136.

The relations of luminous to illuminated bodies.

The middle of the light and shade on an object in light and shade is opposite to the middle of the primary light.  All light and shadow expresses itself in pyramidal lines.  The middle of the shadow on any object must necessarily be opposite the middle of its light, with a direct line passing through the centre of the body.  The middle of the light will be at a, that of the shadow at b. [Again, in bodies shown in light and shade the middle of each must coincide with the centre of the body, and a straight line will pass through both and through that centre.]

[Footnote:  In the original MS., at the spot marked a of the first diagram Leonardo wrote primitiuo, and at the spot marked c—­primitiva (primary); at the spot marked b he wrote dirivatiuo and at d deriuatiua (derived).]

Experiments on the relation of light and shadow within a room (137—­140).

137.

SHOWS HOW LIGHT FROM ANY SIDE CONVERGES TO ONE POINT.

Although the balls a b c are lighted from one window, nevertheless, if you follow the lines of their shadows you will see they intersect at a point forming the angle n.

[Footnote:  The diagram belonging to this passage is slightly sketched on Pl.  XXXII; a square with three balls below it.  The first three lines of the text belonging to it are written above the sketch and the six others below it.]

138.

Every shadow cast by a body has a central line directed to a single point produced by the intersection of luminous lines in the middle of the opening and thickness of the window.  The proposition stated above, is plainly seen by experiment.  Thus if you draw a place with a window looking northwards, and let this be s f, you will see a line starting from the horizon to the east, which, touching the 2 angles of the window o f, reaches d; and from the horizon on the west another line, touching the other 2 angles r s, and ending at c; and their intersection falls exactly in the middle of the opening and thickness of the window.  Again, you can still better confirm this proof by placing two sticks, as shown at g h; and you will see the line drawn from the centre of the shadow directed to the centre m and prolonged to the horizon n f.

[Footnote:  B here stands for cerchio del’ orizonte tramontano on the original diagram (the circle of the horizon towards the North); A for levante (East) and C for ponete (West).]

139.

Every shadow with all its variations, which becomes larger as its distance from the object is greater, has its external lines intersecting in the middle, between the light and the object.  This proposition is very evident and is confirmed by experience.  For, if a b is a window without any object interposed, the luminous atmosphere to the right hand at a is seen to the left at d.  And the atmosphere at the left illuminates on the right at c, and the lines intersect at the point m.