notes on Optics or on Perspective as bear exclusively
on Mathematics or Physics could not be included in
the arrangement of the
libro di pittura which
is here presented to the reader. They are however
but few.]. But its axioms being laid down at
great length, I shall abridge them to a conclusive
brevity, arranging them on the method both of their
natural order and of mathematical demonstration; sometimes
by deduction of the effects from the causes, and sometimes
arguing the causes from the effects; adding also to
my own conclusions some which, though not included
in them, may nevertheless be inferred from them.
Thus, if the Lord—who is the light of all
things—vouchsafe to enlighten me, I will
treat of Light; wherefore I will divide the present
work into 3 Parts [Footnote: 10. In the
middle ages—for instance, by ROGER BACON,
by VITELLONE, with whose works Leonardo was certainly
familiar, and by all the writers of the Renaissance
Perspective and Optics were not regarded as distinct
sciences. Perspective, indeed, is in its widest
application the science of seeing. Although to
Leonardo the two sciences were clearly separate, it
is not so as to their names; thus we find axioms in
Optics under the heading Perspective. According
to this arrangement of the materials for the theoretical
portion of the
libro di pittura propositions
in Perspective and in Optics stand side by side or
occur alternately. Although this particular chapter
deals only with Optics, it is not improbable that the
words
partiro la presente opera in 3 parti
may refer to the same division into three sections
which is spoken of in chapters 14 to 17.].
The plan of the book on Painting (14—17).
14.
ON THE THREE BRANCHES OF PERSPECTIVE.
There are three branches of perspective; the first
deals with the reasons of the (apparent) diminution
of objects as they recede from the eye, and is known
as Diminishing Perspective.—The second
contains the way in which colours vary as they recede
from the eye. The third and last is concerned
with the explanation of how the objects [in a picture]
ought to be less finished in proportion as they are
remote (and the names are as follows):
Linear Perspective. The Perspective of Colour.
The Perspective of
Disappearance.
[Footnote: 13. From the character of the
handwriting I infer that this passage was written
before the year 1490.].
15.
ON PAINTING AND PERSPECTIVE.
The divisions of Perspective are 3, as used in drawing;
of these, the first includes the diminution in size
of opaque objects; the second treats of the diminution
and loss of outline in such opaque objects; the third,
of the diminution and loss of colour at long distances.
[Footnote: The division is here the same as in
the previous chapter No. 14, and this is worthy of
note when we connect it with the fact that a space
of about 20 years must have intervened between the
writing of the two passages.]