Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/418

 This Proposition, at first sight to me, that am neither Geometrician nor Astronomer, hath the appearance of a very great Paradox; and if it should be true, that the motion of the whole, being regular, that of the parts, which are all united to their whole, may be irregular, the Paradox will overthrow the Axiome that affirmeth, Eandem esse rationem totius & partium.

I will demonstrate my Paradox, and leave it to your care, Simplicius, to defend the Axiome from it, or else to reconcile them; and my demonstration shall be short and familiar, depending on the things largely handled in our precedent conferences, without introducing the least syllable, in favour of the flux and reflux.

We have said, that the motions assigned to the Terrestrial Globe are two, the first Annual, made by its centre about the circumference of the Grand Orb, under the Ecliptick, according to the order of the Signes, that is, from West to East; the other made by the said Globe revolving about its own centre in twenty four hours; and this likewise from West to East: though about an Axis somewhat inclined, and not equidistant from that of the Annual conversion. From the mixture of these two motions, each of it self uniform, I say, that there doth result an uneven and deformed motion in the parts of the Earth. Which, that it may the more easily be understood, I will explain, by drawing a Scheme thereof. And first, about the centre A [in Fig. 1. of this Dialogue] I will describe the circumference of the Grand Orb B C, in which any point being taken, as B, about it as a centre we will describe this lesser circle D E F G, representing the Terrestrial Globe; the which we will suppose to run thorow the whole circumference of the Grand Orb, with its centre B, from the West towards the East, that is, from the part B towards C; and moreover we will suppose the Terrestrial Globe to turn about its own centre B likewise from West to East, that is, according to the succession of the points D E F G, in the space of twenty four hours. But here we ought carefully to note, that a circle turning round upon its own centre, each part of it must, at different times, move with contrary motions: the which is manifest, considering that whilst the parts of the circumference, about the point D move to the left hand, that is, towards E, the opposite parts that are about F, approach to the right hand, that is, towards G; so that when the parts D shall be in F, their motion shall be contrary to what it was before. when it was in D. Furthermore, the same time that the parts E descend, if I may so speak, towards F, those in G ascend towards D. It being therefore presupposed, that