Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/332

 the said irradiation of four inches to a circle that hath but two inches of diameter onely, the diameter of the irradiation or Garland would be ten inches, and the superficial content of the circle would be the area of the naked body, as 100. to 4. for those are the squares of 10. and of 2. the agrandizement would therefore be 25. times so much; and lastly, the four inches of hair or fringe, added to a small circle of an inch in diameter, the same would be increased 81. times; and so continually the augmentations are made with a proportion greater and greater, according as the real objects that increase, are lesser and lesser.

The doubt which puzzled Simplicius never troubled me, but certain other things indeed there are, of which I desire a more distinct understanding; and in particular, I would know upon what ground you affirm that the said agrandizement is alwayes equal in all visible objects.

I have already declared the same in part, when I said, that onely lucid objects so increased, and not the obscure; now I adde what remaines, that of the resplendent objects those that are of a more bright light, make the reflection greater and more resplendent upon our pupil; whereupon they seem to augment much more than the lesse lucid: and that I may no more inlarge my self upon this particular, come we to that which the true Mistris of Astronomy, Experience, teacheth us. Let us this evening, when the air is very obscure, observe the star of Jupiter; we shall see it very glittering, and very great; let us afterwards look through a tube, or else through a small trunk, which clutching the hand close, and accosting it to the eye, we lean between the palm of the hands and the fingers, or else by an hole made with a small needle in a paper; and we shall see the said star divested of its beams, but so small, that we shall judge it lesse, even than a sixtieth part of its great glittering light seen with the eye at liberty: we may afterwards behold the Dog-stars beautiful and bigger than any of the other fixed stars, which seemeth to the bare eye no great matter lesse than Jupiter; but taking from it, as before, the irradiation, its Discus will shew so little, that it will not be thought the twentieth part of that of Jupiter, nay, he that hath not very good eyes, will very hardly discern it; from whence it may be rationally inferred, that the said star, as having a much more lively light than Jupiter, maketh its irradiation greater than Jupiter doth his. In the next place, as to the irradiation of the Sun and Moon, it is as nothing, by means of their magnitude, which possesseth of it self alone so great a space in our eye, that it leaveth no place for the adventitious rayes; so that their faces seem close clipt, and terminate. We may assure our selves of the same truth by another experiment which I have often made triall of;