Perspective Propositions and the Bisected Right Triangle
Near objects overlap far ones seen through an aperture; a right triangle halved and subdivided endlessly
The upper half of the sheet continues the perspective propositions: with the eye placed above, a lower but more distant object still appears higher than a nearer one, and the reverse holds when the eye is below; and a nearer small object can always cover or surround a larger, more distant one — proved by looking through a small aperture. The lower half turns to geometry: a right (orthogonal) triangle cut from the midpoint of one side to the opposite angle is divided into two equal halves, which Leonardo verifies by splitting them into four equal parts meeting at point l, then into eighths, concluding that such triangles can be subdivided into an even number of equal parts to infinity. A row of four labeled right triangles illustrates the successive divisions.
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A distant low object still looks higher (eye placed above)
No object farther away can be set so much lower than a nearer object — the eye being above — that the farther object will not appear the higher of the two. The companion proposition reverses the case for an eye placed below.
Near objects cover or surround distant larger ones
Distant objects are never so large that smaller, nearer ones do not cover them over or surround them; and looking at a farther square through the centre of a smaller, nearer one, the larger appears surrounded by the smaller.
Seeing a large thing through a small aperture
Proved by experience: through a small aperture nothing is so large that you cannot view it, and the thing seen appears bounded by the outer edges of the hole. Plug the hole, and that small plug is what blocks the view of the large thing.
A right triangle halved and subdivided to infinity (a b c; K l m; o p q)
An orthogonal triangle cut from the middle of one side to the opposite angle is always divided in half. Splitting the two parts into four that meet at point l shows them equal; if K l m is one quarter, o p q is one eighth, and such triangles can nest into one another an even number of times without end.