Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/342

 proach towards the Æquilibrium, the incurvation of the arches of the courses on the contrary shall, by degrees, increase.

I confesse, Salviatus, that to interrupt you in your Discourse is ill manners, but I esteem it no lesse rudeness to permit you to run on any farther in words, whilst they are, as the saying is, cast into the air: for, to speak freely, I know not how to form any distinct conceit of so much as one of these conclusions, that you have pronounced; but because, as I thus generally and confusedly apprehend them, they hold forth things of admirable consequence, I would gladly, some way or other, be made to understand the same.

The same that befalls you, befell me also, whilst my Guest transported me with bare words; who afterwards assisted my capacity, by describing the businesse upon a material Instrument, which was no other than a simple Sphere, making use of some of its circles, but to a different purpose from that, to which they are commonly applied. Now I will supply the defect of the Sphere, by drawing the same upon a piece of paper, as need shall require. And to represent the first accident by me propounded, which was, that the courses or journeys of the spots, twice a year, and no more, might be seen to be made in right lines, let us suppose this point O [in Fig. 4.] to be the centre of the grand Orb, or, if you will, of the Ecliptick, and likewise also of the Globe of the Sun it self; of which, by reason of the great distance that is between it and the Earth, we that live upon the Earth, may suppose that we see the one half: we will therefore describe this circle ABCD about the said centre O, which representeth unto us the extream term that divideth and separates the Hemisphere of the Sun that is apparent to us, from the other that is occult. And because that our eye, no lesse than the centre of the Earth, is understood to be in the plane of the Ecliptick, in which is likewise the centre of the Sun, therefore, if we should fancy to our selves the body of the Sun to be cut thorow by the said plane, the section will appear to our eye a right line, which let be BOD, and upon that a perpendicular being let fall AOC, it shall be the Axis of the said Ecliptick, and of the annual motion of the Terrestrial Globe. Let us next suppose the Solar body (without changing centre) to revolve in it self, not about the Axis AOC (which is the erect Axis upon the plane of the Ecliptick) but about one somewhat inclined, which let be this EOI, the which fixed and unchangeable Axis maintaineth it self perpetually in the same inclination and direction towards the same points of the Firmament, and of the Universe. And because, in the revolutions of the Solar Globe, each point of its superficies (the Poles excepted) describeth the circumference of a