2. Let there be a circle given (in the second figure) whose centre is A, and radius A B; and upon the centre B and any radius B C let the epicycle C D E be described. Let the centre B be understood to be carried about the centre A, and the whole epicycle with it till it be coincident with the circle F G H, whose centre is I; and let B A I be any angle given. But in the time that the centre B is moved to I, let the epicycle C D E have a contrary revolution upon its own centre, namely from E by D to C, according to the same proportions; that is, in such manner, that in both the circles, equal angles be made in equal times. I say E C, the axis of the epicycle, will be always carried parallel to itself. Let the angle F I G be made equal to the angle B A I; I F and A B will therefore be parallel; and how much the axis A G has departed from its former place A C (the measure of which progression is the angle C A G, or C B D, which I suppose equal to it) so much in the same time has the axis I G, the same with B C, departed from its own former situation. Wherefore, in what time B C comes to I G by the motion from B to I upon the centre A, in the same time G will come to F by the contrary motion of the epicycle; that is, it will be turned backwards to F, and I G will lie in I F. But the angles F I G and G A C are equal; and therefore A C, that is, B C, and I F, (that is the axis, though in different places) will be parallel. Wherefore, the axis of the epicycle E D C will be carried always parallel to itself; which was to be proved. Coroll. From hence it is manifest, that those two annual motions which Copernicus ascribes to the earth, are reducible to this one circular simple motion, by which all the points of the moved body are carried always with equal velocity, that is, in equal times they make equal revolutions uniformly. This, as it is the most simple, so it is the most frequent of all circular motions; being the same which is used by all men when they turn anything round with their arms, as they do in grinding or sifting. For all the points of the thing moved describe lines which are like and equal to one another. So that if a man had a ruler, in which many pens' points of equal length were fastened, he might with this one motion write many lines at once. [Sidenote: Properties of simple motion.] 3. Having shown what simple motion is, I will here also set down some properties of the same. First, when a body is moved with simple motion in a fluid medium which hath no vacuity, it changes the situation of all the parts of the fluid ambient which resist its motion; I say there are no parts so small of the fluid ambient, how far soever it be continued, but do change their situation in such manner, as that they leave their places continually to other small parts that come into the same.