About 140 BC, the Greek astronomer Hipparchus of Rhodes invented the science of trigonometry. Hipparchus figured out that you could use an imaginary right triangle whose corners were the sun, the earth, and the planets or stars, to calculate the movements of the planets and stars. To measure the angles of these right triangles accurately, Hipparchus invented a metal tool called an astrolabe. It’s a kind of analog calculator, like a slide rule.
Later West Asian scientists, first Greek, then Christian, then Muslim, made gradual improvements to the astrolabe over the next thousand years. Islamic astronomers added markings so that you could find how far away from due north you were.
In the late Middle Ages, Chinese scientists shared the idea of making a magnetic compass with Islamic astronomers and from there the news spread to Europe. Then sailors – or at least highly skilled navigators – were able to combine the use of the astrolabe with the use of the compass to figure out where they were on the ocean when they couldn’t see the land.
Greek and Roman Science, by Don Nardo (1998). Nardo has written a lot of good books about the ancient world for kids; this one is no exception.
Ancient Science: 40 Time-Traveling, World-Exploring, History-Making Activities , by Jim Wiese (2003). Activities, as the title says – how to make your own sundial, and so on. The author is a science teacher.
Greek Science After Aristotle, by G. E. R. Lloyd (1975).