2. Mathesis Universalis. Recent studies of Leonar-
do's thought have tended to find the basis of Leonar-
do's universality in his distinctive fusion of mathe-
matics and sensory experience. Ernst Cassirer (1927),
Ludwig H. Heydenreich (1944), Erwin Panofsky
(1953), V. P. Zubov (1962), and Eugenio Garin (1965)
all stress the significance of Leonardo's geometric
formulation of technical and physical problems in ac-
counting for the scope and unity of his thought. This
also holds true for Alberti's artistic and scientific work.
Burckhardt was right in maintaining that Leonardo
brought to fulfillment what Alberti had begun, for
Alberti and Leonardo are very much akin. They were
both practicing artists, practicing surveyors and map-
makers, practicing engineers. Both figure in the history
of astronomy, geography, mechanics, anatomy, optics,
and perspective. Leonardo's chief art was painting,
of course, whereas Alberti's was architecture; and
Leonardo brought his mathematical vision to bear on
a greater variety of problems than Alberti did and he
penetrated them more deeply; but both had the same
intention of discovering in the world of experience its
lawful, proportional structure. This was the methodo-
logical objective that made it possible for them to unite
art and science, and theory and practice, as they did.
The diversity of their interests sprang in both cases
from a commitment to practice and experience, “the
common mother of all the sciences and arts”
(Leonardo, ed. Richter, I, # 18). And both used mathe-
matics in the several arts and sciences they pursued
as the instrument by which to grasp the rational prin-
ciples of experience. If the studia humanitatis may be
regarded as a revised and expanded Trivium, the disci-
plines comprehended by Alberti and Leonardo repre-
sent a Quadrivium systematically expanded to include
all the sciences of measurement.
Alike as they are in their artistic and scientific
pursuits, however, Alberti and Leonardo did not share
the same “universe” of learning. It is not simply that
Leonardo's thought includes sciences such as botany,
zoology, geology, and hydraulics which are either not
found at all, or found only in very rudimentary form,
in Alberti. What is more remarkable is Leonardo's utter
disregard of humanistic values and the classical, literary
method of humanistic study. Leonardo was, as he
confessed, an omo sanza lettere. But his disinterest in
the studia humanitatis and his strictures against book-
learning cannot be accounted for solely by the fact
that he was trained as an apprentice in a workshop
rather than educated, as Alberti was, in a humanistic
gymnasium. Self-taught in almost everything he did,
Leonardo would have mastered the humanistic learning
of the time had he been vitally interested in it. He
did teach himself Latin, in fact, when he was forty-two,
but he used it to gain access to the physical knowledge,
not the literary culture of antiquity and the Middle
Ages. The humanistic mode of learning was alien to
him because, as his work and statements prove, the
kind of knowledge he sought was to be found in nature,
not books. He restricted himself quite deliberately to
sperienza (by which he meant chiefly visual experi-
ence), having won from its mathematical analysis, so
he thought, the rare prize of certain knowledge.
This divergence between humanism and what was
to become in the scientific academies of the seven-
teenth century an independent, empirical-mathemat-
ical mode of inquiry, is not yet felt in Alberti. In many
respects, technical and empirical thought was still
more primitive in the early fifteenth century than it
had been in antiquity, so that Alberti found many
of his most fruitful technical ideas in the classical
authors. Moreover, his humanistic ideas mingle with
his artistic and mathematical ones at the deeper level
of his fundamental intuition of the world and man. The
idea of proportion which figures in his thought as an
ideal of morality and mores—an idea that echoes
Cicero's notion of decorum and Plato's idea of justice—
complements his vision of the “outer” world of nature.
Balance, measure, or proportion in man reflects the
definition Alberti gave of cosmic beauty, that natural
“Harmony of all the parts, in whatsoever subject it
appears, fitted together with such proportion and con-
nection that nothing can be added, diminished, or
altered but for the worse” (De re aedificatoria IX, 5).
Alberti's successor knew nothing of this vital bond
between the moral and the physical world, between
man and nature. The proportion or measure that con-
stitutes the form of both the inner and outer world
in Alberti's thought is metaphysically conceived, of
course, and Leonardo, who developed and sharpened
the empirical-mathematical method he shared with
Alberti, evidently could not admit this conception into
his thought. With Leonardo's greater awareness of his
distinctively “scientific” methods and objectives, the
two currents of thought that Alberti held together in
one view of man and the world parted ways.
The humanistic movement also encouraged this sep-
aration. In contrast to early humanistic treatises on
education which included mathematics, dialectics, and
astronomy in their ideal curricula, the humanistic cur-
riculum of the late fifteenth and sixteenth centuries
came to be strictly defined as a program of literary,
historical, and ethical studies. The artistic-technical
interests of an Alberti could not be an integral part
of this studia humanitatis any more than the investi-
gation of nature could be pursued by means of litera-
ture. Humanism and the natural-scientific mode of
thought were found to follow different methodological
principles, and this intellectual fact shaped the specific
“universality,” i.e., the particular completeness and
comprehensive content of thought, of the two main
examples of the Renaissance universal man.
