"Ah, now you are bound to lose me," said Dorotheus. "I've never had a head for logic and mathematics. Remember, Agathinus, how our old tutor used to have weeping fits, trying to get me to under-stand Pythagoras and all that?"
"Ah, but the principle of the golden crown is quite simple to explain," said Cicero brightly. "Do you know the story?"
"In a vague, general, roundabout way," said Dorotheus, with laughing eyes.
"I'll make the tale brief," promised Cicero. "It seems that Hiero gave a certain weight of gold to an artisan, with a commission to make him a crown. Soon enough, the man returned with a splendid gold crown. But Hiero heard a rumor that the artisan had pilfered some of the gold, and had substituted silver for the core of the crown. It weighed the correct amount, but was the crown made of solid gold or not? The piece was exquisitely crafted, and Hiero hated to damage it, but he could think of no way to determine its compo-sition short of melting it down or cutting into it. So he called on Archimedes, who had helped him with so many problems in the past, and asked if he could find a solution.
"Archimedes thought and thought, but to no avail. Gold was heavier than silver, that much he knew, and a blind man could tell the two apart by weighing them in his hands; but how could one tell if a given object was made of silver covered with gold? They say that Archimedes was sitting in a tub at the baths, noticing how the level of the water rose and fell as the bathers got in and out, when the solution suddenly came to him. He was so excited that he jumped from the tub and ran naked through the streets, shouting, 'Eureka! Eureka!'-'I have found it! I have found it!'"
Dorotheus laughed. "All the world knows that part of the tale, Cicero. And for better or worse, that's how the world pictures Archimedes-as an absentminded old genius."
"A naked absentminded old genius," Agathinus amended tartly.
"Not a pretty picture," said Margero. "A man of a certain age should know better than to subject others to his bony nakedness, even in private." It seemed to me that he shot a caustic look at Agathinus, who stared straight ahead. I realized that the two of them had hardly said a word to each other or exchanged a glance all night.
"Gentlemen, we digress," said Cicero. "The point of the story is the solution that Archimedes devised."
"Ah, now this is the part that I've never been quite able to follow," said Dorotheus, laughing.
"But it's really quite simple," Cicero assured him. "This is what Archimedes did. He took an amount of gold of a certain weight-a single Roman uncia, let's say. He placed the uncia of gold in a vessel of water, and marked how high the waterline rose. Then he took an uncia of silver, placed it in the same vessel, and marked the water-line. Being a lighter substance, the uncia of silver was larger than the uncia of gold, and so displaced more water, and thus caused a higher waterline. Then Archimedes took the crown and, knowing the exact number of uncias of gold that Hiero had given the artisan, calculated how high it should cause the waterline to rise. If the waterline rose higher than expected, then the crown could not be made of solid gold, and must contain some material of greater volume per uncia, such as silver. Sure enough, the crown displaced more water than it should have. The artisan, his deception discovered, confessed to having covered a silver crown with gold."
"I see," said Dorotheus slowly and without irony. A light seemed genuinely to dawn in his eyes. "Do you know, Cicero, I have never before been able to grasp Archimedes's principle."
"Ah, but you should. It can be of great practical use to a man dealing in payments and commodities, as you do."
"Yes, I can see that," said Dorotheus, nodding thoughtfully.
Cicero smiled. "You see, it's really simple, as most basic principles are. But it takes a man like Archimedes to discover such princi-ples in the first place." He gazed at his wine by the lamplight. "But absentminded he certainly was, always drifting into his world of pure geometry. At the baths, they say, he would even use himself as a tablet, drawing geometrical shapes in the massage oil on his belly."
This image pleased Dorotheus, who slapped his own belly and laughed heartily. Even Agathinus grinned. Margero merely raised an eyebrow.
"Thus Archimedes met his death as absentmindedly absorbed in mathematics as ever," said Cicero. "But I'm sure you all know the story of his end already…"
"Vaguely," allowed Agathinus.
"Oh, but you must enlighten us," said Dorotheus.
"Very well, if you insist. After Hiero died, the Romans occupied Sicily, to keep it as a bulwark against Carthage. On the day that Syracuse was taken by the general Marcellus, Archimedes was on the beach, working out a theorem by drawing figures with a stick in the sand, when a troop of Roman soldiers came marching up. Archimedes, who didn't even know that the city had been taken, took no notice until the soldiers began to tramp across his drawings. He made a rude remark-"
"He suggested that they all go copulate with their mothers, as I recall," said Margero, smiling languidly.
Cicero cleared his throat. "At any rate, one of the soldiers flew into a rage and killed Archimedes on the spot."
"1 had no idea that a preoccupation with mathematics could be so dangerous," quipped Agathinus, straight-faced.
"At least Archimedes knew how to mind his own business," said Margero quietly. Again, I thought I saw him glare at Agathinus, who showed no reaction.
Cicero ignored the interruption. "When the Roman general learned of the tragedy, he was mortified, of course. He ordered a grand funeral procession and the construction of an elaborately or-namented tomb inscribed with the greatest of Archimedes's theorems and decorated with sculptures of the forms whose properties he discovered-the sphere, the cone, the cylinder, and so on. I say- where is the tomb of Archimedes? I should like to see it while I'm here."
Agathinus and Dorotheus looked at each other and shrugged. Margero's face was as unreadable as a cat's.
"Do you mean to say that none of you knows the location of Archimedes's tomb? Is it not general knowledge?"
"Somewhere in the old necropolis outside the city walls, I suppose," said Agathinus vaguely.
"Not everyone is as preoccupied with their dead ancestors as you Romans," said Margero.
"But surely the tomb of a man as great as Archimedes should be regarded as a shrine." Cicero suddenly stiffened. His eyes flashed. His jaw quivered. "Eureka! I have found it!" He was suddenly so animated that we all gave a start, even the heavy-lidded Margero. "Gor-dianus the Finder, it was the Fates who brought us two Romans together here in Syracuse! I have a purpose here, and so have you."
"What are you talking about, Cicero?"
"What do you say to a bit of employment? You shall locate the lost tomb of Archimedes for me-if it still exists-and I shall restore it to its former glory! It shall be the crowning achievement of my year in Sicily. Brilliant! Who can doubt it was the Fates who engi-neered this evening and its outcome, who brought us all together, we two Romans and our new Syracusan friends? Eureka! I feel like Archimedes in the bathing tub."
"Just don't go running naked though the streets," quipped Dorotheus, his round body shaking with mirth.
The evening had come to a natural conclusion, and the three Syracusans made ready to leave. Cicero retired, leaving it to Tiro to show them out and to conduct Eco and me to our beds. At the door, Agathinus lingered behind his departing companions and drew me aside.
"I take it that Cicero is serious about hiring you to go looking for Archimedes's tomb tomorrow?"
"So it appears. They call me Finder, after all."
Agathinus pursed his thin lips and studied me with cool, apprais-ing eyes that betrayed a hint of amusement. "You seem to be a decent enough fellow, Gordianus-for a Roman. Ah, yes, don't deny it-I saw you laughing in silence tonight along with us, while your countryman lectured us about Hiero and Archimedes. As if we were schoolboys, indeed! As if he were the native Syracusan, not us! But as I say, you seem decent enough. Shall I do you a favor and tell you where to find the tomb?"
"You know?"
"It's not exactly common knowledge, but yes, I know where it is." "Yet you didn't tell Cicero."
"Never! I think you know why. The know-it-all! From what I've heard, he's more honest than most of the bureaucrats Rome sends us, but still-the gall of the man! But I like you, Gordianus. And I like your son; I liked the way he laughed at Dorotheus's awful jokes. Shall I show you where to find the tomb of Archimedes? Then you can show it to Cicero, or not, as you please-and charge him a stiff fee for your services, I hope."
I smiled. "I appreciate the favor, Agathinus. Where exactly is the tomb?"
"In the old necropolis outside the Achradina Gate, about a hundred paces north of the road. There are a lot of old monuments there; it's a bit of a maze. My father showed me the tomb when I was a boy. The inscriptions of the theorems had largely worn away, but I remember the geometrical sculptures quite vividly. The necropolis has fallen into neglect, I'm afraid. The monuments are all overgrown." He thought for a moment. "It's hard to give exact directions. It would be easier simply to show you. Can you meet me outside the gate tomorrow morning?"
"You're a busy man, Agathinus. I don't want to impose on you."
"It's no imposition, so long as we do it first thing in the morning. Meet me an hour after dawn."
I nodded, and Agathinus departed.
"How did the dinner go?" asked Tiro as he showed us to our room. "I know that Eco didn't think much of the evening." He mimicked Eco yawning. Meanwhile Eco, yawning for real, tumbled backward onto a sleeping couch that looked infinitely more comfortable than the vermin-ridden mats at the inn where we had been staying.
"An evening is never too dull if it ends with a full stomach, a roof over my head, and the prospect of gainful employment." I said. "As for the company, Dorotheus is likable enough, if a bit loud. And Agathinus appears to be an alright fellow."
"Rather dour-looking."
"I think he just has a very dry sense of humor."
"And the poet?"
"Margero was clearly in no mood to recite poetry. He seemed to be rather preoccupied. There was something going on between him and Agathinus…"
"I think I can explain that," offered Tiro.
"You weren't in the room."
"No, but I was in the kitchen, soaking up local gossip from the slaves. Agathinus and Dorotheus are Margero's patrons, you see; every poet needs patrons if he's to eat. But lately there's been a chill between Agathinus and Margero."
"A chill?"
"Jealousy. It seems they're both paying court to the same pretty boy down at the gymnasium."
"I see." The two were rivals in love, then. Margero was younger and more handsome than Agathinus, and could compose love poems; but Agathinus had the attractions of money and power. Clearly, the two of them had not yet fallen out completely-Margero still depended on Agathinus for patronage, Agathinus still used the poet as an ornament-but there was friction between them. "Any other interesting gossip from the kitchen slaves?"
"Only that Agathinus and Dorotheus just received payment for their largest shipment ever of imported goods from the East. Some people say that they're now the richest men in Syracuse."
"No wonder Cicero was advised to make friends with them."
"Do you need anything else before you retire?" asked Tiro, lowering his voice. Eco, not even undressed, was already softly snoring on his couch.
"Something to read, perhaps?"
"There are some scrolls in the room that Cicero uses for an office…"
I ended the night curled under a coverlet on my couch, puzzling by lamplight over a musty old scroll of the works of Archimedes, amazed at his genius. Here were such wonders as a method for deter-mining the surface area of a sphere, explained so lucidly that even I could almost understand it. At length I came upon the proposition which had resulted from the problem of the gold crown:
Proposed: A solid heavier than a fluid will, if placed in it, descend to the bottom of the fluid, and the solid will, when weighed in the fluid, be lighter than its true weight by the weight of the fluid.
Yes, well, that much was obvious, of course. I read on.
Let A be a solid heavier than the same volume of fluid, and let (G + H) represent its weight, while G represents the weight of the same volume of the fluid…
This was not quite so clear, and I was getting drowsy. Cicero's explanation had been easier to follow. I pressed on.
Take a solid B lighter than the same volume of the fluid, and such that the weight of B is G, while the weight of the same vol-ume of the fluid is (G + H). Let A and B be now combined into one solid and immersed. Then, since (A + B) will be of the same weight as the same volume of fluid, both weights being equal to (G + H) + G, it follows that…
I gave a great yawn, put aside the scroll, and extinguished the lamp. Alas, it was all Greek to me.
The next morning, at daybreak, I roused Eco, grabbed a handful of bread from the pantry, and the two of us set out for the Achradina Gate.
The stretch of road outside the walls was just as Agathinus had described it, with a great maze of tombs on either side, all overgrown with brambles and vines. It was an unsettling place, even in the pale morning light, with an air of decay and desolation. Some of the stone monuments were as large as small temples. Others were simple stelae set in the earth, and many of these were no longer upright but had been knocked this way and that. Crumbling sculptural reliefs depicted funeral garlands and horses' heads, the traditional symbols of life's brief flowering and the speedy passage toward death. Some of the monuments were decorated with the faces of the dead, worn so smooth by time that they were as bland and featureless as the statues of the Cyclades.
Agathinus was nowhere to be seen. "Perhaps we're early," I said. Eco, full of energy, began nosing about the monuments, peering at the worn reliefs, looking for pathways into the thicket. "Don't go getting lost," I told him, but he might as well have been deaf as well as mute. He was soon out of sight.
I waited, but Agathinus did not appear. It was possible that he had arrived before us and lacked the patience to wait, or that his business had kept him from coming. There was also the chance that he had changed his mind about helping me, decent enough fellow for a Roman though I might be.
I tried to remember his description of the tomb's location. On the north side, he had said, about a hundred paces from the road, and decorated with sculptures of geometrical shapes. Surely it couldn't be that hard to find.
I began nosing about as Eco had done, looking for ways into the thicket. I found his tracks and followed them into a sort of tunnel through the thorns and woody vines that choked the pathways between the monuments. I moved deeper and deeper into a strange world of shadowy foliage and cold, dank stone covered with lichen and moss. Dead leaves rustled underfoot. Whenever the pathway branched I tried to follow Eco's footsteps and called out his name to let him know that I was behind him. I soon realized that finding Archimedes's tomb would not be such a simple task after all. I con-sidered turning and retracing my steps back to the road. Agathinus might have arrived, and be waiting for me.
Then I heard a strange, twisted cry that was not quite a scream, but rather the noise a mute boy might make if he tried to scream.
Eco!
I rushed toward the noise, but was confounded by the branching maze and the echo of his cry among the stone tombs. "Cry out again, Eco! Cry out until I find you!"
The noise echoed from a different direction. I wheeled about, banged my head against the projecting corner of a monument, and cursed. I reached up to wipe the sweat from my eyes and realized I was bleeding. Eco cried out again. I followed, stumbling over creeping vines and dodging crooked stelae.
Suddenly, above a tangle of thorns, I glimpsed the upper part of what could only be the tomb of Archimedes. Surmounting a tall square column chiseled with faded inscriptions in Greek was a sphere, and surmounting the sphere, balanced on its round edge, was a solid cylinder. These two forms were the concrete representation of one of the principles I
had encountered in my reading the night before-but all such thoughts fled from my mind as I found a way through the thicket and stepped into a small clearing before the tomb.
In front of the column there were several other geometrical sculptures. Upon one of them, a cube almost as tall as he was, stood Eco, his eyes wide with alarm. Next to the cube and equally as tall was a slender cone that came to a very sharp point. The point was dark with blood. Impaled on the cone, face-up, long, spindly limbs splayed in agony, was the lifeless body of Agathinus. His upside-down features were frozen in a rictus of pain and shock.
"You found him like this?"
Eco nodded.
How had such a thing happened? Agathinus must have been standing on the cube where Eco now stood, and somehow fallen backward onto the point. I flinched, picturing it. The force of his fall had pushed his body halfway down the cone. But why should he have been standing on the cube at all? The faded inscriptions on the column could as easily be read from the ground. And how could he have been so careless as to fall in such a dangerous spot?
Unless someone had pushed him.
I thought of a triangle, not of the sort which Archimedes studied, but with properties just as predictable-a triangle made not of abstract lines but of the powerful forces that link mortal to mortal.
I told Eco to stop gawking and get down from the cube.
Given the circumstances of our discovery, and the fact that we were strangers in Syracuse, Eco and I might very well fall under suspicion ourselves if it was decided that Agathinus had been murdered. I thought it best to report what I had seen to Cicero, to let him handle reporting the death to the appropriate provincial magistrate, and then to book passage for Rome and have as little to do with the mat-ter as possible.
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