They’re superb machines. My congratulations.”

Archimedes waved his hand. “Please, they’re nothing really. Ordinary hurling mechanisms — mere toys, that’s all. Scientifically, they have little value.”

“But militarily they do,” said Lucius. “Listen, Archimedes, I’ve come to ask you to work with us.”

“With whom?”

“With us, the Romans. Surely you know that Carthage is in decline. Why go on helping them? We’ll teach them a lesson instead! You’d do better to be on our side, all of you.”

“Why?” grumbled Archimedes. “As fate would have it, we Syracusans are Greeks. Why should we side with you?”

“Because you live in Sicily, and we need Sicily.”

“And why do you need it?”

“Because we intend to control the Mediterranean Sea.”

“Aha,” Archimedes said, and he contemplated his tablet. “And why do you want to do that?”

“Whoever is master of the Mediterranean,” said Lucius, “is master of the world. That’s clear enough.”

“And must you be masters of the world?”

“Yes. The mission of Rome is to be master of the world. And I’m telling you that it will be.”

“Possibly,” Archimedes said, and he rubbed out a line on his tablet. “But I wouldn’t advise it, Lucius. Listen, to be master of the world — someday defending your position’s going to be one big headache. It wouldn’t be worth the effort, given all you’d have to do.”

“No matter; we shall be a great empire.”

“A great empire,” muttered Archimedes. “Whether I draw a small circle or a large circle, it’s still only a circle. There are still frontiers — you will never be without frontiers, Lucius. Do you think a large circle is more perfect than a small circle? Do you think you’re a greater geometrician if you draw a larger circle?”

“You Greeks are forever playing with arguments,” Capt. Lucius objected. “We have another way of proving that we’re right.”

“How?”

“Action. For instance, we have conquered your Syracuse. Ergo, Syracuse belongs to us. Is that a clear proof?”

“It is,” Archimedes said, and he scratched his head with his stylus. “Yes, you have conquered Syracuse, except that it is not and never will be the same Syracuse it was before. It was a great and celebrated city, my good fellow; now it will never be great again. Poor Syracuse!”

“But Rome will be great. Rome must be the strongest of all the lands in the world.”

“Why?”

“To maintain her position. The stronger we are, the more enemies we have.