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We're back in 1809, and it's class time again. Thomasina is working on her lesson, while Septimus is reading a letter that the butler, Jellaby, has just delivered.
The table has acquired more objects: not just that same copy of The Couch of Eros, but also Septimus's portfolio, a tortoise (now named Plautus after a famous Roman playwright), and an apple (identical to the one that ended the last scene).
Thomasina is working on translating a text from Latin to English, which she painfully reads to Septimus as he sends Jellaby away.
While Thomasina continues to stab her way through the Latin, Septimus pulls the stem and leaf off the apple, which he cuts into pieces to feed to himself and to Plautus.
Thomasina is trying to figure out who wrote the Latin text, and suggests that it's Septimus's friend, Lord Byron. Thomasina suspects that her mother is in love with Byron, a belief she bases on observing them in the gazebo, in the midst, not of "carnal embrace" (thankfully preventing some childhood trauma about parental sexuality), but of a poetry reading.
Thomasina also mentions an interesting conversation at breakfast, which Septimus missed – Lord Byron was quoting to Chater an amusingly snarky review of one of Chater's poems, written by none other than Septimus Hodge.
Septimus returns Thomasina's math assignment, which received an A-minus – the minus thanks to Thomasina's going beyond what the assignment asked.
Thomasina, however, still believes in her discovery, which takes a little explanation, so get comfortable (as Septimus does, finishing up a letter while she is speaking). Her assignment was to fill in values in formulas and graph the results, which gives her geometrical shapes – the shapes of things machines build. What Thomasina thinks she has discovered is that you should be able to use the same process to chart the shapes of natural objects, such as plants. She intends to test her theory by going in reverse – graphing the shape of the apple leaf she finds on the table and trying to figure out the formula that describes it.
Septimus, however, seems unimpressed, or at least distracted, and forces her attention back to the Latin text, which he reveals is about Cleopatra.
Thomasina is not, however, a Cleopatra fan, thinking that she should have spent less energy on sex and more on politics.
Not only that, Thomasina continues, Cleo was literally sleeping with the enemy, and the enemy burned the Library of Alexandria, leading to complete loss of thousands of irreplaceable texts.
Or are they so irreplaceable? Septimus says no, that nothing is truly lost, and all will be written or discovered again.
Septimus picks up Thomasina's Latin assignment and begins a fluent translation – which drives Thomasina crazy once she realizes he's cheating because he knows the text in English (it's Shakespeare).
Thomasina slams out in a huff, nearly running over her uncle, Captain Brice, who is followed by a sheepish-looking Chater.
And on to the comedy routine: Chater says that anything Septimus has to say to him he should say to Brice, so Septimus addresses Brice as Chater; confusion follows, but one thing that keeps coming up is the idea of a duel.
Lady Croom interrupts them and carries off Septimus's note-containing copy of The Couch of Eros, which Byron wants to borrow to include Chater in Byron's book English Bards and Scotch Reviewers, which mocks the prominent poets of the day.
Lady Croom tells Septimus that he should take charge of Byron's pistols, since 1) it would prevent him from going off to visit the rougher parts of Europe and 2) he's a terrible shot.
Lady Croom remarks on Thomasina's awful piano-playing in the next room.
Lady Croom departs, and Septimus agrees to fight a duel with Chater.
In making his agreement, he also manages to insult Brice, whom he schedules for duel #2 right after Chater.