Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/353

 Orb. And because the distance of the Sun from the Earth, contains by common consent 1208. Semidiameters of the said Earth, and the distance of the fixed Stars (as hath been said) 2160. Semediameters of the grand Orb, therefore the Semidiameter of the Earth is much greater (that is almost double) in comparison of the grand Orb, than the Semidiameter of the grand Orb, in relation to the distance of the Starry Sphære; and therefore the variation of aspect in the fixed Stars, caused by the Diameter of the grand Orb, can be but little more observable, than that which is observed in the Sun, occasioned by the Semidiameter of the Earth.

This is a great fall for the first step.

It is doubtlesse an errour; for a fixed Star of the sixth magnitude, which by the computation of this Authour, ought, for the upholding the proposition of Copernicus, to be as big as the whole grand Orb, onely by supposing it equal to the Sun, which Sun is lesse by far, than the hundred and six millionth part of the said grand Orb, maketh the starry Sphære so great and high as sufficeth to overthrow the instance brought against the said Copernicus.

Favour me with this computation.

The supputation is easie and short. The Diameter of the Sun, is eleven semidiameters of the Earth, and the Diameter of the grand Orb, contains 2416. of those same semidiameters, by the ascent of both parties; so that the Diameter of the said Orb, contains the Suns Diameter 220. times very near. And because the Spheres are to one another, as the Cubes of their Diameters, let us make the Cube of 220. which is 106480000. and we shall have the grand Orb, an hundred and six millions, four hundred and eighty thousand times bigger than the Sun, to which grand Orb, a star of the sixth magnitude, ought to be equal, according to the assertion of this Authour.

The errour then of these men, consisteth in being extreamly mistaken, in taking the apparent Diameter of the fixed Stars.

This is one, but not the onely errour of them; and indeed, I do very much admire how so many Astronomers, and those very famous, as are Alfagranus, Albategnus, Tebizius, and much more modernly the Tycho's and Clavins's, and in sum, all the predecessors of our Academian, should have been so grosly mistaken, in determining the magnitudes of all the Stars, as well fixed as moveable, the two Luminaries excepted out of that number; and that they have not taken any heed to the adventitious irradiations that deceitfully represent them an hundred and more times bigger, than when they are beheld, without those capilli-