elements, with its proof, in under five minutes each. You pass when your reconstruction survives a second reading of the book and each proposition and proof is stated in full when you check it against the book of the Elements.

On the site: Proof and Precise Reasoning: From Arguments to Theorems

Grammar Logic

Seminar

• Plato, Republic: Book 10

Tutorial: Language

Greek: conditional sentences. Learn the types of condition your grammar lists, then translate ten sentences from Book 10 that contain conditions and name the type of each.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Write out the types of Greek condition your grammar lists, with one example of each, then translate ten sentences from Republic, Book 10, that contain conditions, naming the type of each. Write 300 words in English on the book's final argument and the strongest objection to it, answered from the text. You pass when each condition is typed correctly against the Greek, and your objection is answered from the book when you reopen it.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Grammar

Seminar

• Plato, Symposium: first half

Tutorial: Laboratory

Balance and weighing: use a ruler on a pivot with coins of known mass to weigh three small objects, and measure your error. Record five trials in a table, with the error for each.

Acts

Understand exactly, Check it against evidence

Pass when: Summarise the first half of Symposium in 200 words, and state the strongest objection to one speech there, answered from the dialogue. Then use a ruler balanced on a pivot, with coins of known mass looked up, to weigh three small objects, and record five trials in a table with the error for each. You pass when your summary matches the dialogue and each trial's error is stated and within the range you set before you began.

On the site: Quantitative Reasoning with Stated Assumptions

Arithmetic Geometry

Seminar

• Plato, Symposium: second half

Tutorial: Mathematics

Plane trigonometry: chords, sines and solving triangles. Solve five triangles from two sides and the angle between them, and check each answer with a drawing made to scale on paper.

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the second half of Symposium in 200 words, and answer one objection to the dialogue's conclusion from the text. Then solve five triangles from two known sides and the angle between them, and check each answer with a scaled drawing. You pass when your summary matches the dialogue and each drawn triangle agrees with your calculated sides within the error of your drawing.

On the site: Squares, diagonals and the incommensurable: Geometry, Round 1

Grammar Music

Seminar

• Plato, Phaedrus: the whole dialogue

Tutorial: Music

Intervals by ear: every interval within the octave. Sing or play each interval from its lower note, then identify twenty random intervals a day for a week, keeping a score for each day.

Acts

Understand exactly, Examine the reasons

Pass when: Summarise the whole Phaedrus in 300 words, and answer one objection to its account of speech from the dialogue. Then have twenty intervals played at random within the octave and name each one, recording your score for each day of one week. You pass when your summary matches the dialogue when you reopen it and your score on the last day is at least seventeen of twenty.

On the site: Measuring intervals in cents and hearing beats: Music, Round 1

Grammar Logic

Seminar

• Plato, Theaetetus: first half

Tutorial: Language

Greek: purpose, result and temporal clauses. Translate ten sentences from the first half that contain each kind of clause, and name the kind of each.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Translate ten sentences from the first half of Theaetetus that contain purpose, result or temporal clauses, and name the kind of each. Write 200 words in English on the question the dialogue asks about knowledge, and state the strongest objection to one answer offered in this half, answered from the text. You pass when each clause is named correctly against the Greek and your objection is answered from the half when you reopen it.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Arithmetic Logic

Seminar

• Plato, Theaetetus: second half

Tutorial: Laboratory

Pascal: the equilibrium of liquids. Read the treatise and write, in three sentences, what Pascal claims about liquids at rest, then test one part of it with a tube of water and a ruler.

• Blaise Pascal, Treatise on the Equilibrium of Liquids: the treatise

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the argument of the second half of Theaetetus in 300 words, and answer one objection to its final account of knowledge from the dialogue. Then write Pascal's central claim about liquids at rest in three sentences, and test one part of it with a tube of water and a ruler, recording the heights in a table against a stated prediction. You pass when your reconstruction survives a second reading of the half and your recorded heights match the prediction within the error you state.

On the site: Hypotheses, Predictions and Tests

Grammar Logic Astronomy

Seminar

• Plato, Parmenides: selections, a variable selection

Tutorial: Mathematics

Ptolemy: the first principles of the Almagest. Read Book 1 and write its first principles as five numbered sentences in your own words, each with the reason the book gives for it.

• Ptolemy, Almagest: Book 1, the arrangement of the heavens

Acts

Understand exactly, Examine the reasons

Pass when: Reconstruct the argument of the Parmenides selections in 300 words, and state one objection to a claim made in the selections, answered from the text. Then write the first principles of Ptolemy's Almagest, Book 1, as five numbered sentences in your own words, and give one observation from the book that supports them. You pass when your reconstruction survives a second reading of the selections and each principle matches the book when you reopen it.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Rhetoric

Seminar

• Plato, Sophist: selections, a variable selection

Tutorial: Language

Greek and English compared: case, word order, and what each language makes easy. Write a table of five sentences from the selections with their English translations, and note what each language makes easy or hard to say.

Acts

Understand exactly, Express it truly

Pass when: Compare Greek and English on five sentences from the Sophist selections in a table, marking case, word order and what each language makes easy or hard to say. Then write 200 words on one distinction the selections draw, and state the strongest objection to it, answered from the text. You pass when each comparison in your table matches the Greek and the English you cite, and your objection is answered from the selections when you reopen them.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Grammar

Seminar

• Plato, Timaeus: first half

Tutorial: Laboratory

Temperature: calibrate a thermometer and compare temperature scales. Read the Fahrenheit selections first and note how he fixed his scale. Mark two fixed points you can reproduce on your thermometer, then read a second thermometer beside it at three temperatures and compare the two scales in a table.

• Fahrenheit, Selected writings: selections

Acts

Check it against evidence, Understand exactly

Pass when: Summarise the first half of Timaeus in 200 words, and state one objection to a claim about the making of the world there, answered from the dialogue. Then state in two sentences how the Fahrenheit selections fix the points of his scale, calibrate a thermometer at two fixed points you can reproduce, read it beside a second thermometer at three temperatures, and compare the scales in a table. You pass when your summary matches the half and your table shows the two scales agreeing within the error you state.

On the site: Evidence-Based Troubleshooting: Separating Explanations

Arithmetic Geometry Astronomy

Seminar

• Plato, Timaeus: second half

Tutorial: Mathematics

Ptolemy: building the table of chords. Choose a circle of a stated radius, and build a table of chords for angles at steps you choose, showing the calculation for each entry.

• Ptolemy, Almagest: Book 1, the table of chords

Acts

Understand exactly, Check it against evidence

Pass when: Reconstruct the argument of the second half of Timaeus in 300 words, and answer one objection to its account of the elements from the dialogue. Then build a table of chords for a circle of a stated radius at angles you choose, showing each calculation, and check three entries against a published table of sines, using chord = 2 x radius x sine of half the angle. You pass when your reconstruction survives a second reading of the half and each checked chord matches the published value within the error you state.

On the site: Compare Ptolemy, Copernicus, Tycho and Kepler: Astronomy, Round 1

Grammar Logic

Seminar

• Aristotle, Nicomachean Ethics: Book 1

Tutorial: Language

Logic in the language tutorial: the Categories read closely, with a table of its distinctions. Read the whole work closely and set out each distinction in a table with one example of each.

• Aristotle, Categories: the whole work

Acts

Understand exactly, Examine the reasons

Pass when: Summarise Nicomachean Ethics, Book 1, in 200 words, and state the strongest objection to Aristotle's account of the good, answered from the text. Then read the Categories closely and set out its distinctions in a table, with one example of each. You pass when your summary matches the book, your objection is answered from it, and each example in your table fits its distinction when you reopen the Categories.

On the site: The Seven Liberal Arts, Hands-On: Logic, Proof and the Quadrivium

Grammar Arithmetic

Seminar

• Aristotle, Nicomachean Ethics: Books 2-3

Tutorial: Laboratory

Black: heat and temperature distinguished. Read the selections on heat and write the distinction in three sentences, then state one observation that would test it.

• Joseph Black, Chemistry lectures: selections on heat

Acts

Understand exactly, Check it against evidence

Pass when: Summarise Nicomachean Ethics, Books 2-3, in 200 words, and state one objection to Aristotle's account of virtue, answered from the text. Then write Black's distinction between heat and temperature in three sentences from his selections, and state one observation that would test it, with what you would record. You pass when your summary matches the books and your stated observation would really separate heat from temperature when you check it against the selections.

On the site: Evidence-Based Troubleshooting: Separating Explanations

Arithmetic Geometry Astronomy

Seminar

• Aristotle, Nicomachean Ethics: Books 4-5

Tutorial: Mathematics

Spherical trigonometry: the celestial sphere and its great circles. Draw a sphere with two great circles, mark their intersection, and measure the angle between them.

Acts

Understand exactly, Check it against evidence

Pass when: Summarise Nicomachean Ethics, Books 4-5, in 200 words, and answer one objection to its account of justice from the text. Then draw a sphere with two great circles, mark their intersection, and state in three sentences what a great circle is on it. State the angle you set between the circles when you drew them, measure it on your drawing and compare the two. You pass when your summary matches the books and your drawn angle agrees with the calculation within the error of your drawing.

On the site: Explain the sky: days, seasons and phases: Astronomy, Round 1

Grammar Logic

Seminar

• Aristotle, Nicomachean Ethics: Books 6-7

Tutorial: Language

Logic in the language tutorial: statements, contradiction and the problem of future contingents. Read On Interpretation closely and write out the problem of future contingent statements in your own words, with one answer to it.

• Aristotle, On Interpretation: the whole work

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Summarise Nicomachean Ethics, Books 6-7, in 200 words, and state one objection to its account of practical wisdom, answered from the text. Then write out in 200 words the problem of future contingent statements from On Interpretation, with the strongest objection to one answer and your reply. You pass when your summary matches the books and your reply answers the objection using the text when you reopen it.

On the site: Reconstruct an argument: Logic, Round 1

Arithmetic Grammar

Seminar

• Aristotle, Nicomachean Ethics: Books 8-9

Tutorial: Laboratory

Mariotte: the spring of the air, and a pressure-volume experiment with a syringe. Read the selections on the air, then load a sealed syringe with four stated weights and record the volume at each.

• Mariotte, Selected writings: selections on the air

Acts

Check it against evidence, Understand exactly

Pass when: Summarise Nicomachean Ethics, Books 8-9, in 200 words, and answer one objection to its account of friendship from the text. Then describe Mariotte's claim about the spring of the air in three sentences from his selections, and record the volume of a sealed syringe at four stated loads on the plunger in a table. You pass when your summary matches the books and your table shows whether the readings fit the claim, with the limits of the test stated.

On the site: Hypotheses, Predictions and Tests

Arithmetic Astronomy

Seminar

• Aristotle, Nicomachean Ethics: Book 10

Tutorial: Mathematics

Ptolemy: the lengths of days at different latitudes. Read the selections from Book 2 and calculate the longest day at three latitudes you choose, writing down each assumption your method uses.

• Ptolemy, Almagest: Book 2, selections

Acts

Understand exactly, Check it against evidence

Pass when: Summarise Nicomachean Ethics, Book 10, in 200 words, and answer one objection to its account of the best life from the text. Then calculate the length of the longest day at three latitudes you choose, using the method of the Almagest selections, and compare each result with a published table. You pass when your summary matches the book, each calculated length agrees with the published table within the error you state, and every assumption of your method is written down.

On the site: The Sky as a Sphere: Days, Seasons and the Phases of the Moon

Grammar Logic

Seminar

• Aristotle, Politics: Books 1-2

Tutorial: Language

Logic in the language tutorial: the three figures of the syllogism. Set out the three figures from Book 1 of the Prior Analytics as a table, with one valid example of each figure.

• Aristotle, Prior Analytics: Book 1, the three figures

Acts

Understand exactly, Examine the reasons

Pass when: Summarise Politics, Books 1-2, in 200 words, and state one objection to its account of the household, answered from the text. Then set out the three figures of the syllogism from Prior Analytics, Book 1, in a table with one valid example of each, and test each example by putting other terms in its place. You pass when your summary matches the books and each example in your table stays valid when you test it with other terms.

On the site: Reconstruct an argument: Logic, Round 1

Grammar Astronomy Geometry

Seminar

• Aristotle, Politics: Book 3

Tutorial: Mathematics

Ptolemy: the sun's anomaly, by eccentric and by epicycle. Draw both models of the sun's motion from Book 3, and mark on each the sun's position at three points in its year.

• Ptolemy, Almagest: Book 3, the sun's motion

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise Politics, Book 3, in 200 words, and answer one objection to its account of citizenship from the text. Then draw the sun's anomaly by an eccentric and by an epicycle, mark the sun's position at three points on each drawing, and state whether any observation you could make would separate the two models. You pass when your summary matches the book and your statement about separating the models is supported by your own drawings.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Arithmetic Logic

Seminar

• Aristotle, Politics: Books 4-6, selections

Tutorial: Laboratory

Lavoisier: elements, gases and the method of chemistry. Read Part 1, selections, and write Lavoisier's method as three numbered steps, then apply the method to one change you can observe safely.

• Lavoisier, Elements of Chemistry: Part 1, selections

Acts

Understand exactly, Check it against evidence

Pass when: Summarise the selections from Politics, Books 4-6, in 200 words, and state one objection to its account of one kind of regime, answered from the text. Then write the steps Lavoisier follows in the Part 1 selections as three numbered steps, and apply it to one change you can observe safely, recording the mass before and after. You pass when your summary matches the selections and your mass record shows what the method says it should show, with your reasons stated.

On the site: Evidence-Based Troubleshooting: Separating Explanations

Grammar Logic

Seminar

• Aristotle, Politics: Books 7-8

Tutorial: Language

Logic in the language tutorial: reducing the moods to the first figure. Reduce two valid moods of the second figure to the first figure, step by step, and name the rule each step uses.

• Aristotle, Prior Analytics: Book 1, the reduction of the moods

Acts

Understand exactly, Examine the reasons

Pass when: Summarise Politics, Books 7-8, in 200 words, and answer one objection to its account of education, from the text. Then reduce two valid moods of the second figure to the first figure, step by step, and name the rule each step uses. You pass when your summary matches the books and each reduction checks out step by step when you reopen Prior Analytics, Book 1.

On the site: Reconstruct an argument: Logic, Round 1

Grammar Logic Astronomy

Seminar

• Aristotle, Poetics: the whole work

Tutorial: Mathematics

Ptolemy: the sun's tables, used. Use the sun's tables from Book 3 to predict the sun's position on two dates you choose, and write down each step of the prediction.

• Ptolemy, Almagest: Book 3, further selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the account of tragedy in the Poetics in 300 words, and state the strongest objection to one of its definitions, answered from the text. Then use Ptolemy's sun tables from Almagest, Book 3, to predict the sun's position on two dates you choose, and check each prediction against a published almanac. You pass when your reconstruction survives a second reading of the work and each prediction falls within the error you state for the tables.

On the site: The Sky as a Sphere: Days, Seasons and the Phases of the Moon

Grammar Rhetoric

Seminar

• Aristotle, Rhetoric: Books 2-3, selections

Tutorial: Language

Translation: the Meno's opening exchange, literally and then readably. Translate the exchange first word for word, then as a readable English passage, and write a note on what the second version changes.

• Plato, Meno: the opening exchange, in Greek

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Summarise the selections from Rhetoric, Books 2-3, in 200 words, and answer one objection to Aristotle's account of the audience, from the text. Then translate the Meno's opening exchange twice, first literally and then readably, and write 100 words on what the two versions lose. You pass when your summary matches the selections and both translations follow the Greek when you reopen the exchange.

On the site: Rhetoric: one of the seven liberal arts

Grammar Arithmetic

Seminar

• Aristotle, Physics: Books 1-2

Tutorial: Laboratory

Lavoisier: combustion, and the case against phlogiston. Read the selections on combustion and write Lavoisier's case in three sentences, then compare the masses in one published record of a combustion before and after.

• Lavoisier, Elements of Chemistry: selections on combustion

Acts

Understand exactly, Check it against evidence

Pass when: Summarise Physics, Books 1-2, in 200 words, and state the strongest objection to Aristotle's account of change, answered from the text. Then write Lavoisier's account of combustion in three sentences from his selections, and say what it implies for the phlogiston view, and compare the masses in one published record of a combustion before and after. You pass when your summary matches the books and your comparison shows whether the masses support or count against his case, with the reasons stated.

On the site: Hypotheses, Predictions and Tests

Grammar Logic Astronomy

Seminar

• Aristotle, Physics: Books 3-4

Tutorial: Mathematics

Ptolemy: the moon's first anomaly. Read the selections from Book 4, and draw the model of the moon's first anomaly at three positions of the moon you choose, labelling each part of the model.

• Ptolemy, Almagest: Book 4, selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise Physics, Books 3-4, in 200 words, and answer one objection to its account of the infinite, from the text. Then draw the moon's first anomaly as Ptolemy models it in the Book 4 selections, at three positions of the moon you choose, labelling each part. You pass when your summary matches the books and each drawing matches the model's description of the moon's position when you reopen the selections.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Logic

Seminar

• Aristotle, Physics: Books 5-8, selections

Tutorial: Language

Translation: the geometry lesson in the Meno. Translate the lesson from Greek, literally and then readably, and mark every point where the two versions differ.

• Plato, Meno: the slave-boy passage, in Greek

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Summarise the Physics selections from Books 5-8 in 200 words, and state the strongest objection to one claim about motion, answered from the text. Then translate the geometry lesson in the Meno from Greek, literally and then readably, and mark every point where the two versions differ. You pass when your summary matches the selections and each marked difference rests on a real choice in the Greek when you reopen the passage.

On the site: Grammar: one of the seven liberal arts

Grammar Arithmetic

Seminar

• Aristotle, On Generation and Corruption: selections

Tutorial: Laboratory

Proust and Berthollet: do compounds have fixed proportions? Read the selections from both writers and write each position in three sentences, then state one observation that would decide between them.

• Proust, Selected writings: selections
• Berthollet, Selected writings: selections

Acts

Understand exactly, Examine the reasons

Pass when: Summarise the selections from On Generation and Corruption in 200 words, and state one objection to its account of mixture, answered from the text. Then write the two positions on fixed proportions from Proust and Berthollet in three sentences each, and state one observation that would decide between them. You pass when your summary matches the selections and your observation would really separate the two positions when you check it against both writers.

On the site: Hypotheses, Predictions and Tests

Grammar Logic Astronomy

Seminar

• Aristotle, On the Soul: Books 1-2

Tutorial: Mathematics

Ptolemy: the order and models of the planets. Write the order of the planets by distance in Ptolemy's arrangement, then draw the model of the planet the selections describe, with its deferent and epicycle.

• Ptolemy, Almagest: Book 9, selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise On the Soul, Books 1-2, in 200 words, and state the strongest objection to its definition of the soul, answered from the text. Then write the order of the planets in Ptolemy's arrangement from the Book 9 selections, and draw the model of the planet the selections describe, with its deferent and epicycle. You pass when your summary matches the books, your order matches the selections, and your drawing matches the model the selections describe.

On the site: Compare Ptolemy, Copernicus, Tycho and Kepler: Astronomy, Round 1

Grammar Rhetoric

Seminar

• Aristotle, On the Soul: Book 3

Tutorial: Language

Translation: the Meno's closing pages. Translate the closing pages from Greek, literally and then readably, and mark each passage where you chose one rendering over another.

• Plato, Meno: the closing pages, in Greek

Acts

Understand exactly, Express it truly

Pass when: Summarise On the Soul, Book 3, in 200 words, and answer one objection to its account of thinking from the text. Then translate the Meno's closing pages from Greek, literally and then readably, and write 100 words on one passage where the two versions disagree. You pass when your summary matches the book and your disagreement is grounded in the Greek when you reopen the pages.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Music

Seminar

• Aristotle, Metaphysics: Books 1 and 4

Tutorial: Music

Rhythm, metre and accent: conduct and sing in two, three and four. Conduct a steady beat in each metre, and sing a short phrase in each, marking the accent on every beat.

Acts

Understand exactly, Express it truly

Pass when: Summarise Metaphysics, Books 1 and 4, in 200 words, and state one objection to its account of being, answered from the text. Then conduct and sing a short phrase in two, three and four beats, marking the accent on each beat, and have a listener name the metre of each pattern. You pass when your summary matches the books and your listener names the metre of each pattern you sang.

On the site: Intervals as ratios of string length: Music, Round 1

Grammar Arithmetic

Seminar

• Aristotle, Metaphysics: Books 7-9, selections

Tutorial: Laboratory

Dalton: atoms and relative weights. Read the selections and write Dalton's view in three sentences, then calculate one relative weight from two masses in a published record, stating each assumption.

• Dalton, A New System of Chemical Philosophy: selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the Metaphysics selections from Books 7-9 in 200 words, and state one objection to its account of substance, answered from the text. Then write Dalton's view of atoms and relative weights in three sentences from his selections, and calculate one relative weight from two masses in a published record. You pass when your summary matches the selections and your calculated weight follows from the masses and the assumptions you wrote down.

On the site: Proof and Precise Reasoning: From Arguments to Theorems

Grammar Arithmetic

Seminar

• Aristotle, Metaphysics: Book 12

Tutorial: Mathematics

Algebra at speed: polynomials, factoring and exponents. Factor twenty polynomials and simplify ten expressions with exponents, timing yourself and checking every answer by substitution.

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Reconstruct the argument of Metaphysics, Book 12, in 300 words, and answer one objection to its account of the first mover from the text. Then factor twenty polynomials and simplify ten expressions with exponents, timing yourself and checking each answer by substitution. You pass when your reconstruction survives a second reading and at least twenty-seven of your thirty factorings and simplifications check out by substitution.

On the site: Algebra: The Skills That Carry Everything

Grammar Rhetoric

Seminar

• Philip J. Ivanhoe and Bryan W. Van Norden, editors, Readings in Classical Chinese Philosophy: Kongzi (Confucius), the Analects

Tutorial: Language

Translation: literal and interpretive renderings of one Meno passage, compared. Choose one Meno passage, render it literally and then interpretively, and write a short comparison of the two.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Summarise the Analects selections in 200 words, and state one objection to a saying's meaning there, answered from the text. Then render one Meno passage twice, literally and interpretively, and compare the two in 150 words, marking where the choice changes the sense. You pass when your summary matches the selections, and your comparison names the choices that change the sense when you reopen the passage.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Arithmetic

Seminar

• Philip J. Ivanhoe and Bryan W. Van Norden, editors, Readings in Classical Chinese Philosophy: Mozi and Mengzi, selections

Tutorial: Laboratory

Gay-Lussac and Avogadro: combining volumes and molecules. Read the selections from both writers, state each claim in two sentences, and compare a published table of gas volumes in one reaction.

• Gay-Lussac, Selected writings: selections
• Avogadro, Selected writings: selections

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Summarise the Mozi and Mengzi selections in 200 words, and state one objection to a claim about human nature there, answered from the text. Then state Gay-Lussac's claim about combining volumes and Avogadro's hypothesis in two sentences each, and test them against a published table of gas volumes for one reaction, stating the proportions you find. You pass when your summary matches the selections and your stated proportions follow from the table.

On the site: Proof and Precise Reasoning: From Arguments to Theorems

Grammar Arithmetic

Seminar

• Philip J. Ivanhoe and Bryan W. Van Norden, editors, Readings in Classical Chinese Philosophy: Laozi, the Daodejing

Tutorial: Mathematics

Algebra at speed: rational expressions and simultaneous equations. Solve twenty simultaneous equations and simplify ten rational expressions, timing yourself and checking each answer by substitution.

Acts

Understand exactly, Examine the reasons, Check it against evidence

Pass when: Restate the main claims of the Daodejing selections in 300 words, and state one objection to its account of the Way, answered from the text. Then solve twenty simultaneous equations and simplify ten rational expressions, timing yourself and checking each answer by substitution. You pass when your reconstruction survives a second reading and at least twenty-seven of your thirty solutions check out by substitution.

On the site: Algebra: The Skills That Carry Everything

Grammar Rhetoric

Seminar

• Philip J. Ivanhoe and Bryan W. Van Norden, editors, Readings in Classical Chinese Philosophy: Zhuangzi, selections

Tutorial: Language

Translation: ambiguity, idiom and alternative renderings in the Meno. Find three ambiguous or idiomatic phrases in one Meno passage, and give two renderings of each.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Summarise the Zhuangzi selections in 200 words, and answer one objection to one of their arguments about knowledge, from the text. Then choose three ambiguous or idiomatic phrases in one Meno passage, give two renderings of each, and state in 150 words which rendering you would defend and why. You pass when your summary matches the selections and each rendering you defend can be justified from the Greek when you reopen the passage.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Grammar Arithmetic

Seminar

• Philip J. Ivanhoe and Bryan W. Van Norden, editors, Readings in Classical Chinese Philosophy: Xunzi and Han Feizi, selections

Tutorial: Laboratory

Cannizzaro: settling the atomic weights. Read the letter and write Cannizzaro's method in three numbered steps, then apply it to the published gas densities of at least four compounds of one element.

• Stanislao Cannizzaro, Letter to Professor S. De Luca: the letter

Acts

Understand exactly, Check it against evidence

Pass when: Summarise the Xunzi and Han Feizi selections in 200 words, and state one objection to a claim about law or ritual there, answered from the text. Then write Cannizzaro's method from his letter in three numbered steps, and apply it to the published gas densities of at least four compounds of one element, stating the molecular weight each gives, the atomic weight of the element they suggest, and your assumptions. You pass when your summary matches the selections and each weight you calculate follows from the steps and assumptions you wrote down.

On the site: Proof and Precise Reasoning: From Arguments to Theorems

Logic Rhetoric Arithmetic

Seminar

Task: The first-year essay: choose a question that two of the year's authors answer differently

Tutorial: Mathematics

Algebra at speed: quadratics and their graphs. Solve twenty quadratic equations and sketch five of their graphs, checking each root against its graph.

Acts

Understand exactly, Examine the reasons

Pass when: Choose one question that two of the year's authors answer differently, and write a plan of 200 words stating each author's answer and the exact point on which they disagree. Solve twenty quadratic equations and sketch five of their graphs, checking each root against its graph. You pass when your plan names the point of disagreement exactly and every root you check matches its graph.

On the site: The Weekly Loop: Read, Reconstruct, Make, Defend, Log

Grammar Rhetoric

Seminar

Task: The first-year essay: the draft

Tutorial: Language

Translation: a passage of the Republic. Translate one passage from Book 7 in Greek, literally and then readably, and set both versions beside your draft.

• Plato, Republic: a passage from Book 7, in Greek

Acts

Understand exactly, Express it truly

Pass when: Write the draft of your first-year essay in 1,200 words, answering the question you chose, and, if your question touches the Republic, use your translation of one passage from Book 7 as evidence. Set both versions of the translation beside the draft. You pass when your draft states a thesis and each claim points to a passage a reader can find in the text when they reopen it.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard

Rhetoric Arithmetic

Seminar

Task: The first-year essay: a reader's criticism, and your reply

Tutorial: Laboratory

Mendeleev: the periodic law, and his predictions tested. Read the essay and list the predictions he made, then check two of them against a published table of the elements.

• Dmitri Mendeleev, The Periodic Law of the Chemical Elements: the essay

Acts

Express it truly, Check it against evidence

Pass when: Ask a reader to criticise your draft in writing, and write a reply of 500 words that accepts, answers or rejects each criticism, with a reason. List Mendeleev's predictions from his essay and check two of them against a published table of the elements. You pass when every criticism in the reader's note is answered in your reply, and each prediction you check is marked right or wrong against the table.

On the site: The Weekly Loop: Read, Reconstruct, Make, Defend, Log

Rhetoric Astronomy

Seminar

Task: The first-year essay: the final text

Tutorial: Mathematics

Observation and hypothesis: what one of the Almagest's models predicts, and how to test it by naked-eye observation. Choose one model, state what it predicts for the sky, and write the prediction down before you observe.

Acts

Express it truly, Check it against evidence

Pass when: Revise the essay into its final text of 1,500 words, marking every change made after the reader's criticism, with a reason beside each. Then state what one of the Almagest's models predicts for the sky, and test the prediction by naked-eye observation on three nights you record. You pass when the final text answers the criticism it set out to answer, and each observation is recorded against its prediction with the result stated, whether it agrees or not.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Rhetoric Grammar Logic

Seminar

Task: The first-year examination: the essay defended aloud, then questions across the year

Tutorial: Language

Translation: a passage of the Nicomachean Ethics. Translate one passage from Book 1 in Greek, literally and then readably, and mark every choice you made.

• Aristotle, Nicomachean Ethics: a passage from Book 1, in Greek

Acts

Express it truly, Examine the reasons, Understand exactly

Pass when: Defend your first-year essay aloud for ten minutes to a listener, then answer the listener's questions for twenty minutes across the year's authors. Read one passage from Nicomachean Ethics, Book 1, aloud in Greek, and translate it with each choice marked. You pass when the listener can follow your defence, each answer you give points to a passage you can name, and your translation reads correctly against the Greek.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard