[Footnote: Diagrams are inserted before lines 2 and 4.]
218.
In all the proportions I lay down it must be understood that the medium between the bodies is always the same. [2] The smaller the
luminous body the more distinct will the transmission of the shadows be.
[3] When of two opposite shadows, produced by the same body, one is twice as dark as the other though similar in form, one of the two lights causing them must have twice the diameter that the other has and be at twice the distance from the opaque body. If the object is lowly moved across the luminous body, and the shadow is intercepted at some distance from the object, there will be the same relative proportion between the motion of the derived shadow and the motion of the primary shadow, as between the distance from the object to the light, and that from the object to the spot where the shadow is intercepted; so that though the object is moved slowly the shadow moves fast.
[Footnote: There are diagrams inserted before lines 2 and 3 but they are not reproduced here. The diagram above line 6 is written
upon as follows: at A lume (light), at B obbietto (body), at C ombra d'obbietto (shadow of the object).]
219.
A luminous body will appear less brilliant when surrounded by a bright background.
[2] I have found that the stars which are nearest to the horizon look larger than the others because light falls upon them from a larger proportion of the solar body than when they are above us; and having more light from the sun they give more light, and the bodies which are most luminous appear the largest. As may be seen by the sun through a mist, and overhead; it appears larger where there
is no mist and diminished through mist. No portion of the luminous body is ever visible from any spot within the pyramid of pure derived shadow.
[Footnote: Between lines 1 and 2 there is in the original a large diagram which does not refer to this text. ]
220.
A body on which the solar rays fall between the thin branches of trees far apart will cast but a single shadow.
[2] If an opaque body and a luminous one are (both) spherical the base of the pyramid of rays will bear the same proportion to the luminous body as the base of the pyramid of shade to the opaque body.
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[4] When the transmitted shadow is intercepted by a plane surface placed opposite to it and farther away from the luminous body than from the object [which casts it] it will appear proportionately darker and the edges more distinct.
[Footnote: The diagram which, in the original, is placed above line 2, is similar to the one, here given on page 73 (section 120).--The
diagram here given in the margin stands, in the original, between lines 3 and 4.]
221.
A body illuminated by the solar rays passing between the thick branches of trees will produce as many shadows as there are branches between the sun and itself.
Where the shadow-rays from an opaque pyramidal body are intercepted they will cast a shadow of bifurcate outline and various depth at the points. A light which is broader than the apex but narrower than the base of an opaque pyramidal body placed in front of it, will cause that pyramid to cast a shadow of bifurcate form and various degrees of depth.
If an opaque body, smaller than the light, casts two shadows and if it is the same size or larger, casts but one, it follows that a py-
ramidal body, of which part is smaller, part equal to, and part larger than, the luminous body, will cast a bifurcate shadow.
[Footnote: Between lines 2 and 3 there are in the original two large diagrams.]
IV.
Perspective of Disappearance.
The theory of the "Prospettiva de' perdimenti" would, in many important details, be quite unintelligible if it had not been led up by the principles of light and shade on which it is based. The word "Prospettiva" in the language of the time included the principles of optics; what Leonardo understood by "Perdimenti" will be clearly seen in the early chapters, Nos. 222--224. It is in the very nature of the case that the farther explanations given in the subsequent chapters must be limited to general rules. The sections given as
227--231 "On indistinctness at short distances" have, it is true, only an indirect bearing on the subject; but on the other hand, the following chapters, 232--234, "On indistinctness at great distances," go fully into the matter, and in chapters 235--239, which treat "Of the importance of light and shade in the Perspective of Disappearance", the practical issues are distinctly insisted on in their relation to the theory. This is naturally followed by the statements as to "the effect of light or dark backgrounds on the apparent size of bodies" (Nos. 240--250). At the end I have placed, in the order of the original, those sections from the MS. C which treat of the "Perspective of Disappearance" and serve to some extent to complete the treatment of the subject (251--262).
Definition (222. 223).
222.
OF THE DIMINISHED DISTINCTNESS OF THE OUTLINES OF OPAQUE BODIES.
If the real outlines of opaque bodies are indistinguishable at even a very short distance, they will be more so at long distances; and, since it is by its outlines that we are able to know the real form of any opaque body, when by its remoteness we fail to discern it as a whole, much more must we fail to discern its parts and outlines.
223.
OF THE DIMINUTION IN PERSPECTIVE OF OPAQUE OBJECTS.
Among opaque objects of equal size the apparent diminution of size will be in proportion to their distance from the eye of the spectator; but it is an inverse proportion, since, where the distance is greater, the opaque body will appear smaller, and the less the distance the larger will the object appear. And this is the fundamental principle of linear perspective and it follows:--[11]every object as it becomes more remote loses first those parts which are smallest. Thus of a horse, we should lose the legs before the head, because the legs are thinner than the head; and the neck before the body for the same reason. Hence it follows that the last part of the horse which would be discernible by the eye would be the mass of the body in an oval form, or rather in a cylindrical form and this would lose its apparent thickness before its length--according to the 2nd rule given above, &c. [Footnote 23: Compare line 11.].
If the eye remains stationary the perspective terminates in the distance in a point. But if the eye moves in a straight [horizontal] line
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the perspective terminates in a line and the reason is that this line is generated by the motion of the point and our sight; therefore it follows that as we move our sight [eye], the point moves, and as we move the point, the line is generated, &c.
An illustration by experiment.
224.
Every visible body, in so far as it affects the eye, includes three attributes; that is to say: mass, form and colour; and the mass is recognisable at a greater distance from the place of its actual existence than either colour or form. Again, colour is discernible at a greater distance than form, but this law does not apply to luminous bodies.
The above proposition is plainly shown and proved by experiment; because: if you see a man close to you, you discern the exact appearance of the mass and of the form and also of the colouring; if he goes to some distance you will not recognise who he is, because the character of the details will disappear, if he goes still farther you will not be able to distinguish his colouring, but he will appear as a dark object, and still farther he will appear as a very small dark rounded object. It appears rounded because distance so greatly diminishes the various details that nothing remains visible but the larger mass. And the reason is this: We know very well that all the images of objects reach the senses by a small aperture in the eye; hence, if the whole horizon a d is