Tyler, who read the text aloud:

The spy of King Hieron has brought us a gift that may yet win our war. While seeking an underground path to enter the Roman fortress, the spy came upon the treasure of King Midas, a vault of gold the likes of which has never before been seen. As proof of his find, the spy produced a golden hand of such excellent design, it could not have been fabricated. Three keys-this tablet, a manuscript, and the Parthenon-provide the map for finding the treasure, which cannot fall into Roman hands or they will rule the Earth and all who dwell within it.

Grant gaped at Tyler. “So it’s real?”

“Apparently,” Tyler said. “And Archimedes created this puzzle so that someone other than the Romans would find the treasure. But why didn’t they go after the gold themselves?”

“Because for two years,” Stacy said, “the city of Syracuse, which was a Greek city-state on what is now the island of Sicily, was under siege by the Roman Navy. If the city fell-which it eventually did, resulting in the death of Archimedes-the Romans could have found the map and claimed the treasure, funding their military campaigns for a hundred years. That’s why Archimedes used the Parthenon as the third key. It was the most famous building in the world at the time, but the Romans wouldn’t have access to it.”

“And we know the Romans never found the gold,” Tyler said, “because Orr and Cavano saw it. Now we have to follow Archimedes’ instructions to find it again.”

“Keep reading,” Stacy said. “I’ve tried to translate his writing as plainly as possible.”

As the seat of Herakles is to the island of Megaride, the feet of Aphrodite are to the Parthenope acropolis. All dials must start by pointing to the top position. When you are facing the Parthenon, the geolabe must lie on its side with its knobs up so that it blocks all but the pediment. As the shadow moves on the sundial, rotate the left- hand knob so that its dial points at the seat of Herakles. The opposing dial will now reveal the direction from Megaride. With the geolabe in the same position, rotate the right-hand knob so that its dial points to the feet of Aphrodite. The opposing dial will now reveal the direction from the Acropolis. Thus, the combination of directions will reveal the well from which you will begin your journey. From that point, marked by the sign of Scorpio, the geolabe will show the way.

Tyler read it a second time to make sure he got what Archimedes was suggesting.

“Incredible,” he said. “He’s telling us to use triangulation to home in on how we get into the tunnels.”

“How does triangulation work?” Stacy asked.

“You use triangulation to pinpoint a location using two other points. You don’t need the distance to the location from those two points, just the angles. Once you have those, you can draw a line from each point, and where they cross is the location you’re looking for. So the directions from the island of Megaride and the Parthenope acropolis will point to the tunnel entrance. It’ll be a crude approximation because the angles provided by the geolabe won’t be exact, but it will give us a small region to search.”

“And we get those angles from the Parthenon?”

“In a way. Let’s take it one step at a time.” Tyler read the first paragraph out loud:

As the seat of Herakles is to the island of Megaride, the feet of Aphrodite are to the Parthenope acropolis.

Tyler turned to Grant. “You said that Lumley showed you statues of Herakles and Aphrodite on the Parthenon’s pediments, right?”

“Yeah. But they’re both in the British Museum now.”

“Doesn’t matter. We can look up where they used to be on the building itself. I’ll text Aiden to find some detailed schematics of the Parthenon.”

“Why?” Stacy said as he typed the message.

“Because I think Archimedes had visited the Parthenon at some point and constructed the geolabe based on its dimensions.”

“What is Megaride?” Grant asked. “Sounds like a roller coaster at Disney World.”

“Tyler pronounced it wrong,” Stacy said. “It’s Maygah-REE-day. I know I’ve heard it before. Let me look it up.”

She used Tyler’s laptop.

“Aha!” she said. “Megaride used to be an island off the coast of Neapolis, but they’ve built a stone pier to it now, creating a peninsula. It’s now a famous attraction in Naples called Castel dell’Ovo, a fortress first built in the twelfth century.”

“But it says the second point is the Acropolis,” Grant said. “You’re telling me the triangle is formed with two of its points in Naples and Athens?”

“It says the Parthenope acropolis,” Stacy corrected. “ Acropolis is a generic Greek term for the high point of the city. In Parthenope-Naples today-the acropolis would have been what’s now another castle called Castel Sant’Elmo, on a bluff that has a commanding view of the city. Megaride and the acropolis would have been the two most prominent locations in Neapolis in Archimedes’ time.”

“Which makes them perfect for two triangulation anchors,” Tyler said. He looked at the map of Naples that Stacy had brought up on the laptop. “Once we have the angles from those two points, we’ll know where to start our search for the tunnel.”

“So how do we get those angles?” Stacy asked.

Tyler read the next two paragraphs to them:

All dials must start by pointing to the top position. When you are facing the Parthenon, the geolabe must lie on its side with its knobs up so that it blocks all but the pediment. As the shadow moves on the sundial, rotate the left-hand knob so that its dial points to the seat of Herakles. The opposing dial will now reveal the direction from Megaride. With the geolabe in the same position, rotate the right-hand knob so that its dial points to the feet of Aphrodite. The opposing dial will now reveal the direction from the Acropolis.

“The shadow on a sundial moves in the clockwise direction, of course,” Stacy said.

“And all dials pointing to the top refers to the calibration we did,” Tyler said. “That’s why we needed the Stomachion puzzle. Orr’s original translator realized it related to the geolabe, but he didn’t know how. The dials had to be zeroed out to the twelve o’clock position before we could use the geolabe. Archimedes says that the geolabe must lie on its side to reveal only the pediment, which is the triangular part at the top.”

“Makes sense,” Grant said. “Lumley said the facade of the Parthenon was build in the shape of a golden rectangle.”

“And if the geolabe is also in the shape of a golden rectangle, it would be a perfect match.”

“But we need to be at the Parthenon to use it,” Stacy said. “I get it now. Only a Greek would be able to go to Athens and see the Parthenon in person. Even if you had the other two keys, they would be useless if you couldn’t get to the Parthenon.”

“Right. We have to actually be standing there, knowing where the seat of Herakles and the feet of Aphrodite would be, and then twist the knobs until the dials point to those locations. That’s what the three hundred and sixty notches on the third dial of the geolabe are for. They’ll give us the correct triangulation angles. Then we transpose those to the island of Megaride and the Parthenope acropolis.”

Tyler read the last paragraph:

Thus, the combination of directions will reveal the well from which you will begin your journey. From that point, marked by the sign of Scorpio, the geolabe will show the way.

“So the triangulation will lead us to a well?” Grant asked.

“Many of the points of entry into the Naples underground are wells leading to the cisterns and aqueducts that carry water into the city,” Stacy said. “The spy must have come out of the Midas treasure chamber and wended his way through the tunnels until he found an exit. Droughts were not uncommon, which would make it possible for him to walk through the tunnels that served as aqueducts and were normally filled with water. The spy marked his exit well with the sign of Scorpio so that he could find it again. Maybe the mark on the well will still be there.”

“So all we have to do to find this well,” Tyler said, “is go to the Parthenon with the geolabe, turn it on its side, twist the knobs to get the angles of triangulation, and transfer them to a map of Naples.”

“Sounds easy when you put it that way,” Stacy said. “But we need the geolabe to do it. Then the triangulation will lead us to the map.”

“Wait a minute,” Grant said, snapping his fingers. “There is no map.”

No map? Tyler thought. There had to be a map. How else would they find the treasure?

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