ces from the sun. d and I will move the place to stand, AL principles physics. at a which es. ,ururncu meuleval cosmology an From ancient times through the days of Copernicus and Tycho y mechamCo, planet's LA. orbit must be a circle had been unchallenged. Indeed, a circle was accepted as the perfect geometrical form, and perfection was accepted as the normal state of heavenly affairs. That the real orbits of planets were ellipses was a triumph for the new astronomy and the right of Western scientists to pursue their investigations independent of theological doctrines. One fundamental question could not yet be answered: What held the planets in their courses? As we shall see, the vortex theory of Descartes and Newton's theory of universal gravitation were responses to this challenge. of Venice also sent another courier to Rome, who should reach Rome in 9 days. And from Rome to Venice is 250 miles. It happened that by the order of these lords the couriers started their journeys 8.1 Problems 1. Solve the following problems from the Treviso at the same time. It is required to find in how Arithmetic: many days they will meet. 2. From Nicolas Chuquet’s Tripary, 1484: I am owed 3240 florins by a debtor who pays me 1 florin the first day, 2 the second day, 3 the third day, and so on. In how many days will the debt be paid off? A man finds a purse with an unknown number of (a) ducats in it. After he spends 1/4, 1/5, and 1/6 of the amount, 9 ducats remain. It is required to find out how much money was in the purse. 3. From Robert Recorde's The Whetstone of Witte, 1557: A captain marshalls his army in a square formation. When the square is of one size, he has 284 men too many. But when he rearranges them in a square one man more on a side than before, he lacks 25 men. How A hare is 150 paces ahead of a hound which pursues him. The hare covers 6 paces each time the hound covers 10. It is required to know how (b) many paces the hound has made when he overtakes the hare. many men does he have? (c) Venice, commanding him that he should reach Venice in 7 days. The most illustrious Signoria The Holy Father sent a courier from Rome to 4. From Christoph Clavius's Algebra, 1608: If I gave 7 lire to each beggar that came to my door, I would have