The Pillars of the Earth - Ken Follett [384]
Jack was living with a small group of English clerics in Toledo. They were part of an international community of scholars that included Jews, Muslims and Arab Christians. The Englishmen were occupied translating works of mathematics from Arabic into Latin, so they could be read by Christians. There was an atmosphere of feverish excitement among them as they discovered and explored the treasure-house of Arab learning, and they had casually welcomed Jack as a student: they admitted into their circle anyone who understood what they were doing and shared their enthusiasm for it. They were like peasants who have labored for years to scratch a crop out of poor soil and then suddenly move to a rich alluvial valley. Jack had abandoned building to study mathematics. He had not yet needed to work for money: the clerics casually gave him a bed and any meals he wanted, and they would have provided him with a new robe and sandals if he had needed them.
Raschid was one of their sponsors. As an international trader he was multilingual and cosmopolitan in his attitudes. At home he spoke Castilian, the language of Christian Spain, rather than Mozarabic. His family also all spoke French, the language of the Normans, who were important traders. Although he was a man of commerce, he had a powerful intellect and a wide-ranging curiosity. He loved to talk to scholars about their theories. He had taken a liking to Jack immediately, and Jack dined at his house several times a week.
Now, as they began to eat, Raschid asked Jack: “What have the philosophers taught us this week?”
“I’ve been reading Euclid.” Euclid’s Elements of Geometry had been one of the first books translated.
“Euclid is a funny name for an Arab,” said Ismail, Raschid’s brother.
“He was Greek,” Jack explained. “He lived before the birth of Christ. His work was lost by the Romans but preserved by the Egyptians—so it comes to us in Arabic.”
“And now Englishmen are translating it into Latin!” Raschid said. “This amuses me.”
“But what have you learned?” said Josef, the fiance of Raya.
Jack hesitated. It was hard to explain. He tried to make it practical. “My stepfather, the builder, taught me how to perform certain operations in geometry: how to divide a line exactly in half, how to draw a right angle, and how to draw one square inside another so that the smaller is half the area of the larger.”
“What is the purpose of such skills?” Josef interrupted. There was a note of scorn in his voice. He saw Jack as something of an upstart, and was jealous of the attention Raschid paid to Jack’s conversation.
“Those operations are essential in planning buildings,” Jack replied pleasantly, pretending not to notice Josef’s tone. “Take a look at this courtyard. The area of the covered arcades around the edges is exactly the same as the open area in the middle. Most small courtyards are built like that, including the cloisters of monasteries. It’s because these proportions are most pleasing. If the middle is bigger, it looks like a marketplace, and if it’s smaller, it just looks as if there’s a hole in the roof. But to get it exactly right, the builder has to be able to draw the open part in the middle so that it’s precisely half the area of the whole thing.”
“I never knew that!” Raschid said triumphantly. He liked nothing better than to learn something new.
“Euclid explains why these techniques work,” Jack went on. “For example, the two parts of the divided line are equal because they form corresponding sides of congruent triangles.”
“Congruent?” Raschid queried.
“It means exactly alike.”
“Ah—now I see.”
However, no one else did, Jack could tell.
Josef said: “But you could perform all these geometric operations before you read Euclid—so I don’t see that you’re any better off now.”
Raschid