The regent was not appeased. He was a tall man, grim-faced and gray-haired. He stopped beside the fountain and gave Archimedes a scathing look.
Archimedes went crimson. He realized afterward that he probably should have been frightened, but at the time he was just excruciatingly embarrassed. Of all the idiotic ways to lose a job! 'I, uh, I didn't know who was playing,' he stammered defensively. 'I didn't even realize it was a woman. I just, uh, heard the music, and I thought I'd share a trick with a fellow aulist. I didn't mean any disrespect, sir.'
The regent appeared somewhat mollified at this, but he still asked icily, 'Do you normally wander about the private parts of other men's houses uninvited, young man?'
'We're not in a private part of the house, Father!' exclaimed the girl. 'We're in the garden.'
'Delia, that's enough!' said Leptines severely. 'Go to your rooms!'
Delia, thought Archimedes, stupidly pleased, even in the middle of everything, to have learned her name. He could not have asked it: it was almost as improper to ask a young lady's name as it was to talk to her unsupervised. Delia. 'The Delian' was one of the titles of Apollo, the god most closely associated with mathematics. It seemed a good omen that the girl was named for his own patron divinity.
Delia did not go to her rooms; instead she wriggled more firmly into her place on the rim of the fountain. 'I will not go if you're going to pretend I was doing something improper!' she snapped.
Archimedes was somewhat taken aback by this defiance, and more surprised still when Leptines merely rolled his eyes in exasperation and turned away from her. Girls were supposed to be obedient, and the heads of household were supposed to punish them if they weren't. But, of course, Leptines was not the head of Delia's household. Though she was calling him 'Father,' that was only courtesy: the regent was in fact merely her half brother's father-in-law, and it was her half brother who held the real authority.
'I wasn't doing anything wrong!' Delia insisted. 'I was just sitting in the garden trying something tricky on the flute, and this young man- Archimedes, was it? — came up and gave me a tip on how to do it better. Herakles! Where's the impropriety in that?'
The regent looked even more exasperated at this, so Archimedes said, 'I am sorry, sir. I, uh, I realize now it was improper of me to have intruded here uninvited, and I, uh, sincerely apologize for doing so. But, as I said, I had no idea who was playing, and at the time it seemed natural to share a trick with a fellow aulist.'
'Very well,' said the regent stiffly. 'I accept your apology.'
And that, surprisingly, seemed to be the end of the matter. Dionysios caught Archimedes' eye and raised his eyebrows: Archimedes was uncertain whether the look was congratulatory or sympathetic. But he decided that it could not have been the captain who had called his name in that disapproving fashion; it must have been the exalted doorkeeper. He glanced at the doorkeeper, who still looked deeply disapproving, then at the fourth member of the party. This was a man of perhaps fifty, of average height, with graying brown hair and a deeply seamed face. He was dressed in a dusty cloak worn over a workman's apron, and he was scowling at Archimedes more ferociously than any of the others.
'Archimedes son of Phidias,' said Leptines, still very stiffly, 'I understand that you came here this morning looking to serve the city as an engineer.'
'Yes, sir,' agreed Archimedes earnestly. 'Captain Dionysios said you wanted someone to build some stone- hurlers. I'm sorry if-'
'And I understand,' Leptines interrupted, 'that you claim to be able to build a one-talent catapult, although you have never, in fact, built any war machine at all.'
Delia looked surprised; Archimedes was aware of it, and shot an apologetic glance toward her before replying, 'Uh, that's right. You, uh, don't have to have actually built one so long as you understand the mechanical principles.'
'Conceited rubbish!' exclaimed the workman, scowling still harder. 'Experience is the most valuable part of mechanics. You have to develop a sense of how to do things, a wisdom in your hands. That comes only from making machines.'
Archimedes looked at the workman again, and the workman glared back. The others were now watching the two of them, the regent and his doorkeeper like judges, Dionysios with an air of expectancy, and Delia as though she were intently following a play.
'Sir,' said Archimedes respectfully, wondering who the workman was- he hoped not Eudaimon, the man in charge of providing the city with catapults, though he rather feared just that. 'Sir, it's true that you have to have made machines to be able to make machines. I wouldn't quarrel with you on that. But you can't possibly mean to say that before you can make a particular type of machine you have to have made it already!' Delia grinned, and he was encouraged to continue. 'I've made lots of machines. I know what works and what doesn't. As for catapults, I've seen them and studied them and I'm perfectly sure I can make them. I wouldn't be here otherwise. Didn't Captain Dionysios say that you don't have to pay me until you've seen the first catapult work?'
'Waste of wood, strings, and workshop time!' snarled the workman. He turned to Leptines. 'Sir, you should throw this arrogant young fool out!'
'I would throw him out,' said Leptines impatiently, 'if you could promise to produce the catapults the king wants. But since you have failed to, and since he says he can, I am bound to let him try.'
The workman's jaw set with indignation. So, thought Archimedes unhappily, the man was Eudaimon- and he plainly viewed Archimedes' appointment as an insult and a threat. The new job wasn't looking very secure.
But the regent turned back to Archimedes and said, 'I am willing to authorize you to use the royal workshop to build a one-talent catapult. However, in view of your lack of experience, I am going to insist that if your machine doesn't work, not only will you not be paid for it, but I will require you to reimburse the workshop for the materials you have used.'
'That's not fair!' Delia broke in indignantly. 'The materials could be reused by somebody else!'
'Delia, be quiet!' commanded the regent.
'No!' she said angrily. 'You're being unfair to him because he talked to me. You can't expect me to sit quiet for that!'
She cast a concerned glance toward Archimedes. He did not know what to feel in response: it was pleasing that she was worried about him, but humiliating that she so clearly expected him to fail. He pulled himself up straight, tossed his stained cloak back, and declared boldly, 'Please don't be concerned, lady! My machine will work, so I don't mind agreeing to pay for the materials if it doesn't.'
Eudaimon laughed harshly. 'I hope you have money!' he told Archimedes. 'Do you have any idea how much wood and string a one-talenter will need?'
'Yes, I do,' said Archimedes triumphantly. He took his sheet of calculations from his purse again, unfolded it, and offered it to the regent. 'Here are the estimates.'
Leptines stared at the papyrus with surprise, not touching it. Eudaimon, however, glared harder than ever, then snatched the sheet. 'What is this nonsense?' he demanded, scanning it. 'There's no way you could know what the diameter of the bore of a one-talenter should be! There isn't such a machine in the city!'
'The Alexandrians have come up with a formula,' said Archimedes with satisfaction. 'You probably wouldn't know it, because it's still new, but they did a lot of trials on it and it works. You take the weight to be thrown, multiply it by a hundred, take the cube root, add a tenth, and you get the diameter of the bore in finger- breadths.'
Eudaimon sneered. 'And what in the name of all the gods is a cube root?' he asked.
Archimedes blinked, too astonished to speak. The solution to the Delian problem, he thought, the keystone of architecture, the secret of dimension, the plaything of the gods. How could someone who was supposed to build catapults not know what a cube root was?
Eudaimon gave him a look of stark contempt. Then, deliberately, he crumpled up the sheet of papyrus, pretended to wipe his backside with it, and dropped it on the ground.
Archimedes gave a cry of outrage and jumped to rescue his calculations, but Eudaimon set his foot on the papyrus, and he was left tugging at the edge which stuck out from under the imprisoning sandal. 'You think that you can make catapults because you know mathematics?' the chief catapult engineer demanded.
Archimedes, kneeling at his feet, still tugging at the crushed sheet, glared up at him. 'Yes, by Zeus!' he exclaimed hotly. 'In fact, I'd say it's perfectly evident that a man who doesn't know mathematics can't make catapults. You don't, and can't, or I wouldn't be here!'
Eudaimon, infuriated, kicked at him. The gesture was meant more as a threat than with any real intention of
