The Mixed Sciences and Perspective

But there are other (very many) methodical arts, which, declining from the purity, simplicity, and immateriality of our principal science of magnitudes, do nevertheless use the great aid, direction, and method of the said principal science, and have proper names, distinct both from the science of geometry (from which they are derived) and from one another: such as perspective, astronomy, music, Cosmography, astrology, statics, anthropography, Trochilike, Helicosophy, Pneumatithmie, Menadrie, Hypogeiodie, Hydragogie, horometry, painting, architecture, navigation, Thaumaturgike and Archemastrie. I think it necessary to give, in order, some particular description of these, and also to touch on some of their useful applications, and so to make this preface a little sweet, pleasant nosegay for you: to comfort your spirits when they are almost out of courage and in despair (through a brutish turn of mind), supposing that geometry has served only for the building of a house, or an ornate bridge, or the roof of Westminster Hall, or some clever little device or engine suited to a carpenter or a joiner, etc. That things are far otherwise than the world has commonly judged them, to this day, will be well proved both in word and in deed.

Among these arts, by good reason, perspective ought to be had before perfect knowledge of astronomical appearances can be attained. And because light holds the prerogative as the first of God's creatures, and the eye is the light of our body, whose sense is the mightiest and whose organ is the most skillful and geometric, we will begin, therefore, with perspective. Perspective is a mathematical art which demonstrates the manner and properties of all radiations—direct, broken, and reflected. This description, or statement, is brief, but it reaches as far as the world is wide. It concerns all creatures, all actions and passions brought about by the emanation of rays. By rays, or natural lines, I mean here not only those of light or color (though these give the eye appearance, witness, and proof on which to ground the art) but also the certain and determined active radial emanations of other forms, both substantial and accidental. Through this art (setting aside its highest points) we may use our eyes and the light with greater pleasure and more perfect judgment, both of things seen in light and of other things, which work and produce their effects by the same order of the radiation of lights. We should be ashamed to be ignorant of the cause of the many ways our eye is deceived and misled: as when the eye takes a round globe or sphere, far off, to be a flat plain circle, and likewise judges a flat square to be round; supposes parallel walls to draw together at a distance; and takes roof and floor, parallel to each other, the one to bend downward and the other to rise up, at a little distance from you. Again, of things moving at equal speed, to think the nearer moves faster and the farther much slower. And of two things, one of which moves incomparably faster than the other, to judge the slower to move very swiftly and the other to stand still—what an error is this of our eye! Of the rainbow: of its colors, the order of the colors, its size, its place and height, etc.—to know the demonstrative causes, is it not pleasant, is it not necessary? Of two or three suns appearing, of blazing stars, and such things, brought to pass by natural causes (and yet, nevertheless, significant of matters beyond): is it not useful for humankind to know the very true cause and the natural occasion? Is it not, rather, greatly beneath the dignity of human nature to be so misled and deceived by things at hand, before one's eyes: as with a peacock's tail and a dove's neck, or a whole oar held in water seeming broken? Distant things seeming near, and near things seeming distant. Small things seeming great, and great things seeming small. One man seeming an army. Or a person being terribly afraid of his own shadow. Yes, to fear so much that, if you are alone near a certain mirror and make as if to thrust at it with a dagger or sword, you will suddenly be moved to draw back, as it were, by reason of an image,

A marvelous mirror.

appearing in the air between you and the mirror, with the same hand, sword or dagger, and with equal quickness, lunging at your very eye just as you do at the mirror. Strange this is to hear of, but more marvelous to see than these words of mine can express. And yet by optical demonstration the order and cause of it are made certain, even as its effect follows from it. Yes, this much more I dare undertake, toward satisfying the noble spirit that longs ardently for the wisdom of natural causes: to let him understand that in London he may with his own eyes have proof of what I have said here. A gentleman (who, for the good service he has done his country, is famous and honorable:

and for skill in the mathematical sciences and languages is the odd man of this land, etc.) Even he is able, and I am sure will very willingly, let the mirror and the proof be seen; and so I here request it of him: for the increase of wisdom among the honorable, for the stopping of malicious mouths, and for the repressing of the arrogance of the ignorant. You may easily guess what I mean. This art of perspective is of such excellence, and may be led to the establishing and carrying out of such things as no one would readily believe without actual proof perceived. I say nothing of natural philosophy, which, without perspective, cannot be fully understood nor perfectly attained. Nor of astronomy, which, without perspective, cannot well be grounded; nor of astrology, verified and confirmed on natural grounds. That part of it which deals with mirrors (the word mirror being, in this art, a general name for anything from which a ray bounces back) is called catoptrics, and has so many uses, both marvelous and profitable, that it would keep me too long to note the principal conclusions already known in it; and also some things might perhaps lack due credit with you, and I would by that lose my labor, and you would slip into a light judgment,

Before you have learned sufficiently the power of nature and art.

But there are very many other methodical arts. Departing from the purity, simplicity, and immateriality of our principal science of magnitudes, they still make great use of the help, direction, and method of that principal science, and they have their own names, distinct both from the science of geometry, from which they are derived, and from one another: such as perspective, astronomy, music, Cosmography, astrology, statics, anthropography, Trochilike, Helicosophy, Pneumatithmie, Menadrie, Hypogeiodie, Hydragogie, horometry, painting, architecture, navigation, Thaumaturgike, and Archemastrie. I think it necessary to describe these in order, and also to touch on some of their useful purposes, and so to make this Preface a little sweet, pleasant nosegay for you: to comfort your spirits when you are almost out of courage and in despair, through a brutish way of thinking, imagining that geometry had only served to build a house, or a fine bridge, or the roof of Westminster Hall, or some clever little device or engine belonging to a carpenter or a joiner, etc. The truth is far different from what the world has commonly judged, by word and deed, to this day, and good proof of that will be made.

Among these arts, perspective rightly ought to come first, before any perfect knowledge of astronomical appearances can be attained. And because of the special place of light, being the first of God's creations, and because the eye is the light of our body, our most powerful sense, and our most skillful and geometric organ, we will begin with perspective. Perspective is a mathematical art that demonstrates the manner and properties of all radiations: direct, broken, and reflected. This description is brief, but it reaches as far as the world is wide. It concerns all creatures, and all actions and passions performed by the emission of rays. By rays, or natural lines, I mean here not only rays of light or color — though these give the eye the appearance, witness, and proof on which to ground the art — but also the certain and determined active radial emissions of other forms, both substantial and accidental. By this art, leaving aside the highest points, we can use our eyes and the light with greater pleasure and better judgment: both of things seen in light and of other things, which work and produce their effects by the same order of light's radiations. We should be ashamed not to know the cause of the many ways our eye is deceived and misled: how the eye takes a round globe or sphere, seen from far off, to be a flat plain circle, and likewise judges a plain square to be round; supposes parallel walls to draw together from far away; and takes the roof and floor, the one to bend downward and the other to rise upward, when they are a little distance from you. Again, of things moving at the same speed, it thinks the nearer moves faster and the farther much slower. Or, of two things, one of which moves incomparably faster than the other, it judges the slower to move very fast and the other to stand still: what an error of our eye! Of the rainbow — its colors, the order of the colors, its size, its place and height, etc. — is it not pleasant and necessary to know the demonstrative causes? Of two or three suns appearing, of blazing stars, and such like things, brought to pass by natural causes, and yet at the same time signifying matters beyond them: is it not useful for people to know their true and natural cause and occasion? In fact, is it not greatly beneath the dignity of human nature to be so tricked and misled by things at hand, before one's eyes? Such as a peacock's tail and a dove's neck; or a whole oar held in water, seeming broken. Things far off seeming near, and near seeming far off. Small things seeming great, and great things small. One man seeming like an army. Or a person terribly afraid of his own shadow. So much so that, if you are alone near a certain mirror and try to thrust at it with a dagger or sword, you will suddenly be moved to give back, in a manner, by reason of an Image,

A marvelous mirror.

appearing in the air between you and the mirror, with a like hand, sword or dagger, and with like quickness, thrusting at your very eye, just as you do at the mirror. This is strange to hear of, but more marvelous to see than these words of mine can express. And yet by optical demonstration the order and cause of it are just as certain as the effect that follows. I dare take it upon myself even further, to satisfy the noble courage that longs ardently for the wisdom of natural causes: to let him understand that in London he can have proof of what I have said here with his own eyes. A gentleman, who, for his good service to his country, is famous and honorable:

and for skill in the mathematical sciences and languages, is the extraordinary man of this land, etc. He himself is able, and I am sure will very willingly, let the mirror and the proof be seen, and so I ask it of him here: for the increase of wisdom among the honorable, for stopping the mouths of the malicious, and for repressing the arrogance of the ignorant. You can easily guess what I mean. This art of perspective is of such excellence, and can lead to the certifying and carrying out of such things as no one would easily believe without actual proof. I say nothing of natural philosophy, which without perspective cannot be fully understood nor perfectly attained. Nor of astronomy, which without perspective cannot be well grounded; nor of astrology, naturally verified and confirmed. That part of it which deals with glasses — where glass is a general name in this art for anything from which a ray rebounds — is called catoptrics, and has so many uses, both marvelous and profitable, that it would take me too long to note the principal conclusions already known. And also, perhaps, some things might lack due credit with you, and I would lose my labor, and you would slip into a hasty judgment,

Before you have learned enough of the power of nature and art.