Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/381

354345 [sic] facility apprehended in the Ptolomaick Systeme.

I neither ought, nor can deny any thing that Sagredus shall request: And the delay by me desired was to no other end, save only that I might have time once again to methodize those prefatory points, in my fancy, that serve for a large and plain declaration of the manner how the forenamed accidents follow, as well in the Copernican position, as in the Ptolomaick: nay, with much greater facility and simplicity in that than in this. Whence one may manifestly conceive that Hypothesis to be as easie to be effected by nature, as difficult to be apprehended by the understanding: yet neverthelesse, I hope by making use of another kind of explanation, than that used by Copernicus, to render likewise the apprehending of it somewhat lesse obscure. Which that I may do, I will propose certain suppositions of themselves known and manifest, and they shall be these that follow.

First, I suppose that the Earth is a spherical body, turning round upon its own Axis and Poles, and that each point assigned in its superficies, describeth the circumference of a circle, greater or lesser, according as the point assigned shall be neerer or farther from the Poles: And that of these circles the greatest is that which is described by a point equidistant from the said Poles; and all these circles are parallel to each other; and Parallels we will call them.

Secondly, The Earth being of a Spherical Figure, and of an opacous substance, it is continually illuminated by the Sun, according to the half of its surface, the other half remaining obscure, and the boundary that distinguisheth the illuminated part from the dark being a grand circle, we will call that circle the terminator of the light.

Thirdly, If the Circle that is terminator of the light should passe by the Poles of the Earth, it would cut (being a grand and principal circle) all the parallels into equal parts; but not passing by the Poles, it would cut them all in parts unequal, except only the circle in the middle, which, as being a grand circle will be cut into equal parts.

Fourthly, The Earth turning round upon its own Poles, the quantities of dayes and nights are termined by the arches of the Parallels, intersected by the circle, that is, the terminator of the light, and the arch that is scituate in the illuminated Hemisphere prescribeth the length of the day, and the remainer is the quantity of the night.

These things being presupposed, for the more clear understanding of that which remaines to be said, we will lay it down in a Figure. And first, we will draw the circumference of a circle, that shall represent unto us that of the grand Orb descri-