Optics

...and we declare all natural influences from subject bodies to other bodies by way of a certain mode of reflection. For in these diversities the operation of nature is hidden, and from the same agents, according to the mode of this diversity, a diversity of forms occurs; and it happens to sights, if they should come to the place of reflection, that reflection occurs toward them: since, as sights are something posterior to natural forms and existing bodies, their presence adds nothing to natural things. Therefore, we have set forth the common passions of these speculorum [mirrors], and all the properties of plane mirrors, in the fifth book. In the sixth book, indeed, we demonstrate the passions which happen to sights and to things from the reflectione [reflection] made by convex spherical mirrors. In the seventh, we have placed the passions occurring from convex columnar or pyramidal mirrors, and we have joined these two mirrors together because of the conformity of many of their passions. In the eighth, we have treated more at length concerning the reflections which are made from concave spherical mirrors. In the ninth also, concerning those which are made from concave columnar or pyramidal mirrors. And in the same book, we have added a treatise concerning certain irregular mirrors, from whose total surface the reflection of light and power occurs to a single point, which mirrors we call burning mirrors. In the tenth book of this science, indeed, we deal with the third mode of seeing, which is through a medium of another transparent substance, as when vision occurs through air under water or under glass; and concerning the deceptions which happen to sight because of this: for even if sight were not present, the same passions happen to the acting power. And in this tenth treatise we have also added a passion occurring to sight alone from the diversity of media, such as the impression of the bow of the demon, which is called the iris [rainbow]: since its generation also has its origin from this present science. And so, having touched upon almost all the generable passions of visible things, we give an end to the work.

It is clear, therefore, from the premises, that the mode of seeing is threefold. One is through only one medium, which is uisio directa [direct vision]. Another, indeed, is through the reflectionem [reflection] of visible forms from polished bodies. Another, indeed, is through the refractionem [refraction] of visible forms because of the diversity of media. These three modes of seeing are also a sign of the threefold action of forms and of all celestial and natural powers. For some act directly upon a susceptible object, and this action is stronger, because it is directly intended by nature, and occurs according to straight lines. However, it happens to that power, when there is a bodily weakness, because of a greater distance of the agent from the act itself. For the Sun does not heat more distant things as much as closer heatable things which are of the same disposition. Another natural action, however, occurs through reflection from other bodies, as the rays of the Sun are reflected from the body of the Moon: for although, because of the rarity of the lunar body, some solar power passes through, nevertheless most of the rays are reflected downward, as if from a convex spherical mirror. Therefore, everything that we have said regarding the passions of mirrors is applicable to that action, the figure of the body from which reflection occurs assimilating itself to a specular figure. The third kind of natural actions, indeed, is through several media of different transparent substances, which similarly receives a diversity in its mode of acting, which we shall say happens to sights. In these natural actions, therefore, sight is a sign, not a cause, unless perhaps a deception occur proceeding through itself in sight: since, even if visual perception did not exist, the modes of all natural actions are the same.

These things having been premised, let us approach our purpose. Nevertheless, we do not wish this to be hidden from the reader: that when we argue from the book of the Elementorum Euclidis [Elements of Euclid], we are content with the naming of only the book number and the theorem. When, however, we bring forward something from this book of ours, we name both the number and the theorem of this book.