Page 243 - Art In The Age Of Exploration (Great Section on Chinese Art Ming Dynasty)

here (no. 175 /A) exhibits freer pen work than the with six patches. Like the two other sheets in the subsequently produced by Piero himself as the
others and is the only one to exhibit the sharp Uffizi, it has been laid down at the corners, but in model Italian version.
diminution that results from a relatively close this case the added paper at the bottom corners In addition to his treatise on perspective, Piero
viewpoint. Although the mazzocchio not has been removed or come away. The lower edge had already written a Trattato del abaco, an out-
exhibited here (no. 1756A) is seen at a shallow of the sheet has been made up at a later date to line of mathematics as applied to such practical
angle similar to that in no. 175/A and to that illus- complete the lower front edge of the chalice. problems as calculating size, and was subse-
trated in Piero's treatise, the viewing distance is Whatever the attributional and technical prob- quently to write a Libellus de cinque corporibus
very long, inasmuch as the far side of the mazzoc- lems posed by the studies of the mazzocchi and regularibus, on the mathematics of the five regu-
chio is hardly diminished in size compared to the the chalice, they provide vivid testimony to the lar (or "Platonic") polyhedra (Daly Davis 1977).
near side. The chalice is even more puzzling in patient care with which designers in the Renais- When he offered his Libellus to Duke Guidobaldo
this respect, in that the facets on the far side of sance approached such perspectival tasks. The da Montefeltro, Piero suggested that it should be
the chalice are not diminished at all, and the view- draftsmen of such objects were prepared to plot placed next to his book on perspective, which he
ing angle at the different levels of the chalice does projections point by point in a laborious manner had presented to Guidobaldo's father, Federigo,
not change. We do not appear to be looking down to achieve the kinds of results that were to who had died in 1482. The writing of De prospec-
at the base of the chalice to a greater extent than become readily attainable only with the advent of tiva could be assigned to either the 14605 or
at its mouth. The chalice is therefore depicted in computer graphics in this century. M.K. 14705, with the balance of probability favoring the
nonconvergent or orthographic perspective, in later decade.
which the notional viewpoint (according to a later Although Piero's treatise is highly technical in
formulation) may be said to be at infinity. The its mathematical outline of perspectival tech-
complex, see-through nature of the cage of con- 141 niques, it is cast in the guise of practical instruc-
fusing lines has tended to disguise the fact that tions, working through the examples in a step-by-
the chalice is not constructed according to the Piero della Francesca step manner, with a minimum of abstract theory.
laws of single-vanishing point perspective at all. Umbrian, c. 1416-1492 His introduction makes it clear that he is dealing
The drawing of the chalice is also inconsistent in THE CONSTRUCTION OF A VAULT with only the second of the three skills needed by
that only some features —the mazzocchio-like the painter to imitate nature — disegno (the draw-
rings and flat central plane —are shown in a fully OVER A SQUARE PLAN FROM ing of the shapes of objects), commensuratione
see-through manner. De Prospectiva Pingendi (the proportional location of objects in measured
These observations suggest the need for further (On the Perspective of Painting) space according to the laws of perspective), and
investigation both of the constructional methods c. 1470-1480 color are (the distribution of color, light, and
and the attributions. It is difficult to determine manuscript on paper, 91 fols. shade). The prevailing tenor of the treatise may
the extent to which the mazzocchi in Uccello's 3 3 be described as "applied Euclid," exploiting basic
(l! /8X8 /8)
paintings are seen from a relatively close viewing 28.9X21.5 Pacioli 1494; Winterberg 1899; geometry for the perspectival projection of forms
references:
point and fully foreshortened, since their far sides Nicco-Fasola 1942; Daly Davis 1977; Kemp 1990 onto a plane (or termine) rather than becoming
are not visible and the paint surface in the Flood is involved in physiological optics.
badly damaged. Such evidence as is visible sug- Biblioteca Palatina, Parma, MS Parm. 1576, fol. 2^r De prospectiva is divided into three books. The
gests that they may have been drawn as if viewed first deals with basic geometrical terms and the
from a distant point, as in no. 1/56A. On the other The two principal manuscripts of Piero's treatise foreshortening of a square plane onto which vari-
hand, the nonconvergent perspective of the chal- On the Perspective of Painting are the Italian ver- ous flat figures, such as the plan of an octagonal
ice corresponds to the technique used by some of sion of 91 folios in the Biblioteca Palatina, Parma, building, are projected. The second extends this
the designers of intarsia decorations. Although and the Latin text of 115 folios in the Biblioteca method to the erection of three-dimensional
the famous inlaid woodwork of the Studiolo in Ambrosiana, Milan (Cod. Ambr. c 307 inf). There bodies on the foreshortened plane. The last book
Urbino, which contains a mazzocchio among the is a second Italian version without illustrations in shows how to use the plans and elevations of an
other symbols of the liberal arts, appears to use the Ambrosiana (D 200 inf), and three additional object to project that object point by point onto an
convergent perspective throughout, other intarsia Latin versions in the British Museum (Cod. intersecting plane established at a definite dis-
designs exhibit the parallel orthogonals of non- 10366), Bibliotheque Nationale, Paris (Cod. lat. tance from the point of projection (or eye). It is
convergent perspective (cat. 145). The popularity 9337), and Bibliotheque de Bordeaux (Cod. 516), this full technique of projection from plan and
of perspectival intarsie in the period 1450-1520 respectively. Although the attribution of precisely elevation that Piero uses for such complex forms
and the geometrical expertise of the specialist drawn diagrams to a particular hand is always as the mazzocchio (compare cat. 140), column
craftsmen leave open the possibility that some or difficult, the quality of the designs and careful base and capital, and human head. The diagram
all of the surviving drawings may have originated humanist script in the Parma manuscript may illustrated here is from near the end of book n and
in their workshops and certainly indicate that reasonably be regarded as by Piero himself, as is the final demonstration of how to erect three-
there is no need to attribute all such drawings to may the diagrams accompanying the Latin text in dimensional structures on the foreshortened
Uccello. On the other hand, Uccello himself may the Ambrosiana (Nicco-Fasola 1942). Relying square plane with a vanishing point at A. Piero
well have been involved in the design of intarsia upon the testimony of Piero's follower, Luca explains that "the foreshortened [degredato] plane
decorations for chests and other furniture. Until Pacioli, who indicated in his Summa de arithme- is BCDE, on which I intend to place a chapel with a
more evidence comes to light, it is probably best tica that Matteo dal Borgo translated De prospec- cruciform vault, the square of the chapel being
to retain the traditional attribution of the draw- tiva into Latin, one would think that the Italian FGHI." The basic technique consists of the erection
ings to Uccello, albeit in a very qualified manner. text was the earlier, but there are signs that some of a rectangular box in perspectival projection
Such drawings may well have served as tem- elements in the Parma version, including the within which the points necessary for the drawing
plates to be used repeatedly in the workshops; the poems "to the author" at the end, are based on of the vault are plotted. Piero takes the reader
chalice has in fact been pricked through for trans- the Latin text. It is thus probable that the Latin through the construction line by line, like a
fer at the corners of each facet. This sheet shows codex in the Ambrosiana was prepared first from schoolmaster coaching a pupil for an examination.
obvious signs of wear and is repaired on the verso Piero's draft and that the Palatina manuscript was The end result is not unlike the structure of the

242 CIRCA 1492