Page 31 of 443 _II. Linear Perspective. - The Notebooks of Leonardo Da Vinci

81.

HOW THE INNUMERABLE RAYS FROM INNUMERABLE IMAGES CAN CONVERGE TO A POINT.

Just as all lines can meet at a point without interfering with each other--being without breadth or thickness--in the same way all the images of surfaces can meet there; and as each given point faces the object opposite to it and each object faces an opposite point, the converging rays of the image can pass through the point and diverge again beyond it to reproduce and re-magnify the real size of that image. But their impressions will appear reversed--as is shown in the first, above; where it is said that every image intersects as it enters the narrow openings made in a very thin substance.

Read the marginal text on the other side.

In proportion as the opening is smaller than the shaded body, so much less will the images transmitted through this opening intersect each other. The sides of images which pass through openings into a dark room intersect at a point which is nearer to the opening in proportion as the opening is narrower. To prove this let _a b_ be an object in light and shade which sends not its shadow but the image of its darkened form through the opening _d e_ which is as wide as this shaded body; and its sides _a b_, being straight lines (as has been proved) must intersect between the shaded object and the opening; but nearer to the opening in proportion as it is smaller than the object in shade. As is shown, on your right hand and your left hand, in the two diagrams _a_ _b_ _c_ _n_ _m_ _o_ where, the right opening _d_ _e_, being equal in width to the shaded object _a_ _b_, the intersection of the sides of the said shaded object occurs half way between the opening and the shaded object at the point _c_. But this cannot happen in the left hand figure, the opening _o_ being much smaller than the shaded object _n_ _m_.

It is impossible that the images of objects should be seen between the objects and the openings through which the images of these bodies are admitted; and this is plain, because where the atmosphere is illuminated these images are not formed visibly.

When the images are made double by mutually crossing each other they are invariably doubly as dark in tone. To prove this let _d_ _e_ _h_ be such a doubling which although it is only seen within the space between the bodies in _b_ and _i_ this will not hinder its being seen from _f_ _g_ or from _f_ _m_; being composed of the images _a_ _b_ _i_ _k_ which run together in _d_ _e_ _h_.

[Footnote: 81. On the original diagram at the beginning of this chapter Leonardo has written "_azurro_" (blue) where in the facsimile I have marked _A_, and "_giallo_" (yellow) where _B_ stands.]

[Footnote: 15--23. These lines stand between the diagrams I and III.]

[Footnote: 24--53. These lines stand between the diagrams I and II.]

[Footnote: 54--97 are written along the left side of diagram I.]