between the first braccia and the second.

[Footnote: This chapter is included in DUFRESNE'S and MANZI'S
editions of the Treatise on Painting. H. LUDWIG, in his commentary,
calls this chapter "_eines der wichtigsten im ganzen Tractat_", but
at the same time he asserts that its substance has been so
completely disfigured in the best MS. copies that we ought not to
regard Leonardo as responsible for it. However, in the case of this
chapter, the old MS. copies agree with the original as it is
reproduced above. From the chapters given later in this edition,
which were written at a subsequent date, it would appear that
Leonardo corrected himself on these points.]

100.

OF THE DIMINUTION OF OBJECTS AT VARIOUS DISTANCES.

A second object as far distant from the first as the first is from
the eye will appear half the size of the first, though they be of
the same size really.

OF THE DEGREES OF DIMINUTION.

If you place the vertical plane at one braccio from the eye, the
first object, being at a distance of 4 braccia from your eye will
diminish to 3/4 of its height at that plane; and if it is 8 braccia
from the eye, to 7/8; and if it is 16 braccia off, it will diminish
to 15/16 of its height and so on by degrees, as the space doubles
the diminution will double.