Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/331

 I must confesse that all that which Salviatus hath spoken is new unto me, for truth is, I never have had the curiosity to read those Books, nor have I hitherto given any great credit to the Telescope newly introduced; rather treading in the steps of other Peripatetick Philosophers my companions, I have thought those things to be fallacies and delusions of the Chrystals, which others have so much admired for stupendious operations: and therefore if I have hitherto been in an errour, I shall be glad to be freed from it, and allured by these novelties already heard from you, I shall the more attentively hearken to the rest.

The confidence that these men have in their own apprehensivenesse, is no less unreasonable than the small esteem they have of the judgment of others: yet its much that should esteem themselves able to judge better of such an instrument, without ever having made trial of it, than those who have made, and daily do make a thousand experiments of the same: But I pray you, let us leave this kind of pertinacious men, whom we cannot so much as tax without doing them too great honour. And returning to our purpose, I say, that resplendent objects, whether it is that their light doth refract on the humidity that is upon the pupils, or that it doth reflect on the edges of the eye-browes, diffusing its reflex rayes upon the said pupils, or whether it is for some other reason, they do appear to our eye, as if they were environ'd with new rayes, and therefore much bigger than their bodies would represent themselves to us, were they divested of those irradiations. And this aggrandizement is made with a greater and greater proportion, by how much those lucid objects are lesser and lesser; in the same manner for all the world, as if we should suppose that the augmentation of shining locks were v. g. four inches, which addition being made about a circle that hath four inches diameter would increase its appearance to nine times its former bignesse: but

I believe you would have said three times; for adding four inches to this side, and four inches to that side of the diameter of a circle, which is likewise four inches, its quantity is thereby tripled, and not made nine times bigger.

A little more Geometry would do well,Simplicius. True it is, that the diameter is tripled, but the superficies, which is that of which we speak, increaseth nine times: for you must know, Simplicius, that the superficies of circles are to one another, as the squares of their diameters; and a circle that hath four inches diameter is to another that hath twelve, as the square of four to the square of twelve; that is, as 16. is to 144. and therefore it shall be increased nine times, and not three; this, by way of advertisement to Simplicius. And proceeding forwards, if we should add