ON MOTION IN GENERAL.

Corollary 1.

18. Therefore, a body moved by uniform motion original: "motu aequabili." This refers to motion at a constant speed where equal distances are covered in equal time intervals. completes a double distance in a double amount of time, a triple distance in a triple amount of time, and, in general, the distances traversed are proportional to the times, and the times, in turn, are proportional to the distances. For example, a ship moving with uniform motion across the sea: if it traverses two miles in one hour, it will complete four miles in two hours, six miles in three hours, and in n hours it will complete 2n miles.

Corollary 2.

19. For this reason, if uniform motion is given, an accurate measurement of time will be obtained from it; indeed, time cannot be known except through motion. By measuring the distances original: "spatiis." While "space" is the literal translation, in this context it refers to the physical length of the path traveled. that a body moved uniformly traverses, the ratio of the times in which those distances were traversed will become known at the same time.

Scholion A "scholion" is an explanatory note or commentary used in classical and early modern scientific texts to provide further context for a theorem or definition..

20. In fact, we have no other source for the division of time into years, days, and hours except from motion, which we regard as being uniform. For, assuming the Earth to be at rest, the ancients original: "veteres." This refers to the geocentric model of the universe held by astronomers like Ptolemy before the widespread acceptance of the Copernican system. believed that the sun was carried along by uniform motion, and they called the time in which it revolves around the earth a "day." Furthermore, they assumed that the motion of the fixed stars stellae fixae: stars that appear to stay in the same position relative to one another, unlike the "wandering" planets. around the earth was also uniform, and the time in which the sun returns to the same place with respect to the fixed stars, they established as a "year." Finally, they divided these times into equal parts, and in this way hours and minutes were...