The siphon must be moved full and on solid wheels.

Every twenty or twenty-five braccia the retaining wall must have an opening of 2/3 of a braccio, in order to be able to clean the embankment and throw away the material.

At the mouth of the canal at Brivio let there be an inscription.

In cutting the rock, let 3 siphons be set with 6 gantries, and let one begin at the very top of the rock, and let them all descend to one and the same level. But here a difficulty arises in drawing them back up when one wishes to begin the cut again; yet it is done, because the stones that descend do not ...

8 5 8 water 6 air
7 7

* That body shows itself heavier which has the weaker resistance.

* If the body placed on the water is heavier than air rather than lighter than water, it will stand with a greater part within the water than within the air.

* A body heavier than air and lighter than water by equal differences will stand as much within the air as within the water, such a heavy body being of spherical shape.

* But if it is heavier than air rather than lighter than water, it will stand more within the water than within the air.

The gantry can first prepare the road at each step by which it is to be moved, and then work from the other side.

If it is not made known that this is a public canal, it will be necessary to pay for the land; and the king will pay for it by remitting the duties of one year.

Let each gantry be set facing the cut that looks toward the boat-channel; and let such gantries never descend, but let each have its motion by being drawn backward at the same height from which it first worked, down to the bottom of the canal. This is done so as not to have to raise and lower the gantry, because it is much easier to lengthen the rope behind the 'monk' [pulley-post] than for the gantry to have to descend behind that 'monk'.

For the movement made at the level of each gantry the road will be prepared by hand, placing beams in the notches of the rock and levering with picks. The cut made by each gantry will be 10 braccia wide, and by this width the gantry can be shifted with a screw upon the frame on which it rests. And the cutting will pour its material through a channel of beams and discharge it into the Adda; and the gantries will be 4 and the siphons 2.

b a n c – d c – r e m f

That shadowy body will make its simple derivative shadow of greater base and of longer pyramid which is more remote from its luminous body. The first conclusion is proved: and we shall say that the first shadowy body a is nearer to the luminous body c f than the second shadowy body b r.

Among bodies of equal size, the one more remote from the luminous body will make the shadow-pyramid of longer figure. The converse follows, et cetera.

The nearer a shadowy body smaller than the luminous body comes to that luminous body, the smaller the quantity of that luminous body by which it is illuminated. The converse follows.

The nearer a shadowy body larger than the luminous body approaches the luminous body, the greater the quantity of that luminous body by which it is illuminated.

But if the shadowy body is equal to the luminous body, then the quantity that the one sees of the other will never vary with any variety of distance.

That part of the shadowy body will be more illuminated which is illuminated by a greater quantity of the luminous body.

a c b; d e

That part of a body is less illuminated which is more remote from its illuminator, no increase of luminous rays being added to it from the same luminous body.

One and the same luminous body shows itself of greater or lesser splendour according as it comes nearer to or more remote from the thing illuminated by it.

The outer sides of the compound derivative shadow are always seen by the whole luminous body. Never does any of the inner sides of the compound derivative shadow see any part of the luminous body.

The farther the converse pyramid created by the decomposed shadows moves away from its angle, the more of the luminous body it will see, but it will never see half of it — or it will see as much more than half as the luminous body is larger than the shadowy body.

The impact of the luminous ray, which penetrates into the concavity of the angle, never imprints that angle itself, but in place of it imprints a portion of a circle.

But if the angle is convex, then the impression of the obtuse angle will become an acute angle.

How the shadow of the obtuse angle becomes acute, with curved sides.

h m r o L a – g K – c – g ... S d f

The derivative shadow of the convex obtuse angle of straight sides becomes acute and of curved sides. And this is proved: let the luminous body be a h, all of whose rays see the obtuse angle c of the rectilinear triangle K g c, and thus the left ray a passes to the angle c and bends alongside.