The Sand-Reckoner

The Sand-Reckoner by Gillian Bradshaw is a Historical Fiction novel focusing on Archimedes as a young man during the First Punic War. Returning to his hometown of Syracuse when it goes to war with Rome, Archimedes offers himself up to the city's tyrant as a military engineer.

Tropes featured include

 * Actual Pacifist: At the end of the book, Archimedes has become one, having seen firsthand and been disgusted by what his war engines do to people.
 * The Chessmaster: Hieron, the tyrant of Syracuse.
 * Genius Ditz: Archimedes, who's apt to be attacked by geometry at a moment's notice.
 * Heroic Bastard: Hieron.
 * Honor Before Reason: Marcus, Archimedes' slave.
 * I Thought Everyone Could Do That!: Archimedes is surprised to realize that he's so much better at engineering than any of the king's actual engineers. Most of his inventions, he thinks, are obvious.
 * Rags to Royalty: Hieron's backstory involves this. He was born poor, made a name for himself in the wars, and eventually ended up ruling the city.
 * Serial Escalation: Archimedes' catapults. The one he builds as an audition for the engineer's post throws stones that weigh one talent (60 pounds), which is already larger than any catapult the city had before that. By the end of the book, he's built four- and five-talent catapults.
 * Sparing the Aces: Hieron of Syracuse to the brilliant Archimedes.
 * The Wise Prince: Hieron.