Levels 201 to 300

Grammar Rhetoric

Seminar

• Plutarch, Caesar: the whole life

Tutorial: Language

Greek: reading Homer, the opening of the Iliad. Read the opening lines of Book 1 aloud from the printed Greek each day for a week, marking every word you must look up, then translate them without notes.

• Homer, Iliad: Book 1, the opening lines, in Greek

Acts

Understand exactly, Express it truly

Pass when: Translate the opening lines of Iliad Book 1 from Greek into English prose, then write 300 words comparing how Plutarch explains Caesar's decisions by character with how Homer explains Achilles' anger in Book 1, naming one passage from each. You pass when a listener can follow your translation against the Greek, and both passages can be found again on a reopening.

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

Astronomy Arithmetic Grammar

Seminar

• Plutarch, Cato the Younger: the whole life

Tutorial: Mathematics

Ptolemy: the planetary models in detail. Draw the model for one planet from the selections, label each circle, and calculate the planet's position at two times you choose, showing each step.

• Ptolemy, Almagest: Books 9-13, selections

Acts

Understand exactly, Check it against evidence

Pass when: Draw Ptolemy's model for one planet from the selections, label each circle, and calculate the planet's position at two times you choose, showing each step. Then write 250 words comparing how Plutarch explains one choice of Cato with how Ptolemy explains one irregular motion of a planet, naming the cause each author gives and one passage from each. You pass when your diagram and calculation can be redone with the same answer, and your comparison points to a passage in each text on reopening.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler, Astronomy: Seasons, Moon, Earth and Orbits

Grammar Rhetoric Music

Seminar

• Plutarch, Antony: the whole life

Tutorial: Music

Ancient Greek thought on music and education. Read the selections with a notebook open, and list each claim the authors make about what music does to character, with the sentence that supports it.

• Plato and other ancient writers, Selected writings: Plato and others, selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: List the claims the music selections make about what music does to character, with the sentence that supports each, and choose the one you think is weakest. Write 250 words testing that claim: state it in your own words, give the reason its author gives, and name the strongest objection. Then write 200 words on one decision of Antony in Plutarch's Life, comparing Plutarch's explanation with the music author's claim about how character is formed. You pass when a reader can see from your first paragraph which claim you are testing, and both passages can be found again on a reopening.

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

Arithmetic Grammar

Seminar

• Plutarch, Brutus: the whole life

Tutorial: Evidence and inquiry

Statistics: inference for a proportion. Work two examples from the chapter with pencil and paper, then repeat one example with a sample of a different size and record what changes.

• Diez, Çetinkaya-Rundel, and Barr, OpenIntro Statistics: inference for proportions

Acts

Understand exactly, Check it against evidence

Pass when: Calculate a confidence interval for a proportion from a sample in the textbook, at a confidence level you state, and show each step. Repeat the calculation with a sample twice as large and say what changes in the interval. Then write 200 words on one choice Brutus makes in Plutarch's Life and the reasons Plutarch gives for it, stating which of those reasons could be checked against evidence and which could not. You pass when a reader can redo your arithmetic from your table and reach the same interval, and each reason you list is marked as checkable or not.

On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting

Grammar Rhetoric

Seminar

• Livy, Early History of Rome: Book 1

Tutorial: Language

Greek: Homeric forms, and the dactylic hexameter read aloud. Mark each Homeric form you meet in the Iliad, and read ten lines aloud each day in the rhythm of the hexameter, marking the long and short syllables.

• Homer, Iliad: Book 1, further lines, in Greek

Acts

Understand exactly, Express it truly

Pass when: Read ten lines of Iliad Book 1 in Greek aloud in dactylic hexameter, marking the long and short syllables, and translate them into English prose. Then reconstruct in 250 words the order of the early events in Livy's Book 1, and compare his account of a founding act with Homer's account of a quarrel, naming one passage from each. You pass when a listener can follow your syllable marks as you read, and both passages can be found again on a reopening.

Geometry Astronomy Rhetoric

Seminar

• Livy, Early History of Rome: Books 2-5, selections

Tutorial: Mathematics

Ptolemy's planets on paper: draw the model for one planet and predict a retrograde loop. Use the site's astronomy lab to check your prediction, and write down any difference you find.

Acts

Check it against evidence, Examine the reasons, Express it truly

Pass when: Draw the model for one planet with its circles labelled, and predict the place and length of one retrograde loop, showing each calculation. Check the prediction in the site's astronomy lab and record any difference. Then write 250 words on one conflict in Livy's Books 2 to 5, reconstructing how Livy presents it, and compare how Livy explains the outcome of that conflict with how Ptolemy explains the retrograde loop you predicted, naming the cause each gives. You pass when your diagram matches your calculation, and your comparison names a passage in each text you can find again.

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

Music Grammar Logic

Seminar

• Tacitus, Annals: Books 1-2, selections

Tutorial: Music

The Greek modes and their characters. Sing or play the scale of each mode in the further selections once a day for a week, and write one sentence beside each mode on the character the text gives it.

• Plato and other ancient writers, Selected writings: further selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Sing or play the scale of three Greek modes, and write one line for each stating the character the selections give it. Then write 250 words on Tacitus's Annals Books 1 and 2, reconstructing how the historian explains the conduct of one ruler, and compare his explanation with the music writers' account of how a mode affects its hearer. Name the strongest objection to one of the two accounts. You pass when a listener can name the mode you sang, and your comparison points to a passage in each text on reopening.

On the site: Guitar Tools: Tuner, Metronome, Drone, Fretboard

Grammar Rhetoric

Seminar

• Tacitus, Annals: Books 13-16, selections

Tutorial: Language

Greek: the opening of the Odyssey. Read the first lines aloud in Greek, then translate about twenty lines, noting each verb's tense and mood.

• Homer, Odyssey: Book 1, the opening lines, in Greek

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Translate about twenty lines from the opening of the Odyssey from Greek into English prose, noting each verb's tense and mood. Then write 300 words comparing two selections from Tacitus's Annals Books 13 to 16 that present the same ruler, and set one of them beside a passage of the Odyssey that shows a leader's conduct. You pass when your translation can be read beside the Greek line by line, and your comparison points to words in each passage you can find again on reopening.

Rhetoric Logic

Seminar

• Lucretius, On the Nature of Things: Books 1-2

Tutorial: Writing and speaking

Writing: an article of your own in Aquinas's form: objections, a contrary authority, your answer, replies. Choose one question from Books 1 and 2, and write the three objections, a contrary authority from the text, your answer and the replies in 400 words.

• Thomas Aquinas, Summa Theologiae: one article, studied for its form

Acts

Examine the reasons, Express it truly

Pass when: Write an article of about 400 words in Aquinas's form on one question raised in Lucretius Books 1 and 2: state three objections, a contrary authority, your answer, and a reply to each objection. Then write 150 words reconstructing the form of one article from Aquinas's Summa, and compare how that article and Lucretius each state their strongest objection. You pass when a reader can find each part of the form in order, and your replies answer the objections as they are stated.

On the site: The Academy: Proofs, Definitions and the Method of Reason

Arithmetic Grammar Logic

Seminar

• Lucretius, On the Nature of Things: Books 3-4

Tutorial: Evidence and inquiry

Statistics: inference for means. Work three examples from the chapter, then calculate an interval for the mean of one small set of numbers from the chapter, showing each step.

• Diez, Çetinkaya-Rundel, and Barr, OpenIntro Statistics: inference for numerical data

Acts

Check it against evidence, Understand exactly

Pass when: Calculate a confidence interval for a mean from a small set of numbers in the textbook, at a confidence level you state, and show each step. Then write 200 words on one argument in Lucretius Books 3 and 4 and the evidence it uses, reconstructing the argument and comparing that evidence with what your interval can show. You pass when a classmate can redo your interval from your table and reach the same numbers, and your comparison can be checked against the text on reopening.

On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting

Astronomy Arithmetic Grammar

Seminar

• Lucretius, On the Nature of Things: Books 5-6

Tutorial: Mathematics

Retrograde motion in the site's astronomy lab, and what each model must explain. Record the planet's positions at each step the lab offers, and write one line listing what each model must explain about that path.

Acts

Check it against evidence, Understand exactly

Pass when: Use the site's astronomy lab to record one planet's positions at each step the lab offers, make a table of them, and write one line for each model stating what it must explain about that path. Then write 250 words on one account of natural phenomena in Lucretius Books 5 and 6, reconstructing it and comparing it with how one astronomical model explains an apparent reversal of a planet's path. You pass when your table can be checked against the lab, and your comparison points to a passage in Lucretius you can find again.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler, Astronomy: Seasons, Moon, Earth and Orbits

Grammar Logic Music

Seminar

• Epictetus, Discourses: Books 1-2, selections

Tutorial: Music

Vincenzo Galilei against the old theorists. Read the selections, and write a summary of his objection to the theorists in 200 words, naming each theorist he criticises.

• Vincenzo Galilei, Dialogue on Ancient and Modern Music: selections

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Write 200 words stating Galilei's objection to the old theorists of music, naming each theorist he criticises and the reason he gives. Then write 250 words reconstructing one distinction in Epictetus's Discourses Books 1 and 2, and compare how Galilei and Epictetus each argue for a conclusion, naming one passage from each. State the strongest objection to one of the two arguments. You pass when your summary matches the dialogue on reopening, and your objection names a step in the argument.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Grammar Logic Rhetoric

Seminar

• Epictetus, Discourses: Books 3-4, selections

Tutorial: Language

Greek: a choral ode of Sophocles. Read the choral ode aloud in Greek twice, then translate it line by line, marking each word you had to decide on.

• Sophocles, Antigone: the ode on man, in Greek

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Translate the choral ode from Sophocles' Antigone from Greek into English, line by line, and mark the three words that were hardest and how you decided each. Then write 250 words reconstructing one practical claim in Epictetus Books 3 and 4, and compare how the ode and Epictetus each describe what a person can and cannot do. State the strongest objection to one of them. You pass when your translation can be read beside the Greek with each marked word explained, and your objection points to a step in the argument on reopening.

Geometry Logic Grammar

Seminar

• Plotinus, Enneads: selections

Tutorial: Mathematics

Apollonius: cutting the cone. Draw a cone and cut it with a plane at three angles, sketching each section, and write one sentence beside each figure that names the section it makes.

• Apollonius, Conics: Book 1, the cone and the three sections

Acts

Examine the reasons, Check it against evidence

Pass when: Draw a cone and cut it with a plane at three angles, as Apollonius does in Book 1, label each section, and explain in writing how each cut is made, on a sketch of one page. Then write 250 words on one claim about the One or the soul in the Plotinus selections, and compare how Plotinus and Apollonius each argue from a definition to a result. Name the strongest objection to one argument. You pass when each section you drew matches its label on a reopening, and your objection names a step in the claim.

On the site: Geometry: Apollonius' Conic Sections

Arithmetic Music Grammar

Seminar

• Deepak Sarma, Classical Indian Philosophy: A Reader: selections on knowledge and perception

Tutorial: Music

Ratios and the Pythagorean comma, worked by hand and heard on the monochord. Work out twelve pure fifths against seven octaves by hand, then listen to the difference with the 'Hear the comma' control on the site's Science of Sound page for at least ten minutes.

Acts

Check it against evidence, Understand exactly

Pass when: Calculate the ratio of twelve pure fifths to seven octaves by hand, show each step, and state the gap as a ratio and in cents. Then write 200 words on the selections' account of perception as a source of knowledge, and state the strongest objection the text allows to one view. You pass when a listener can hear the gap using the 'Hear the comma' control on the site's Science of Sound page, and your arithmetic can be redone with the same result.

On the site: Twelve fifths and seven octaves: Music, Round 1, The Science of Music: Ratios, Beats, the Comma and String Physics

Grammar Rhetoric

Seminar

• Deepak Sarma, Classical Indian Philosophy: A Reader: selections on mind and self

Tutorial: Language

Greek: tragic dialogue. Read the exchange between Creon and Antigone aloud in Greek, then translate it into English speech by speech.

• Sophocles, Antigone: an exchange between Creon and Antigone, in Greek

Acts

Understand exactly, Express it truly

Pass when: Translate the exchange between Creon and Antigone from Greek into English, speech by speech, and mark each place where an English word choice changes the tone of a speech. Then write 250 words reconstructing one argument in the Sarma selections on mind and self, and compare it with how one speaker in the exchange defends a position. Name the strongest objection to one of the two. You pass when your translation can be set beside the Greek speech by speech, and your comparison points to a line of each text you can reopen.

Arithmetic Logic Grammar

Seminar

• Deepak Sarma, Classical Indian Philosophy: A Reader: selections on reality and liberation

Tutorial: Evidence and inquiry

Statistics: regression, and what it does not show. Fit a line to five pairs of values from the chapter's data by hand, then write what the slope does and does not tell you about cause.

• Diez, Çetinkaya-Rundel, and Barr, OpenIntro Statistics: introduction to linear regression

Acts

Check it against evidence, Examine the reasons

Pass when: Fit a least-squares line to five pairs of values from the textbook's data, by hand or with a calculator, and show the slope and intercept. Write 150 words on what the slope does and does not show about cause. Then write 200 words reconstructing one argument in the Sarma selections on reality and liberation, and compare how that argument and your regression each claim a connection between two things. You pass when a reader can redo the fit from your table and reach the same slope, and your statement about cause names what the data cannot show.

On the site: Hypotheses, Predictions and Tests

Grammar Rhetoric

Seminar

• Virgil, Aeneid: Book 1

Tutorial: Language

Greek: translating epic and translating tragedy, compared. Translate ten lines of Homer and ten lines of Sophocles, then write a paragraph on what each translation had to keep and what it had to lose.

Acts

Understand exactly, Express it truly

Pass when: Translate ten lines of Homeric epic and ten lines of Sophoclean verse from Greek into English, then write 250 words comparing what each translation had to keep and what it had to lose. Then reconstruct in 200 words how Virgil's Aeneid Book 1 opens and what its first scene establishes, and compare that opening with the opening of the Odyssey. You pass when both translations can be set beside the Greek, and your comparison names one specific choice in each.

Geometry Grammar

Seminar

• Virgil, Aeneid: Book 2

Tutorial: Mathematics

Apollonius: the defining properties of the three sections. Draw each section from its defining property with a ruler and set square, and write the property beside each drawing in one sentence.

• Apollonius, Conics: Book 1, the defining properties

Acts

Understand exactly, Check it against evidence

Pass when: Draw the three sections from their defining properties, label each part, and write each property in one sentence beside its figure. Then write 250 words reconstructing the main action of Aeneid Book 2, and compare how the narrator presents one turning point with how a speaker in the book presents the same turning point. You pass when each figure matches its written property on a redraw, and your comparison points to a passage you can find again.

On the site: Geometry: Apollonius' Conic Sections

Music Grammar Logic

Seminar

• Virgil, Aeneid: Book 3

Tutorial: Music

The diatonic system and the church modes. Sing or play each church mode on the site's tools page for ten minutes, then write a one-line label for each.

Acts

Understand exactly, Examine the reasons

Pass when: Sing or play a scale in each church mode, and write one line per mode naming the step pattern you heard. Then write 250 words on the journey Aeneas makes in Book 3, reconstructing the sequence of places, and compare how Aeneas and one prophet or oracle in the book each explain why he goes on. Name the strongest objection to one of the two explanations. You pass when a listener can match each sung mode to your written label, and your sequence can be checked on reopening.

On the site: Guitar Tools: Tuner, Metronome, Drone, Fretboard

Grammar Rhetoric

Seminar

• Virgil, Aeneid: Book 4

Tutorial: Language

Greek: the Septuagint's Genesis. Read Genesis 1 aloud in Greek, then translate the opening verses word by word into English.

• The Septuagint, Selections: Genesis 1, in Greek

Acts

Understand exactly, Examine the reasons

Pass when: Translate the opening verses of Genesis 1 from the Septuagint's Greek into English, and set your translation beside an English Bible translation, marking each word where they differ. Then write 250 words on Dido in Aeneid Book 4, reconstructing how Virgil presents her decision, and compare that presentation with how Genesis 1 presents the first command, naming one passage from each. You pass when your translation can be compared verse by verse with both texts, and your reading points to lines you can reopen.

Arithmetic Grammar

Seminar

• Virgil, Aeneid: Book 5

Tutorial: Evidence and inquiry

Statistics: several variables at once. Reproduce the chapter's example with three variables, then change one variable and record what changes in the output.

• Diez, Çetinkaya-Rundel, and Barr, OpenIntro Statistics: multiple and logistic regression, selections

Acts

Check it against evidence, Understand exactly

Pass when: Reproduce one table of a multiple regression from the textbook, showing how each coefficient is read, then change one input and report what changes in the output. Then write 200 words on the contest in Aeneid Book 5, reconstructing its result, and compare how Virgil frames the winner with how one other text you have read frames a contest. You pass when your table matches the book's on a second run, and your comparison can be checked against the text on reopening.

Geometry Grammar Logic

Seminar

• Virgil, Aeneid: Book 6

Tutorial: Mathematics

Apollonius: tangents and conjugate diameters. Draw a tangent to each section at three points, and check that each tangent meets its curve at one point only.

• Apollonius, Conics: Book 1, tangents and diameters

Acts

Check it against evidence, Examine the reasons

Pass when: Draw a tangent to a parabola, an ellipse and a hyperbola at three points on each, and construct each tangent by the method the text allows. Then write 250 words on the descent in Aeneid Book 6, reconstructing its stages, and compare how the guide and Aeneas each explain what Aeneas sees. You pass when each tangent meets its curve at one point on a redrawing, and your comparison points to a passage you can reopen.

On the site: Geometry: Apollonius' Conic Sections

Music Grammar

Seminar

• Virgil, Aeneid: Book 7

Tutorial: Music

Chant: the modes heard and sung. Sing one chant from the selected chants each day for a week, and note each chant's mode.

• Not named in the source, Gregorian chant: selected chants

Acts

Examine the reasons, Express it truly

Pass when: Sing three chants from the selections aloud, naming the mode of each and the reason you give for it. Then write 250 words on the origin of the conflict in Aeneid Book 7, reconstructing how the poem explains it, and compare that explanation with the one a second text gives. Name the strongest objection to one explanation. You pass when a listener can follow each sung mode name, and your comparison points to passages you can reopen.

On the site: Guitar Tools: Tuner, Metronome, Drone, Fretboard

Grammar Rhetoric

Seminar

• Virgil, Aeneid: Book 8

Tutorial: Language

Greek: the Psalms in the Septuagint. Read two psalms aloud in Greek, translate the first verse of each, and mark every verb form and its tense.

• The Septuagint, Selections: selected Psalms, in Greek

Acts

Understand exactly, Examine the reasons

Pass when: Translate the first verse of each of two psalms in the Septuagint's Greek into English, and mark every verb form with its tense. Then write 250 words on the shield in Aeneid Book 8, reconstructing the scenes it shows, and compare how the shield and one psalm each present a people's past. Name the strongest objection to one reading. You pass when your translations can be set beside the Greek and each marked verb is explained, and your comparison points to a passage you can find again.

Rhetoric Logic

Seminar

• Virgil, Aeneid: Book 9

Tutorial: Writing and speaking

Writing: a dialogue in which two readers of Plato disagree. Write 600 words of dialogue between two readers who disagree about one passage, with each speaker's strongest point stated.

Acts

Express it truly, Examine the reasons

Pass when: Write a 600-word dialogue between two readers of Plato who disagree about one passage, giving each the strongest argument the text allows. Then write 200 words on one episode in Aeneid Book 9, reconstructing how the scene turns, and compare how Virgil and Plato each present a dispute between speakers. Name the strongest objection to one reading. You pass when a reader can tell which speaker holds which position on a reread, and your account of Book 9 can be checked against the text.

On the site: The Academy: Proofs, Definitions and the Method of Reason

Geometry Arithmetic Logic

Seminar

• Virgil, Aeneid: Book 10

Tutorial: Mathematics

Apollonius: asymptotes and the focal properties. Draw a hyperbola with its asymptotes, and mark the foci and the lines from each focus to a point on the curve.

• Apollonius, Conics: Books 2-3, selections

Acts

Check it against evidence, Examine the reasons

Pass when: Draw a hyperbola with its asymptotes and foci, measure the distances from the foci to three points on the curve, and calculate the difference for each point, showing your arithmetic. Then write 250 words on one speech in Aeneid Book 10, reconstructing its argument and comparing it with a speech by a different speaker on the same question. Name the strongest objection to one speech. You pass when your three differences agree with one another within the error of your drawing, and your objection names a step in the speech.

On the site: Geometry: Apollonius' Conic Sections

Music Rhetoric

Seminar

• Virgil, Aeneid: Book 11

Tutorial: Music

Chant: text and melody. Choose one chant, sing it with its text once a day for a week, and mark how many notes fall on each syllable.

• Not named in the source, Gregorian chant: further chants

Acts

Express it truly, Examine the reasons

Pass when: Sing one chant from the selections with its text, marking each syllable with its note count, and write 150 words on how the melody serves the words. Then write 250 words on the speeches of Aeneid Book 11, reconstructing one speaker's argument and comparing it with a second speaker's on the same question. You pass when a listener can follow each syllable against your marks, and your comparison can be checked against the two speeches on reopening.

On the site: Guitar Tools: Tuner, Metronome, Drone, Fretboard

Logic Rhetoric

Seminar

• Virgil, Aeneid: Book 12

Tutorial: Evidence and inquiry

Causal inference: randomised experiments. Read the chapter's part on randomised experiments, then write a two-group example of your own and say what the randomisation protects against.

• Miguel Hernán and James Robins, Causal Inference: What If: Part 1, randomised experiments

Acts

Examine the reasons, Express it truly

Pass when: Write a two-group example of a randomised experiment with a stated outcome, and explain in 150 words what random assignment rules out and what it cannot rule out. Then write 250 words on the final choice in Aeneid Book 12, reconstructing it, and compare how Virgil and one other text you have read present a decisive act in war. State the strongest objection to a reading of the choice. You pass when a reader can name the confounder your design blocks, and your objection points to a line you can reopen.

On the site: Hypotheses, Predictions and Tests

Grammar Logic

Seminar

• Hebrew Bible, Genesis: chapters 1-11

Tutorial: Language

Greek: the prologue of John. Read the prologue aloud in Greek, then translate its opening verses into English, marking each word that differs between two English versions.

• The Greek New Testament, Selections: John 1, in Greek

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Translate the prologue of John from Greek into English, and compare your translation with two English versions, noting each word where they differ and why. Then write 300 words on Genesis 1 to 11, reconstructing how those chapters arrange the first events of the world, and compare two readings of one passage, naming the strongest objection to each. You pass when your translation can be set beside the Greek and each difference is explained by a word you chose, and your readings can be checked against the chapters on reopening.

Geometry Logic

Seminar

• Hebrew Bible, Genesis: chapters 12-25

Tutorial: Mathematics

The conic sections constructed: draw each curve from its defining property. Draw each curve on squared paper, then state the defining property you used for it.

Acts

Check it against evidence, Examine the reasons

Pass when: Draw a parabola, an ellipse and a hyperbola from their defining properties on squared paper, label each part, and write each property in one sentence beside its curve. Then write 250 words on the call of Abraham in Genesis 12 to 25, reconstructing the promise as the chapters state it, and compare two readings of one scene, naming the strongest objection to each. You pass when every drawn curve matches its property on a redraw, and your readings can be checked against the chapters on reopening.

On the site: Geometry: Apollonius' Conic Sections

Music Rhetoric

Seminar

• Hebrew Bible, Genesis: chapters 26-36

Tutorial: Music

Melody: write and sing a short melody in one mode. Write eight bars in one mode, sing them aloud three times, and mark where the melody reaches its final note.

Acts

Express it truly, Examine the reasons

Pass when: Write and sing a melody of eight bars in one mode, marking its final note and its reciting note, and explain each choice in 100 words. Then write 250 words on the narratives of Jacob in Genesis 26 to 36, reconstructing one episode and comparing how the narrator presents two characters in it. You pass when a listener can sing your melody back to you, and your comparison points to words in the chapters you can reopen.

On the site: Guitar Tools: Tuner, Metronome, Drone, Fretboard

Grammar Logic

Seminar

• Hebrew Bible, Genesis: chapters 37-50

Tutorial: Language

Greek: the Sermon on the Mount. Read the opening of the Sermon aloud in Greek, translating each verse as you go.

• The Greek New Testament, Selections: the Sermon on the Mount, in Greek

Acts

Understand exactly, Examine the reasons

Pass when: Translate the opening of the Sermon on the Mount from Greek into English, then compare your translation with two English versions and record each word where they differ. Then write 300 words on Joseph's story in Genesis 37 to 50, reconstructing its sequence and comparing one scene with a saying in the Sermon, naming the strongest objection to one reading. You pass when your translation can be set beside the Greek, and your objection points to a passage you can reopen.

Logic Grammar

Seminar

• Hebrew Bible, Exodus: chapters 1-20

Tutorial: Evidence and inquiry

Causal inference: observational studies and their assumptions. Read the chapter's part on observational studies, then list three assumptions each such study must make and test one of them with a data table.

• Miguel Hernán and James Robins, Causal Inference: What If: Part 1, observational studies

Acts

Check it against evidence, Examine the reasons

Pass when: List three assumptions an observational study of one question must make, and for each state a check you could run with the data in the chapter. Then write 250 words on the narrative of Exodus 1 to 20, reconstructing its sequence, and compare two explanations the text gives for one event, stating the strongest objection to each. You pass when each assumption you listed can be found in the chapter on reopening, and your comparison points to passages you can find again.

Grammar Logic

Seminar

• Hebrew Bible, Exodus: chapters 21-40

Tutorial: Language

Greek: Paul's argument in Romans. Read Romans 5 to 8 aloud in Greek, and translate one paragraph of Paul's argument each day, marking the connecting words.

• The Greek New Testament, Selections: Romans 5-8, selections, in Greek

Acts

Understand exactly, Examine the reasons

Pass when: Translate one paragraph of Romans 5 to 8 from the Greek into English, and mark each connecting word, such as those that signal an inference or an objection. Then write 300 words on how Exodus 21 to 40 arranges law, instruction and building, reconstructing that order, and state the strongest objection to one reading of it. You pass when your translation can be set beside the Greek with each connecting word explained, and your objection can be checked against the chapters on reopening.

Astronomy Logic Rhetoric

Seminar

• Hebrew Bible, Deuteronomy: chapters 1-11

Tutorial: Mathematics

Copernicus: the case for a moving Earth. Read the preface and Book 1 slowly, and write the case for a moving Earth in five numbered steps.

• Copernicus, On the Revolutions of the Heavenly Spheres: the preface and Book 1

Acts

Understand exactly, Examine the reasons

Pass when: Write the case for a moving Earth in five numbered steps, each with the reason Copernicus gives for it. Then write 250 words on the speeches of Moses in Deuteronomy 1 to 11, reconstructing the argument of the first speech, and compare it with Copernicus's way of arguing for a moving Earth. State the strongest objection to one of the two. You pass when a reader can check each of your five steps against the preface or Book 1 on reopening, and your objection names a step in the speech.

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

Music Logic

Seminar

• Hebrew Bible, Deuteronomy: chapters 12-34

Tutorial: Music

Counterpoint: first species, note against note. Write four exercises of eight bars each, one note against each note of a given line, and check each interval against the rules in your textbook.

Acts

Check it against evidence, Examine the reasons

Pass when: Write a first-species counterpoint exercise against a given line of at least eight notes, and mark each interval with its name. Then write 250 words on the law as Deuteronomy 12 to 34 presents it, reconstructing one commandment, and compare its purpose with the purpose of one rule in your exercise. State the strongest objection to a reading of its purpose. You pass when a singer can sing your two lines together, each interval you named matches the sound, and your objection points to a passage you can reopen.

On the site: Guitar Tools: Tuner, Metronome, Drone, Fretboard

Grammar Logic

Seminar

• Hebrew Bible, Samuel: 1 Samuel, selections

Tutorial: Language

Greek: 1 Corinthians 13. Translate the chapter in three sittings, reading it aloud in Greek before each.

• The Greek New Testament, Selections: 1 Corinthians 13, in Greek

Acts

Understand exactly, Examine the reasons

Pass when: Translate 1 Corinthians 13 from the Greek into English, and mark every word where two English versions differ from your translation. Then write 250 words on the rise of David in the 1 Samuel selections, reconstructing one episode, and compare how the narrator presents Saul and David in it, naming one passage from each. You pass when your translation can be set beside the Greek, and your comparison points to words in the episode you can reopen.

Astronomy Arithmetic Grammar

Seminar

• Hebrew Bible, Samuel: 2 Samuel, selections

Tutorial: Mathematics

Copernicus: the order and distances of the planets. Copy Copernicus's order of the planets from Book 1 into a table, with the reason he gives for each step.

• Copernicus, On the Revolutions of the Heavenly Spheres: Book 1, the order of the planets

Acts

Check it against evidence, Examine the reasons

Pass when: Make a table of the planets in Copernicus's order, with the reason given in Book 1 for each place, and calculate the ratio of two of the figures for the planets (periods or distances) that the Book 1 passage gives, showing each step; if it gives none, use two figures from a published table and name it. Then write 250 words on one episode in the 2 Samuel selections, reconstructing it, and compare how that episode and one account in Copernicus each justify a decision. State the strongest objection to one reading. You pass when your table matches Book 1 on reopening and your ratio can be redone with the same result.

On the site: Astronomy: Seasons, Moon, Earth and Orbits

Music Logic

Seminar

• Hebrew Bible, Kings: 1 Kings, selections

Tutorial: Music

Counterpoint: second and third species. Write one exercise in second species and one in third, eight bars each, and mark the dissonances.

Acts

Check it against evidence, Examine the reasons

Pass when: Write one second-species and one third-species counterpoint exercise, eight bars each, marking every dissonance and the rule that allows it. Then write 250 words on the reign of Solomon in the 1 Kings selections, reconstructing its account of wisdom, and state the strongest objection to one reading of it. You pass when a singer can perform both lines, and every dissonance you marked is allowed by the rule you named.

On the site: Guitar Tools: Tuner, Metronome, Drone, Fretboard

Arithmetic Logic

Seminar

• Hebrew Bible, Kings: 2 Kings, selections

Tutorial: Evidence and inquiry

Causal inference: when effects differ between groups. Read the chapter's section on interaction, then write two small tables of results for two groups and say whether the effect differs.

• Miguel Hernán and James Robins, Causal Inference: What If: Part 1, effect modification and interaction

Acts

Check it against evidence, Examine the reasons

Pass when: Write two small tables of results for two groups, one where the effect is the same in both and one where it differs, and calculate the effect in each group. Then write 250 words on one prophet's message in the 2 Kings selections, reconstructing its warning, and compare it with a warning in one other text you have read. State the strongest objection to a reading that treats the warning as a prediction only. You pass when your tables can be redone with the same effects, and your objection names a claim the warning depends on.

On the site: Hypotheses, Predictions and Tests

Grammar Logic

Seminar

• Hebrew Bible, Chronicles: selections

Tutorial: Language

Greek: biblical Greek and Attic Greek compared. Choose three forms that differ between a Septuagint passage and an Attic prose passage, and list them with the difference each shows.

Acts

Understand exactly, Examine the reasons

Pass when: Compare three grammatical forms in a Septuagint passage with the same constructions in an Attic prose passage, and translate one sentence from each. Then write 250 words on the account of kingship in the Chronicles selections, comparing it with the account in Samuel or Kings on one point. Say which reading you find more convincing and why, naming the passage that decides it. You pass when your three comparisons can be checked against both Greek passages, and your reasons point to words you can find again.

Rhetoric Grammar

Seminar

• Hebrew Bible, Psalms: Psalms 1-41

Tutorial: Writing and speaking

Writing: a speech for an occasion, in Cicero's arrangement. Write a speech of about 800 words for an occasion you choose, following the parts of the arrangement in order.

Acts

Express it truly, Examine the reasons

Pass when: Write a speech of about 800 words for an occasion you choose, arranged in the order of the classical parts of a speech as your rhetoric text lists them (for example introduction, statement of the case, proof, reply to objections and conclusion), and label each part in the margin. Then write 250 words on one lament or song of praise in Psalms 1 to 41, reconstructing how the psalm moves between its parts, and compare its movement with your speech's structure. You pass when a listener can name each part of your speech in order, and your comparison points to lines in the psalm you can reopen.

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

Astronomy Geometry Grammar

Seminar

• Hebrew Bible, Psalms: selections from Psalms 42-150

Tutorial: Mathematics

Copernicus: his models compared with Ptolemy's. Draw one of Ptolemy's models and one of Copernicus's for the same planet, and write three lines comparing what each predicts.

• Copernicus, On the Revolutions of the Heavenly Spheres: Books 3-5, selections

Acts

Examine the reasons, Check it against evidence

Pass when: Draw Ptolemy's model and Copernicus's model for the same planet, and write three sentences on what each predicts about that planet's motion. Then write 250 words on one psalm from the selections, reconstructing its movement from complaint or praise to its conclusion, and compare it with one other psalm on the same theme. You pass when your drawings can be checked against the books on reopening, and your comparison names the words that link the two psalms.

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

Music Rhetoric

Seminar

• Hebrew Bible, Jeremiah: chapters 1-20

Tutorial: Music

Palestrina: setting many words clearly. Follow the score of the Gloria and the Credo, marking where each phrase of the text is set, and sing one passage of each.

• Palestrina, Missa Papae Marcelli: the Gloria and Credo

Acts

Understand exactly, Express it truly

Pass when: Mark in the score of the Gloria or the Credo where each phrase of the text begins, and sing one passage aloud so the words can be heard. Then write 250 words on the calls of Jeremiah in chapters 1 to 20, reconstructing one call or complaint, and compare the prophet's complaint with a lament in the Psalms on a similar grievance. You pass when a listener can follow the text in the score by your marks, and your comparison points to passages you can reopen.

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

Grammar Logic

Seminar

• Hebrew Bible, Jeremiah: chapters 21-52, selections

Tutorial: Language

Greek: philosophical prose, Aristotle on nature. Translate one short passage of Book 2 from Greek each day for a week, and make a glossary of its key terms.

• Aristotle, Physics: a passage from Book 2, in Greek

Acts

Understand exactly, Examine the reasons

Pass when: Translate a short passage from Book 2 of the Physics from Greek into English, and make a glossary of three key terms, giving the meaning you chose for each and why. Then write 250 words on the oracles of judgment in the Jeremiah 21 to 52 selections, comparing how the prophet addresses the king with how he addresses the people, and state the strongest objection to one reading. You pass when your translation can be set beside the Greek, and each glossary entry is backed by a word in the passage.

Grammar Logic

Seminar

• Hebrew Bible, Jonah: the whole book

Tutorial: Evidence and inquiry

Modern biology: the cell. Read the cell chapters, then draw a labelled cell from memory and check the labels against the book, once each day for a week.

• OpenStax, Biology 2e: the chapters on the cell

Acts

Check it against evidence, Understand exactly

Pass when: Draw a labelled animal cell and a plant cell from memory after reading the chapter, naming each part and its function in one line, then check the drawings against the book. Then write 250 words on Jonah as a whole book, reconstructing its plot, and compare two readings of its closing scene, naming the strongest objection to each. You pass when your labels match the book on a second check, and your readings can be compared at the book's final scene.

Astronomy Logic

Seminar

• Hebrew Bible, Job: chapters 1-21

Tutorial: Mathematics

Geocentric and heliocentric: what each explains, and which observations could have decided between them in 1543. List three observations for each model in a table, then state which observation, if any, could have decided between them by 1543, and why.

Acts

Check it against evidence, Examine the reasons

Pass when: Make a table with two columns, geocentric and heliocentric, listing what each model explains and which observation, if any, could have decided between them by 1543. Then write 250 words on Job's argument in chapters 1 to 21, reconstructing the friends' position and Job's reply, and state the strongest objection to one of the friends' claims. You pass when your table can be checked against the models on reopening, and your objection names a claim the friends make.

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

Music Rhetoric

Seminar

• Hebrew Bible, Job: chapters 22-42

Tutorial: Music

Palestrina: imitation and cadence. Mark each place where voices imitate one another and each cadence in the Sanctus and Agnus Dei, then sing one section with the score open.

• Palestrina, Missa Papae Marcelli: the Sanctus and Agnus Dei

Acts

Understand exactly, Express it truly

Pass when: Mark in the score of the Sanctus or the Agnus Dei each imitation and each cadence, and sing one section with a partner, or alone with one part at a time. Then write 250 words on the speeches of God in Job 22 to 42, reconstructing the argument of the final speeches, and compare them with Job's demand. You pass when a listener can hear each imitation you marked, and your comparison names a line of each speech you can reopen.

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

Grammar Rhetoric

Seminar

• New Testament, Matthew: chapters 1-9

Tutorial: Language

Greek: sight translation, a page a sitting. Read one page of Matthew 1 to 9 aloud at sight, translating as you go, then check your version against a printed English translation.

Acts

Understand exactly, Express it truly

Pass when: Sight translate one page of Matthew 1 to 9 from the Greek into English aloud, without preparing it, then check your version against a printed English translation and list each place you chose differently. Then write 250 words on the narrative of Matthew 1 to 9, reconstructing the sequence of its scenes and comparing two scenes on one question. You pass when your sight translation can be read aloud beside the Greek, and your comparison points to verses you can reopen.

Grammar Logic

Seminar

• New Testament, Matthew: chapters 10-18

Tutorial: Language

Greek: the verb reviewed from memory. Write out the present, imperfect and aorist of one regular verb from memory, then check each form against your grammar and correct the errors.

Acts

Understand exactly, Examine the reasons

Pass when: Write from memory the present, imperfect and aorist of one regular verb, check every form against your grammar, and mark each error you corrected. Then translate one parable from Matthew 10 to 18 into English, and write 250 words comparing two readings of the parable's point, naming the strongest objection to one reading. You pass when your paradigm matches the grammar on a second check, and your objection points to a verse you can reopen.

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

Astronomy Logic

Seminar

• New Testament, Matthew: chapters 19-28

Tutorial: Mathematics

Kepler: the physical causes of the motions. Read the Introduction, and write one paragraph naming each cause Kepler proposes for planetary motion, with the reason he gives.

• Kepler, Astronomia Nova: the Introduction

Acts

Check it against evidence, Examine the reasons

Pass when: List each physical cause Kepler proposes for planetary motion in the Introduction, with the reason he gives for it, and say in 100 words which cause you find weakest and why. Then write 250 words on the journey to Jerusalem and the Passion in Matthew 19 to 28, reconstructing its order of events, and compare two readings of one episode in these chapters, naming the words that decide between them. You pass when every cause you list matches the Introduction on reopening, and your comparison points to words in the episodes you can find again.

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

Music Rhetoric

Seminar

• New Testament, John: chapters 1-10

Tutorial: Music

Monteverdi: the beginning of opera. Listen to Acts 1 and 2 with the score open, and mark each change between speech-like singing and song.

• Monteverdi, L’Orfeo: Acts 1-2

Acts

Understand exactly, Express it truly

Pass when: Mark in the score of Acts 1 and 2 each change between speech-like singing and song, and sing one passage aloud, explaining what the change does to the words. Then write 250 words on the signs in John 1 to 10, reconstructing the argument of one sign, and compare its meaning in two chapters. State the strongest objection to a reading. You pass when a listener can hear the changes you marked, and your comparison names a word in each chapter.

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

Arithmetic Grammar

Seminar

• New Testament, John: chapters 11-21

Tutorial: Evidence and inquiry

Modern biology: genes and inheritance. Work through the chapter's crosses for two traits, and calculate the expected ratios, showing each step.

• OpenStax, Biology 2e: the chapters on genetics

Acts

Check it against evidence, Examine the reasons

Pass when: Work two genetic crosses for two traits, calculate the expected ratios, and explain in 100 words why an observed count may differ from the expected ratio. Then write 250 words on the narrative of the Passion and resurrection in John 11 to 21, reconstructing one scene, and compare how John presents it with another gospel's account of the same event. Name the strongest objection to one reading. You pass when your ratios can be redone from your working, and your comparison points to verses you can reopen.

Grammar Rhetoric

Seminar

• New Testament, 1 John: the whole letter

Tutorial: Language

Greek: a translation with a commentary on one disputed phrase. Choose one phrase in the letter that English versions translate differently, and write a short commentary on the choice.

Acts

Understand exactly, Express it truly

Pass when: Translate the first chapter of the letter from Greek into English in a draft, then write a commentary of 300 words on one phrase that English versions translate in different ways, giving the options and the reason for your choice. Then write 200 words reconstructing the letter's main argument, and state the strongest objection to one reading of a key phrase in it. You pass when your draft can be set beside the Greek, and your commentary names both English options and the word that decides between them.

Arithmetic Astronomy Grammar

Seminar

• New Testament, Acts: chapters 1-14

Tutorial: Mathematics

Kepler: the vicarious hypothesis and the eight minutes of arc. Read the selection, and calculate the difference between the two positions in arc minutes for one example, showing each step.

• Kepler, Astronomia Nova: Part 2, selections

Acts

Check it against evidence, Examine the reasons

Pass when: Work through one calculation of the difference between the observed and predicted positions of the planet in the selection, in arc minutes, showing each step, and state in 100 words what the difference allowed Kepler to conclude. Then write 250 words on the mission of Paul and Barnabas in Acts 1 to 14, reconstructing one journey, and compare two accounts of one event in these chapters. Name the strongest objection to one reading. You pass when your arithmetic can be redone with the same answer, and your comparison points to passages you can reopen.

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

Music Rhetoric

Seminar

• New Testament, Acts: chapters 15-28

Tutorial: Music

Monteverdi: music that persuades. Listen to Acts 3 to 5 with the score, and mark two places where the music follows the words closely.

• Monteverdi, L’Orfeo: Acts 3-5

Acts

Express it truly, Examine the reasons

Pass when: Mark two places in the score of Acts 3 to 5 where the music follows the words closely, and sing one of them aloud. Then write 250 words on Paul's speeches in Acts 15 to 28, reconstructing one speech and comparing two of Paul's arguments on one question. You pass when a listener can hear the two places you marked, and your comparison points to lines you can reopen.

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

Grammar Logic

Seminar

• New Testament, Romans: chapters 1-8

Tutorial: Language

Greek and English expression compared: what each translation decides for you. Compare three English versions of one passage with the Greek, and list each decision each version makes.

Acts

Understand exactly, Examine the reasons

Pass when: Compare three English translations of one passage from Romans 1 to 8 with the Greek, and list each decision each translation makes for the reader, such as a tense, a pronoun or a connecting word. Then write 250 words on Paul's argument in those chapters, reconstructing one step, and state the strongest objection to a reading that depends on a disputed translation. You pass when your list can be checked against the Greek, and each decision points to a word you can reopen.

Rhetoric Logic

Seminar

• New Testament, Romans: chapters 9-16

Tutorial: Writing and speaking

Writing: revision for a reader, making one essay clear to a newcomer. Choose one short essay you wrote and revise it for a reader who has never studied the topic, in three drafts.

Acts

Express it truly, Examine the reasons

Pass when: Revise one essay of 500 words for a reader who has not studied the topic, in three drafts, and mark each change with the reason it helps that reader. Then write 250 words on one argument in Romans 9 to 16, reconstructing it for a newcomer and naming the strongest objection to it. You pass when a newcomer, reading the final draft alone, can state the essay's claim and one objection, and your summary of the argument matches Romans 9 to 16 on reopening.

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

Grammar Logic Arithmetic

Seminar

• New Testament, 1 Corinthians: the whole letter

Tutorial: Evidence and inquiry

Modern biology: the mechanisms of evolution. Work through the chapter's examples of selection, one with a table of numbers and one in words.

• OpenStax, Biology 2e: the chapters on evolution

Acts

Check it against evidence, Examine the reasons

Pass when: Work two examples of natural selection from the chapter, one with a table of numbers and one in words, and say what each example does and does not show about how a trait spreads. Then write 250 words on one theme in 1 Corinthians, reconstructing the letter's argument on that theme and comparing two passages that address it. You pass when your two examples can be checked against the chapter on reopening, and your comparison points to passages in the letter you can find again.

Geometry Arithmetic Grammar

Seminar

• Augustine, Confessions: Books 1-3

Tutorial: Mathematics

Kepler: the ellipse found. Read the selection on the ellipse and draw the orbit it describes for one planet, checking each point against the numbers in the selection.

• Kepler, Astronomia Nova: Part 4, selections

Acts

Check it against evidence, Understand exactly

Pass when: Draw an ellipse with its foci from Kepler's selection, mark the sun's position at one focus, and check two distances from the foci against the numbers the selection gives, showing your arithmetic. Then write 250 words on one scene in Confessions Books 1 to 3, reconstructing its argument, and compare it with a passage on learning from another text you have read. State the strongest objection to one reading. You pass when your drawing and arithmetic can be redone with the same results, and your comparison can be checked against the texts on reopening.

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

Music Rhetoric

Seminar

• Augustine, Confessions: Books 4-6

Tutorial: Music

Bach: two-part inventions followed in the score. Follow three inventions in the score, marking each subject where it enters, once a day for a week.

• J. S. Bach, Inventions: three more inventions

Acts

Express it truly, Examine the reasons

Pass when: Mark in the score of three two-part inventions each entry of the subject, and sing or play one invention's two voices. Then write 250 words on the episodes Augustine narrates in Confessions Books 4 to 6, reconstructing one of them, and compare how Augustine and one other writer you have read present a loss. State the strongest objection to one reading. You pass when a listener can hear your marked entries, and your comparison names a passage in each text you can find again.

Grammar Rhetoric

Seminar

• Augustine, Confessions: Books 7-9

Tutorial: Language

English poetry: reading Chaucer's Middle English aloud. Read the General Prologue aloud, twenty lines a day, and gloss every word you do not know in the margin.

• Geoffrey Chaucer, Canterbury Tales: the General Prologue, in Middle English

Acts

Understand exactly, Express it truly

Pass when: Read twenty lines of the General Prologue aloud in Middle English, glossing each word you cannot read, and translate them into modern English. Then write 250 words on Augustine's account of his search in Confessions Books 7 to 9, reconstructing one step, and compare what Book 7 says about the cause of evil with what Book 8 says about the divided will. You pass when a listener can follow your reading of the twenty lines, and your translation matches the Middle English on reopening.

Astronomy Arithmetic Grammar

Seminar

• Augustine, Confessions: Book 10

Tutorial: Mathematics

Kepler's laws checked against planetary data. Take a table of planetary data from a source the site links, and test each of the laws against it.

Acts

Check it against evidence, Examine the reasons

Pass when: Test one of Kepler's laws against a table of planetary distances and periods, calculating the ratio for each planet, and state whether the law holds within the accuracy of the table. Then write 250 words on memory in Confessions Book 10, reconstructing how Augustine describes it, and compare his account with one other account of memory you have read. State the strongest objection to one reading. You pass when your ratios can be redone from the table, and your objection names a claim in the book.

On the site: Astronomy: Seasons, Moon, Earth and Orbits

Music Logic

Seminar

• Augustine, Confessions: Books 11-13

Tutorial: Music

Harmony: triads, cadences and the bass. Write a triad on each degree of a major scale, name its bass note, and play the chords in a cadence ending on the tonic.

Acts

Check it against evidence, Examine the reasons

Pass when: Write a triad on each degree of a major scale, name its bass note, and play the chords in a cadence ending on the tonic, naming the cadence type you used. Then write 250 words on the account of time in Confessions Books 11 to 13, reconstructing it, and compare it with one rival view of time that Augustine states in the same books. State the strongest objection to one account. You pass when a listener can hear your cadence, and your objection names a claim the account depends on.

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

Rhetoric Grammar

Seminar

• Augustine, De doctrina christiana: Book 4, on teaching and eloquence

Tutorial: Language

English poetry: the argument of a sonnet sequence. Read ten sonnets in order, and write one sentence for each saying how it moves the argument forward.

• William Shakespeare, Sonnets: a sequence of ten

Acts

Express it truly, Examine the reasons

Pass when: Read ten of Shakespeare's sonnets in order, write one sentence on each stating how it moves the sequence's argument, and then state the argument of the sequence in 150 words. Then write 250 words on Augustine's advice to a teacher on making a point clear and moving a hearer, reconstructing that advice, and compare it with the sonnets' method on one point. You pass when a reader can follow your sentences in order, and your comparison points to a passage in each text you can reopen.

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

Grammar Logic

Seminar

• Hugh of Saint Victor, Didascalicon: A Medieval Guide to the Arts: Books 4-6, on the study of Scripture

Tutorial: Evidence and inquiry

Modern biology: populations and ecosystems. Read the chapters on populations and draw one food web from a local example, labelling each link, then calculate the growth of one population in it with the chapter's method.

• OpenStax, Biology 2e: the chapters on ecology, selections

Acts

Check it against evidence, Examine the reasons

Pass when: Draw a food web for one ecosystem described in the chapters, label each link, and calculate the growth of one population in it, showing each step. Then write 250 words on Hugh's advice on studying Scripture in Didascalicon Books 4 to 6, reconstructing his method, and compare it with a modern method of reading a source. State the strongest objection to one method. You pass when your food web can be checked against the chapter, and your comparison names a step in each method.

Grammar Logic

Seminar

• Anselm, Proslogion: the whole work

Tutorial: Language

English poetry: Anne Locke. Read the selected poems aloud, and mark the metre in one poem, stanza by stanza.

• Anne Locke, Selected writings: selected poems

Acts

Examine the reasons, Express it truly

Pass when: Read one of Anne Locke's selected poems aloud, mark its metre and rhyme in a stanza, and explain in 100 words how the form shapes its argument. Then write 250 words reconstructing the main step of Anselm's Proslogion, stating the strongest objection to it, and comparing how the poem and the argument each reason toward a conclusion. You pass when a listener can follow your metre marks, and your objection names a premise you can point to.

Arithmetic Logic Grammar

Seminar

• Maimonides, Guide of the Perplexed: Part 1, selections on the names and attributes of God

Tutorial: Mathematics

Viète: letters for magnitudes, and the analytic art. Use letters for the unknown and known quantities in three problems of your own, write each as an equation, solve one, and show each step.

• Viète, Introduction to the Analytical Art: selections, a variable selection

Acts

Check it against evidence, Examine the reasons

Pass when: Use letters for the unknown and known quantities in three problems of your own, write each as an equation, solve one, and show each step. Then write 250 words on the names and attributes of God in Maimonides' Guide, Part 1 selections, reconstructing his method of speaking about attributes, and state the strongest objection to it. You pass when your algebra can be redone from your letters, and your objection names a term the method uses.

Music Logic

Seminar

• Maimonides, Guide of the Perplexed: Part 3, selections on providence and evil

Tutorial: Music

Harmony: a four-part chorale analysed. Analyse one four-part chorale, naming the chord on each beat.

Acts

Check it against evidence, Examine the reasons

Pass when: Name the chord on each beat of one four-part chorale, and analyse its cadences in writing, using the terms you have learned. Then write 250 words on providence and evil in the Part 3 selections of Maimonides' Guide, reconstructing his answer to one question about evil, and compare that answer with one answer in another text you have read. State the strongest objection to one of them. You pass when a listener can match your chord names to the chorale's sound, and your objection names a premise in the answer.

Grammar Logic

Seminar

• Thomas Aquinas, Summa Theologiae: First Part: God's existence and attributes, selections

Tutorial: Language

English poetry: Mary Wroth's crown of sonnets. Read the crown of sonnets in order, and write one line summarising each sonnet's turn.

• Lady Mary Wroth, A Crown of Sonnets Dedicated to Love: the crown of sonnets

Acts

Understand exactly, Examine the reasons

Pass when: Read the crown of sonnets in order and write one line on each sonnet's turn, then write a summary of the sequence's argument in 150 words. Then write 250 words on God's existence and attributes in the First Part selections, reconstructing one argument, and compare it with how one sonnet reasons toward its close. State the strongest objection to one of them. You pass when a reader can follow your one-line summaries against the sonnets, and your objection names a premise in the argument.

Logic Grammar

Seminar

• Thomas Aquinas, Summa Theologiae: First Part: creation and providence, selections

Tutorial: Evidence and inquiry

Psychology: how claims about the mind are tested. Read the research methods chapter, and list the steps a study takes from question to conclusion.

• OpenStax, Psychology 2e: the chapter on research methods

Acts

Check it against evidence, Examine the reasons

Pass when: Write the steps a study takes from question to conclusion, and apply them to one claim about the mind, naming the measure and the comparison you would use. Then write 250 words on creation and providence in the First Part selections of Aquinas, reconstructing the argument on one of these, and compare it with the way a modern study would test a similar claim. State the strongest objection to it. You pass when your study design can be checked against the chapter's steps, and your objection names a premise of the argument.

On the site: Hypotheses, Predictions and Tests

Geometry Logic

Seminar

• Thomas Aquinas, Summa Theologiae: First Part of the Second Part: happiness and human acts, selections

Tutorial: Mathematics

Pascal: a theorem on conics. Study the theorem in the essay, draw the figure, and state the theorem in your own words.

• Blaise Pascal, Work on conic sections: the essay on conics, a variable selection

Acts

Understand exactly, Examine the reasons

Pass when: Draw the figure for a theorem on conics from Pascal's essay, label each point, and state the theorem in your own words with its hypotheses. Then write 250 words on happiness and human acts in the First Part of the Second Part selections, reconstructing Aquinas's account of what makes an act good, and state the strongest objection to it. You pass when your figure matches the labels in the essay, and your objection names a premise of the account.

On the site: Geometry: Apollonius' Conic Sections

Music Logic

Seminar

• Thomas Aquinas, Summa Theologiae: First Part of the Second Part: law, selections

Tutorial: Music

Bach: the St Matthew Passion, Part 1. Listen to Part 1 with the score, and mark each recitative, aria and chorale.

• J. S. Bach, St. Matthew Passion: Part 1

Acts

Express it truly, Examine the reasons

Pass when: Mark each recitative, aria and chorale in Part 1 of the St Matthew Passion, and sing one chorale with the score open. Then write 250 words on law in the First Part of the Second Part selections, reconstructing Aquinas's account of the kinds of law, and state the strongest objection to one kind. You pass when a listener can match your marks to the sound, and your objection names a premise in the account.

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

Logic Rhetoric

Seminar

• Thomas Aquinas, Summa Theologiae: Second Part of the Second Part: faith and the virtues, selections

Tutorial: Language

English poetry: Donne's argument in verse. Read the selected poems, including the Holy Sonnets, and mark each argument's first premise and its conclusion.

• John Donne, Selected writings: selected poems, including the Holy Sonnets

Acts

Examine the reasons, Express it truly

Pass when: Read three of Donne's selected poems, including one of the Holy Sonnets, and for each write its argument as a premise and a conclusion. Then write 250 words on faith and the virtues in the Second Part of the Second Part selections, reconstructing one distinction, and compare how Aquinas and one of Donne's poems each reason toward a conclusion. State the strongest objection to one of them. You pass when your premise and conclusion for each poem can be found on reopening, and your objection names a term in the distinction.

Rhetoric Grammar

Seminar

• Dante, Inferno: Cantos 1-9

Tutorial: Writing and speaking

Writing: a review of a book read this year. Choose a book you read this year, and write a 400-word review that states its claim, judges one argument, and gives the evidence for the judgment.

Acts

Express it truly, Examine the reasons

Pass when: Write a 400-word review of a book you read this year, stating its claim, judging one argument, and giving the evidence for your judgment. Then write 250 words on the journey in Inferno Cantos 1 to 9, reconstructing its first stage, and compare two encounters in these cantos on one question. You pass when a reader can state the review's claim and one reason for it, and your comparison points to lines in the cantos you can reopen.

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

Arithmetic Geometry Astronomy

Seminar

• Dante, Inferno: Cantos 10-17

Tutorial: Mathematics

Spherical trigonometry problems: rising times and the length of the day. Work two problems of your own for a latitude you choose, showing each step.

Acts

Check it against evidence, Examine the reasons

Pass when: Work two spherical trigonometry problems on rising time and day length for a latitude you choose, showing each step and checking each answer against a table or a second method. Then write 250 words on the sinners and their punishments in Inferno Cantos 10 to 17, reconstructing the sequence, and compare two scenes on one principle. State the strongest objection to one reading. You pass when both answers can be redone with the same result, and your comparison points to lines you can reopen.

On the site: Astronomy: Seasons, Moon, Earth and Orbits

Music Rhetoric

Seminar

• Dante, Inferno: Cantos 18-26

Tutorial: Music

Bach: the St Matthew Passion, Part 2. Follow Part 2 with the score, marking each chorale and aria, and sing one chorale.

• J. S. Bach, St. Matthew Passion: Part 2

Acts

Express it truly, Examine the reasons

Pass when: Mark each chorale and aria in Part 2 of the St Matthew Passion, and sing one chorale with the score open. Then write 250 words on the episodes in Inferno Cantos 18 to 26, reconstructing one of them, and compare two speakers' accounts of what they did. State the strongest objection to one reading. You pass when a listener can match your marks to Part 2, and your comparison points to lines you can reopen.

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

Grammar Logic

Seminar

• Dante, Inferno: Cantos 27-34

Tutorial: Evidence and inquiry

Psychology: perception and learning. Read the chapter's sections on sensation, perception and learning, and write one example of each from everyday life.

• OpenStax, Psychology 2e: the chapters on sensation, perception and learning

Acts

Understand exactly, Check it against evidence

Pass when: Write one example each of sensation, perception and learning from everyday life, and say what observation would tell them apart. Then write 250 words on the closing cantos of Inferno, Cantos 27 to 34, reconstructing the sequence of scenes, and compare two speakers on the same question. State the strongest objection to one reading. You pass when your three examples can be checked against the chapter's definitions, and your comparison points to lines you can find again.

Grammar Rhetoric

Seminar

• Dante, Purgatorio: Cantos 1-9

Tutorial: Language

English poetry: Marvell. Read three of the selected poems aloud, and state the argument of each in one line.

• Andrew Marvell, Selected writings: selected poems

Acts

Understand exactly, Express it truly

Pass when: Read three of Marvell's selected poems aloud, and state each poem's argument in one line, marking one place where its tone changes. Then write 250 words on the opening of Purgatorio, Cantos 1 to 9, reconstructing the movement from one stage to the next, and compare one image in these cantos with one in a Marvell poem you read. You pass when a listener can follow your one-line arguments, and your comparison points to lines you can reopen.

Arithmetic Geometry Grammar

Seminar

• Dante, Purgatorio: Cantos 10-18

Tutorial: Mathematics

Plane and spherical trigonometry reviewed: a problem set. Work twelve problems, six plane and six spherical, checking each answer by a second method.

Acts

Check it against evidence, Examine the reasons

Pass when: Work twelve trigonometry problems, six plane and six spherical, showing each step, and check each answer by a second method. Then write 250 words on the climb in Purgatorio Cantos 10 to 18, reconstructing one scene, and compare it with a scene from Inferno you have read. State the strongest objection to one reading. You pass when a reader can check each answer by the second method, and your comparison points to lines in both cantos you can reopen.

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

Music Grammar

Seminar

• Dante, Purgatorio: Cantos 19-27

Tutorial: Music

Text and setting: how a composer serves the words. Choose one short song or motet, and mark how the setting follows each word and phrase.

Acts

Check it against evidence, Express it truly

Pass when: Mark in one short song or motet how the setting follows each phrase of the text, and sing the marked passage aloud. Then write 250 words on the visions in Purgatorio Cantos 19 to 27, reconstructing their sequence, and compare the poet's treatment of one image across two cantos. State the strongest objection to one reading. You pass when a listener can follow your marks as you sing, and your comparison points to lines you can reopen.

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

Grammar Rhetoric

Seminar

• Dante, Purgatorio: Cantos 28-33

Tutorial: Language

English poetry: Anne Bradstreet. Read the selected poems aloud, and write one paragraph on each poem's central image.

• Anne Bradstreet, Selected writings: selected poems

Acts

Understand exactly, Express it truly

Pass when: Read three of Bradstreet's selected poems aloud, and write one paragraph on each stating its central image and its argument. Then write 250 words on the procession and the final cantos of Purgatorio, Cantos 28 to 33, reconstructing the scene, and compare one image from the poems with one from these cantos. State the strongest objection to one reading. You pass when a reader can follow each paragraph against its poem, and your comparison points to passages you can reopen.

Logic Grammar

Seminar

• Dante, Paradiso: Cantos 1-9

Tutorial: Evidence and inquiry

Psychology: memory and cognition. Read the memory and thinking chapters, and write one test of how a memory is formed.

• OpenStax, Psychology 2e: the chapters on memory and thinking

Acts

Check it against evidence, Examine the reasons

Pass when: Design a simple test of memory with a stated outcome, a comparison group and one confound you would control, and write it out in 150 words. Then write 250 words on the way the poem moves through the heavens in Paradiso, Cantos 1 to 9, reconstructing the poem's account of one heaven, and state the strongest objection to one reading. You pass when your design can be checked against the chapter, and your objection names a claim the reading depends on.

Grammar Rhetoric

Seminar

• Dante, Paradiso: Cantos 10-17

Tutorial: Language

English poetry: Aphra Behn's "The Disappointment". Read the poem aloud twice, and write its argument in ten lines.

• Aphra Behn, The Disappointment: the poem

Acts

Understand exactly, Express it truly

Pass when: Read Behn's poem aloud twice and write its argument in ten lines, marking the point where the speaker's account changes. Then write 250 words on one speech in Paradiso, Cantos 10 to 17, reconstructing its reasoning, and compare its way of reasoning with the poem's. State the strongest objection to one reading. You pass when a listener can follow your marked change in the speaker's account, and your comparison points to lines you can reopen.

Astronomy Grammar Logic

Seminar

• Dante, Paradiso: Cantos 18-26

Tutorial: Mathematics

Comparison and revision of astronomical models: write the history of one revision. Choose one model from the site's astronomy pages, and trace each change from its first version to its revision, in order, in 300 words, and calculate one prediction from each version.

Acts

Check it against evidence, Examine the reasons

Pass when: Trace in 300 words the history of one model of the heavens from its first version to a later revision, naming the observation that prompted each change, and calculate one prediction from each version. Then write 250 words on one passage about the heavens in Paradiso, Cantos 18 to 26, reconstructing it, and compare how the poem describes the heavens with how the model accounts for them. You pass when each prediction can be redone from its version, and your comparison points to a passage in each text you can reopen.

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

Music Grammar

Seminar

• Dante, Paradiso: Cantos 27-33

Tutorial: Music

Score reading: following four voices at once. Read a four-part score with a pencil, marking each voice's entries for ten bars, then sing one line.

Acts

Check it against evidence, Express it truly

Pass when: Follow the four voices of one short choral score for ten bars, marking each voice's entry, and sing one line with the others. Then write 250 words on the closing cantos of Paradiso, Cantos 27 to 33, reconstructing the last vision, and compare its movement with one earlier canto. State the strongest objection to one reading. You pass when a listener can follow your entries against the score, and your comparison points to lines you can reopen.

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

Grammar Rhetoric

Seminar

• Geoffrey Chaucer, Canterbury Tales: the General Prologue

Tutorial: Language

English poetry: metre, rhyme and stanza across the century. Scan twenty lines of the General Prologue and of two poems you have read this year, marking stresses, and name the form of each.

Acts

Understand exactly, Examine the reasons

Pass when: Scan twenty lines of the General Prologue and two poems you have read this year, marking stresses and rhymes, and name the form of each. Then write 250 words on how one portrait in the General Prologue is built, reconstructing its method, and compare that method with one passage of Dante. State the strongest objection to one reading. You pass when a reader can check your stress marks against the lines, and your comparison points to lines you can reopen.

Arithmetic Geometry Rhetoric

Seminar

• Geoffrey Chaucer, Canterbury Tales: selected tales

Tutorial: Mathematics

Ratio and proportion revisited: from Euclid's Book 5 to symbols. Restate one proposition of Book 5 in symbols, and check it with three sets of numbers.

Acts

Check it against evidence, Examine the reasons

Pass when: Restate one proposition of Euclid's Book 5 in modern symbols, then check it with three sets of numbers, showing each calculation. Then write 250 words on the frame and voice of one selected tale, reconstructing how its teller presents the story, and compare two tellers' purposes. State the strongest objection to one reading. You pass when your symbols match the proposition on a second reading, and the numbers confirm it in each case.

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

Music Grammar

Seminar

• Geoffrey Chaucer, Canterbury Tales: further selected tales

Tutorial: Music

Rhythm, metre and accent in polyphony. Sing a short polyphonic passage with its text, marking each accented syllable against the beat.

Acts

Check it against evidence, Express it truly

Pass when: Sing one short polyphonic passage with its text, marking each accented syllable against the beat, and read one line of Chaucer aloud with the same marks. Then write 250 words on one further tale, reconstructing its ending, and compare how its verse and its teller's purpose fit together. State the strongest objection to one reading. You pass when a listener can follow your marks as you sing, and your comparison points to lines you can reopen.

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

Logic Grammar

Seminar

• Niccolò Machiavelli, The Prince: chapters 1-14

Tutorial: Evidence and inquiry

Psychology: social behaviour, read with replication in mind. Read the social psychology chapter, and write a summary of one study with its sample, its measure and whether another team could repeat it.

• OpenStax, Psychology 2e: the chapter on social psychology

Acts

Check it against evidence, Examine the reasons

Pass when: Summarise one social psychology study from the chapter in 150 words, naming its sample, its measure, its comparison, and whether another team could repeat it. Then write 250 words on the advice to princes in The Prince, chapters 1 to 14, reconstructing one argument, and compare it with the way the study reasons from a sample to a claim. State the strongest objection to the argument. You pass when a reader can find each feature of the study in the chapter, and your objection names a premise of the argument.

On the site: Hypotheses, Predictions and Tests

Grammar Rhetoric

Seminar

• Niccolò Machiavelli, The Prince: chapters 15-26

Tutorial: Language

English poetry: speaker, voice and dramatic situation. Choose one poem from the selections and write who speaks, to whom, and when, in one paragraph.

Acts

Understand exactly, Examine the reasons

Pass when: Write one paragraph on a poem you have read, stating who speaks, to whom, and in what situation, and show how two lines establish each. Then write 250 words on one argument in The Prince, chapters 15 to 26, reconstructing it, and compare the speaker's stance in the book with the speaker of the poem. State the strongest objection to one reading. You pass when each claim in your paragraph can be found in the lines you cited, and your objection names a premise of the argument.

Rhetoric Logic

Seminar

• Michel de Montaigne, Essays: selected essays, first part

Tutorial: Writing and speaking

Speaking: an oral explanation of a proposition, recorded and reviewed. Explain one proposition aloud for about five minutes, record it on a device you already own, and list each unclear step you hear on replay.

Acts

Express it truly, Examine the reasons

Pass when: Explain one proposition of Euclid or Apollonius that you have worked aloud for about five minutes, recording it on a device you already own, and list each unclear step you hear on replay. Then write 250 words on the way Montaigne frames one question in these essays, reconstructing his argument, and state the strongest objection to it. You pass when your explanation runs to the end without a skipped step, and your objection names a premise in the essay.

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

Geometry Astronomy Rhetoric

Seminar

• Michel de Montaigne, Essays: selected essays, second part

Tutorial: Mathematics

Oral examination: a proposition of Apollonius and a model of Copernicus. Prepare the proposition and the model on one side of a page, and explain both aloud to a listener for ten minutes.

Acts

Express it truly, Examine the reasons

Pass when: Explain one proposition of Apollonius and one model of Copernicus aloud for ten minutes, with a sketch of each, to a listener who asks at least two questions. Then write 250 words on the way Montaigne tests opinions in the second-part essays, reconstructing one test, and state the strongest objection to it. You pass when your explanation survives the listener's questions without a skipped step, and your objection names a premise of the test.

On the site: Geometry: Apollonius' Conic Sections, Astronomy: Seasons, Moon, Earth and Orbits

Music Rhetoric

Seminar

• Michel de Montaigne, Essays: selected essays, third part

Tutorial: Music

Musical form: the shapes music takes. Mark the sections of one piece of music with letters, and name the form each letter pattern shows.

Acts

Check it against evidence, Express it truly

Pass when: Mark the sections of one piece of music with letters, name the form the pattern shows, and explain in 100 words how repetition and contrast shape the piece. Then write 250 words on one third-part essay of Montaigne, reconstructing its shape in sections, and compare that shape with the piece's. State the strongest objection to one reading. You pass when a listener can follow your letters as the piece plays, and your comparison points to passages you can reopen.

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

Logic Rhetoric

Seminar

Task: The second-year essay: choose a question that joins a classical and a biblical or medieval author

Tutorial: Language

English poetry: poetic argument, or how a poem reasons. Read one poem from the selections and write a 200-word account of how it reasons, to prepare the question for the essay.

Acts

Examine the reasons, Express it truly

Pass when: Choose one question that joins a classical author and a biblical or medieval author, and write it in one sentence, with 150 words on why the two authors speak to it. Then read one poem from the selections and write 200 words on how it reasons, stating the strongest objection to its argument. You pass when your question names both authors, and a reader can state your question back to you on a reread.

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

Arithmetic Rhetoric Logic

Seminar

Task: The second-year essay: the draft

Tutorial: Evidence and inquiry

A statistics project: answer one question with public data, and report its uncertainty. Choose a public data set, calculate one interval from it, and write the report in 800 words.

Acts

Check it against evidence, Express it truly

Pass when: Draft 1,000 words answering the question you chose at the start of the essay. Then, in an 800-word report, answer one question of your own with a public data set: calculate one interval, state its uncertainty, name the data's source and say what the data cannot show. You pass when the draft states a thesis a reader can find on a reread, and a reader can redo your interval from the source you name.

Rhetoric Logic

Seminar

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

Tutorial: Mathematics

Mathematics and observation: 800 words on what makes a mathematical hypothesis about the heavens true. Name the model you rely on and one observation that bears on it.

Acts

Express it truly, Examine the reasons

Pass when: Send your draft to one reader who has not studied the topic, and write a reply of 500 words to their criticism, accepting, rejecting or changing each point and giving the reason. Then revise one paragraph of the draft in response, and mark the change. Then write 800 words on what makes a mathematical hypothesis about the heavens true, naming one model you have studied and one observation that bears on it. You pass when each criticism you received has a stated reply that a reader can find in your revised paragraph, the revised paragraph still states your question, and your 800 words name the model and the observation.

Rhetoric Music Logic

Seminar

Task: The second-year essay: the final text

Tutorial: Music

Music, poetry, mathematics and emotion: 800 words on what the year's music shows. Write the 800 words from one piece of music you studied this year, naming the passage you rely on.

Acts

Express it truly, Examine the reasons

Pass when: Write the final text of the essay, of about 1,500 words, including your reply to criticism and a statement of its strongest objection with your answer to it. Then perform one passage of the music you studied this year aloud, write 800 words on what that piece shows about music, poetry, mathematics and emotion, naming the passage you rely on, and say in the last 150 words how it bears on your question. You pass when the final text states its claim and answers its objection, and a listener can follow your performance against the passage it names.

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

Rhetoric Logic

Seminar

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

Tutorial: Language

English poetry: two interpretations of one poem compared. Find two published readings of one poem, and write 300 words comparing their interpretations and the evidence each uses.

Acts

Express it truly, Examine the reasons

Pass when: Defend your essay aloud for about twenty minutes to a listener, then answer that listener's questions across the year's work. Write a 300-word comparison of two readings of one poem with the evidence each uses, and reconstruct the main argument of your essay in 200 words from memory. You pass when your listener can follow the defence without a skipped step, and each answer points to a passage in a text you studied this year.

On the site: Liberal Arts and Reasoning: Start Here