Robert Grosseteste's colours

Here I am proposing a translation and discussion of the De Colore, one of the short scientific treatises written by Robert Grosseteste. In this very short treatise of the mid-1220s, Grosseteste continued the discussion on light and colours he started in the De Iride. He describes two manners of counting colours: one gives an infinity of tones, the other counts seven colours. In both cases, colours are created by the purity or impurity of the transparent medium when light is passing through it. This medieval framework survived until Newton's experiments with prisms.

INCIPIT: Color is light incorporated in a transparent medium. END: and so through the skill of combining all the modes, the colours that we want can be rendered visible. This is the end of the treatise on colours by a Lincolnian.
Color is light incorporated in a transparent medium. But, in fact, there are two different media: there are pure transparent media separated from earth materials or impure media mixed with them. The light, however, is four-fold differentiated: there is the bright and the obscure light, and the intense or the tenuous light. I do not say that an intense light is a light diffused by a great object, but it is the light that we can observe in a point where a large amount of it is collected by means of a concave mirror, and the light falling on the entire surface of the mirror facing the sun is reflected in the center of the sphere of the mirror. And then the power of light collected in this center ignites immediately a combustible material.
First of all, we find that concave mirrors and the focusing of rays were well known. Let us tell also that Grosseteste's "lux multa" is the intensity of light, because he is clearly referring to the focus of the mirror, where we can have a "radiorum multiplicatio", because in the focus we collect several rays of light. Grosseteste is distinguishing pure and impure transparent media, impure because of the mixture with earth materials. "Earth" is one of the four classical elements in ancient Greek philosophy and science, commonly associated with qualities of heaviness and matter. Here we can associate the earth materials to the defects and the impurities that we have in transparent media such as crystals. However, since Grosseteste is discussing about colours, we could also suppose that he was trying to merge the pure colours that we can see in the dispersion by a prism to those that we can obtain using pigments. We have for instance the earth pigments for painting, some of them well known since prehistoric times. The clay earth pigments, ochre and sienna for instance, are naturally occurring minerals, principally iron oxides. For what concerns the dispersion of light from prisms, this was a phenomenon described even in the Natural History by Pliny [9]. Since this book was one of the ancient books that the scholars of the Middle Age used for their treatises on Nature, it is quite probable that Grosseteste experimented with prisms, even if he did not discuss the phenomenon in his treatises. "Et hic intendebat Philosophus per 'nigredinem' privationem albedinis", wrote Henricus Bate, a Flemish astronomer around 1300 [10], in his Speculum divinorum et quorundam naturalium [11]. Of course, we could imagine a symbolic meaning too [12]. In the early Middle Ages, Ref.12 tells that black was commonly associated with darkness and evil. Clothes of black colour were worn by Benedictine monks as a sign of humility and penitence. In the 12th century a theological dispute about the colours of clothes broke out between the Cistercian monks, who wore white, and the Benedictines. Pierre the Venerable, a Benedictine, accused the Cistercians of excessive pride in wearing white, but Saint Bernard of Clairvaux, founder of the Cistercians, replied that black was the color of the devil, while white represented purity and "all the virtues" [12,13]. Let us also note that albedo is one of the four major stages of the "magnum opus" of the alchemy; along with nigredo, citrinitas and rubedo. From the nigredo stage, the alchemist undertakes a purification in albedo, passing through a chromatic sequence [14].
It also follows from this speech, that the colors near the white, in which we can arrive regressing from the whiteness and by variation, are seven, no more, no fewer. Similarly, there will be seven colours near the black, which we find when progressing from darkness towards whiteness, until we have a combination with the other seven colors, to which we arrive descending from white. Since the essence of whiteness is made of three features, the intensity of light, its brightness and the purity of the transparent medium, two of them remaining fixed as we like, the third can be relaxed, and then this is how three colours are created, or anyone of these three features remains fixed, and the other two relaxed, and so will have other three colors, besides the three colors of the first triple generation; or all the three features are at the same time relaxed, and so the overall seven colors from the whiteness will directly obtained.
Let us consider the white as given by brightness, intensity and purity: we can relax one, two or all these three features to obtain seven colours, as in the calculus of combinations shown in the

to be intensified and released, that is, the intensity, the brightness of light and the purity of transparent media and their opposites, the colours that can be made are nine; by counting the degrees of tension and remission will be an infinite number of tones of intensity. Now then, it is clear to whom who knew deeply and inwardly the principles of the natural science and of optics, not only by reasoning, but also by experience, that we have, according to the manner stated above, the essence of colours and their multitude. That is, knowing how to form a transparent medium, whether it were pure or impure, in such a way to receive a bright light, or, if it is preferred a dark light, and through the devised form in this very transparent medium, the light is reduced, or multiplied at pleasure; and so through the skill of combining all the modes, the colours that we want can be rendered visible. This is the end of the treatise on colours by a Lincolnian.
The procedure shown in the Figure 1 from white, can be used to ascending from black to obtain seven colours. At Ref. 15, there is a quite interesting image related to the Grosseteste's theory, which is adapted in the Figure 2. We see that, from white we have seven colours, and seven colours from black. But these colours move on two cones, merging in the middle, where we have seven "average" colours. White, black and these seven colours give the nine colours mentioned by Grosseteste. However, he counted the colours in two manners: the first is that based on combinations (Figure 1), the second is based on a continuous scale of tones, as we can have in the palette of the Paint software. As shown in the Figure 3 we have an infinite number of greens: in any case, it is the green. Let me note that recently, a discussion of the Grosseteste's colours in the RGB space has been proposed in Ref. 16. In the paper, the authors are arguing that the colour space described by Grosseteste is explicitly three-dimensional. For what concerns the Latin text, let us note that Grosseteste is using to describe the light the terms lux and lumen. In Ref. 17, it is proposed that lux is light in its source, whereas lumen is reflected or radiated light. In the Figure 2, adapted from [15], we see a circle of colours obtained considering the average of the colours coming from white and black. Sir Isaac Newton proposed a circle of colours containing seven colours too. He called them Aureus, Flavus, Viridis, Caeruleus, Indicus, Violaceus and Rubeus. Newton used seven colours by analogy to the number of notes in a musical scale [18]. It would be interesting a comparison of Newton's colours with those of Grosseteste. However, Grosseteste did not provide the name of them, besides one, the Hyacinthus which is a violaceus (violet) color.
We can ask ourselves whether the Grosseteste's work had some influences until the Newton's times or not. It seems that this is so, as we can find in the book on the life of Sir Isaac Newton, written by David Brewster [19]. Let us consider what Brewster is telling on colours. He reports that Newton's friend and tutor, Isaac Barrow (1630-1677), delivered some optical lectures, which were published in 1669. "In the preface of this work -Brewster writes -he acknowledges his obligations to his colleague, Mr. Isaac Newton, for having revised the manuscripts, and corrected several oversights, and made some important suggestions. In the twelfth lecture there are some observations on the nature and origin of colours … According to Dr. Barrow, White is that which discharges a copious light equally clear in every direction; Black is that which does not emit light at all, or which does it very sparingly. Red is that which emits a light more clear than usual, but interrupted by shady interstices. Blue is that which discharges a rarified light, as in bodies which consist of white and black particles arranged alternately. Green is nearly allied to blue. Yellow is a mixture of much white and a little red; and Purple consists of a great deal of blue mixed with a small portion of red. The blue colour of the sea arises from the whiteness of the salt which it contains, mixed with the blackness of the pure water in which the salt is dissolved; and the blueness of the shadows of bodies, seen at the same time by candle and daylight, arises from the whiteness of the paper mixed with the faint light or blackness of the twilight". [19] Here we find that the Grosseteste's framework of the combinations of the features of light (copious and clear) and of transparent media (pure or not) is maintained in the Barrow's approach to colours. The first Newton's studies on prisms were made on 1666, aiming to improve the optical instruments, in particular telescopes. He found the white light a mixture of colours refracted differently by a transparent medium. Experimenting with two prisms, he showed that a second prism can be used to put back together the light into white light [19]. If the origin of colours were the impurity of the transparent medium, this recombination would be impossible. Newton therefore, with his experiments, disrupted the medieval framework of optics, showing that it is not the purity or impurity of a medium that, interacting with light, gives the colours, but the different refractions of the components of the white light. Figure 1: The colours can be created by white, which is brightness, intensity and purity. We can relax one, two or all these three features to obtain seven colours, as in the calculus of combinations. The relaxation of one of the white features is rendered by a grey circles. The same we can do from the black. Figure 2: The seven colours from white and the seven colours from black are merging in "average" colours, which gives a circle of seven colours [15]. White, black and these seven colours provide nine colours. Figure 3 -An example from the palette of Paint software. We see a light green and a dark green. In any case, it is green.