1. The Renaissance painters knew that what we see as size is really angular size. They worked out rules for representing objects in a 3-dimensional scene on a 2-dimensional canvas such that from one special point everything in the painting would have the same angular size that it would have in reality, if one were looking at the actual scene. The result was paintings that looked realistic.

2. Pendulum clocks, invented in the mid 17th century, were about two orders of magnitude more accurate than previously available clocks. They must have led to new ways of organizing households and societies, and there is no question that they enabled new discoveries in astronomy, and new understanding of the earth. For instance the variation in the effective strength of the earth's gravitational field with latitude and altitude were discovered, as well as the fact that the speed of light is not infinite, in the lateness of the observed eclipses of the moons of Jupiter when Jupiter is farthest away from earth.

Multiple choice questions:

1B, 2C, 3C, 4D, 5D, 6A, 7B, 8B, 9B, 10D, 11A, 12B.