Florentine Interest in Ptolemaic Cartography as Background for Renaissance Painting,Architecture, and the Discovery of AmericaAuthor(s): Samuel Y. Edgerton, Jr.Source: Journal of the Society of Architectural Historians, Vol. 33, No. 4 (Dec., 1974), pp. 275-292Published by: University of California Press on behalf of the Society of Architectural HistoriansStable URL: http://www.jstor.org/stable/988935Accessed: 16/11/2010 13:37

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=sah.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

Society of Architectural Historians and University of California Press are collaborating with JSTOR todigitize, preserve and extend access to Journal of the Society of Architectural Historians.

http://www.jstor.org

Florentine Interest in Ptolemaic

Cartography as Background for Renaissance Painting,

Architecture, and the Discovery of America

SAMUEL Y. EDGERTON, JR. Department of Fine Arts, Boston University

EXACTLY five hundred years ago, on 25 June 1474, a Flor- entine physician named Paolo dal Pozzo Toscanelli

(i397- 1482) wrote to Fernam Martins, Canon of Lisbon and coun- cilor to the King of Portugal. That letter may be one of the most decisive documents in the history of the Western world:

On another occasion I spoke with you about a shorter sea route to the lands of spices than that which you take for Guinea. And now [your] Most Serene King requests of me some statement, or preferably a graphic sketch, whereby that route might become understandable and comprehensible, even to men of slight education. Although I know this can be shown in a spherical form like that of the Earth, I have nevertheless decided, in order to gain clarity and save trouble, to represent [that route] in a manner that charts of navigation do. Ac- cordingly, I am sending His Majesty a chart done with my own hands in which are designated your shores and islands from which you should begin to sail ever westward, and the lands you should touch at and how you should deviate from the pole or from the equator and after what distance, that is, after how many miles, you should reach the most fertile lands of all spices and gems, and you must not be surprised that I call the regions in which spices are found "western," although they are usually called "eastern," for those who sail in the other hemisphere always find these regions in the west. But if we should go overland and by the higher routes we should come upon these places in the east. The straight lines, therefore, drawn vertically on the chart, indicate distance from east to west, but those drawn horizontally indicate the spaces from south to north.... From the city of Lisbon westward in a straight line to the very noble and splendid city of Quinsay [China] 26 spaces are indicated on the chart, each of which covers 250 miles .... So there is not a great space to be tra-

The ideas and materials in this article were originally researched under a special summer grant awarded in 1967 by the National Endowment for the Humanities. I am grateful also to the Graduate School of Boston University for nominating me to this award, and to the staffs of the Laurentian Library, Florence; the Map Room of the Lamont Library, Harvard University, Cam- bridge, Mass.; and the John Carter Brown Library, Brown University, Providence, R.I. I also wish to thank O. Neugebauer, James Ackerman, Creighton Gilbert, and Hunter Dupree for their generous assistance. A chapter similar to this but set in the broader, cultural context of fifteenth- century Florence will appear in my forthcoming book, The Renaissance Rediscovery of Linear Perspective; 1425-1435.

versed over unknown waters. More details should, perhaps, be set forth with greater clarity, but the diligent reader will be able from this to infer the rest for himself.'

A few years later a copy of this letter, together with the chart Toscanelli mentioned (but now lost), came into the hands of Christopher Columbus. Columbus wrote for more

information, and Toscanelli responded, encouraging the Genoese's developing interest in a sea route to the East. Al-

though the Portuguese turned him down, Columbus man-

aged to sell his idea to the Spanish, and on 3 August 1492 set sail on his climactic voyage into history, inspired, as much as

by any man, by Toscanelli the Florentine.2 What Toscanelli demonstrated to Martins and hence to

Columbus was that once the surface of the Earth was con- ceptually organized into a rectilinear grid, it took on a new sense of conformity. It was no longer to be thought of as a

heterogeneous assemblage of frightening unknowns. I would now like to suggest that Toscanelli's ideas were as important to Filippo Brunelleschi and Leon Battista Alberti as they were to Christopher Columbus. The ideas that underlay the new cartography were also applicable to the art of Renais- sance Florence. Judging by painting, sculpture, and architec- ture, mediaeval "visual space" was usually additive. It was governed by no single, controlling viewpoint. Contempo- raneous with Toscanelli's new cartographic thinking, how- ever, there arose in Florence a new concept of "visual

space" as continuous and relative to the fixed eye of the individual observer. This was to have profound effect upon

i. This remarkable letter, which was the cause of much controversy in the late nineteenth century, is now generally accepted as genuine. See Samuel Eliot Morison, Journals and Other Documents on the Life and Voyages of Christopher Columbus (New York, 1963), pp. 11-17.

2. Gustavo Uzielli, La vita e i tempi di Paolo dal Pozzo Toscanelli (Rome, 1894); Uzielli, Paolo dal Pozzo Toscanelli, iniziatore della scoperta d'Ameri- ca (Florence, I892); Eugenio Garin, "Ritratto di Paolo dal Pozzo Toscanel- li," in La cultura filosofica del Rinascimento italiano (Florence, I96I), pp. 313-334.

z75

lit

Pg.

I- A- o .l` 16

W-r

A Ar

Fig. i. Civitas Florentiae, ca. 1350. Detail of a fresco in the Loggia del Bigallo, Florence (photo: Alinari-Art Reference Bureau).

~4 9

Gili

Fig. z. Florence shown in the Map with a Chain (detail), ca. 1480. Woodcut (photo: Alinari-Art Reference Bureau).

276

the way painters and architects composed the spaces and masses that gave Renaissance style to their pictures and

buildings. Oddly, for a man so close to one of the great ideas in his-

tory, little is known about Toscanelli. His biography is not found in the Encyclopedia Americana or even the Britannica

(although it does appear in the Enciclopedia Italiana). He

apparently wrote little, and very few of his works survive.

Nevertheless, he was regarded as a man of prodigious learn-

ing. A medical doctor, he was also sought out as an authority on astronomy and geography.3 It has recently been shown that during the fifteenth century the mathematical sciences in Florence reached a level of considerable competence, and that Toscanelli was an influential friend of nearly all the famous humanists, bibliophiles, and other important schol- ars.4 It has also been well documented that he was close to both Brunelleschi and Alberti. Vasari noted the ties between Toscanelli and Brunelleschi in the 1568 edition of the Vite:

Maestro Paolo dal Pozzo Toscanelli, who returned at that time from his studies, was having dinner with certain of his friends ... and in- vited Filippo. Filippo, having listened to Toscanelli argue on the arts of mathematics, showed such familiarity that he learned geometry from him. Filippo did not even have advanced education but did

everything so rationally with the naturalness of practical experience that he often confounded Toscanelli.5

Vasari goes on to say how much Toscanelli admired

Brunelleschi, how they discussed the Scriptures and "sites and measurements" from Dante's Divine Comedy, and how

Toscanelli considered Brunelleschi a "new Saint Paul" be-

cause he was so articulate. While Vasari himself was not a

contemporary of these men, his anecdote reflects a con-

tinuing tradition about Toscanelli's close ties with Brunel-

leschi.6 Alberti held the learned physician in such regard that

he dedicated a book to him.7

Other than sharing the general scientific and technological interests of Brunelleschi and Alberti, what specific contribu- tions might Toscanelli have made to their art? Alessandro Parronchi has already argued that Toscanelli influenced Brunelleschi's demonstrations of linear perspective.8 It is

generally held that Brunelleschi was the first man since classical antiquity to devise a method of linear perspective in

picture-making.9 This seems to have occurred around 1425 when, in an intriguing set of experiments described by An- tonio di Tuccio Manetti, Brunelleschi painted two panels, one of the Baptistery of Florence, the other of the Palazzo Vecchio.10 Within the next ten years, Brunelleschi's per-

spective ideas passed on to his friends Masaccio, Masolino, and Donatello. In 1435/6 Alberti codified Brunelleschi's

principles in his Treatise on Painting, regarded as the Magna Carta of Renaissance art.1

Linear perspective has always been credited with estab-

lishing a new standard of "realism" in picture-making, but

its effects upon the seeing process itself have not been suffi-

ciently emphasized. I think it is possible to show not only that the advent of linear perspective was important to art, but also important to the way people began to "structure"

the physical world in their mind's eye. This is poignantly

pointed up in two well-known views of the city of Florence

that fall chronologically to either side of Brunelleschi's per-

spective demonstrations. The first is a detail of a fresco

dating about 1350 in the Loggia del Bigallo across from the

Baptistery (Fig. i). The second is a large woodcut after a

painting of about 1480 known as the Map with a Chain (Fig.

2). They depict the same city in which little topographical change had taken place. Only the addition of Brunelleschi's

cupola gave the Map reason to be different.12 Why then such

a fundamental change in pictorial attitude?

Clearly the advent of linear perspective had more than

just a taste-making effect upon the artist of the Map. It influ- enced his very psychological perception. Instead of viewing the city as a heterogeneous collection of interesting details,

the charming overhangs, cornices, and projecting corners

that make the city so attractive to the casual stroller, the

artist of the Map saw it from one all-governing viewpoint.

3. Giorgio de Santillana, "Paolo Toscanelli and His Friends," in his Re-

flections on Men and Ideas (Cambridge, Mass., 1968), pp. 33-47.

4. Paul Lawrence Rose, "Humanist Culture and Renaissance Mathe-

matics," Studies in the Renaissance, xx (1973), 46-1o6.

5. Giorgio Vasari, Le vite de'piau eccellenti pittori scultori ed architettori

. con nuove annotazioni e commenti di Gaetano Milanese (Florence,

1906), II, 333: "Tornando poi da studio maestro Paulo dal Toscanelli, e una

sera trovandosi in un orto a cena con certi suoi amici, invito Filippo, il quale, uditolo ragionare dell' arti matematiche, prese tal familiarita con

seco, che egli imparo la geometria da lui; e sebbene Filippo non aveva lettere,

gli rendeva si ragione di tutte le cose con il naturale della pratica esperienza, che molte volte lo confondeva."

6. For instance, Toscanelli's friendship with Brunelleschi is mentioned in

the late fifteenth-century biography of the architect by Antonio di Tuccio

Manetti (see Howard Saalman and Catherine Enggass, The Life of Brunel-

leschi by Antonio di Tuccio Manetti [University Park, Pa., 1970], pp. 409-

41o) and the mid-sixteenth-century anonymous account in the Codex

Magliabechiano (Karl Frey, ed. [Berlin, 1892], p. 6z). 7. The Intercoenales; see Girolamo Mancini, ed., Leonis Biaptistae Al-

berti opera inedita (Florence, 1890), pp. 122-123.

8. Alessandro Parronchi, Studi su la dolce prospettiva (Milan, 1964).

9. Samuel Y. Edgerton, Jr., "Brunelleschi's First Perspective Picture," Arte Lombarda, xviII (1973), 172-195; also Edgerton, The Renaissance Re-

discovery of Linear Perspective. io. Life of Brunelleschi, pp. 42-46. ii. Samuel Y. Edgerton, Jr., "Alberti's Perspective; a New Discovery and

a New Interpretation," The Art Bulletin, XLVIII (1966), 367-378; also

Edgerton, Renaissance Rediscovery. 12. In a similar context these two "maps" have been published and dis-

cussed in Hans Baron, Crisis of the Early Italian Renaissance (Princeton,

N.J., 1966), pp. I99-zII. See also Giuseppe Bofitto and Attilio Mori, Piante

e vedute di Firenze (Florence, 1926), pp. 7, 12-21.

277

Unlike the view in the Loggia, in which the viewer may ex- perience what it is like to see, touch, and walk around the protruding walls and corners of buildings, the Map forces the viewer to think of the city from a fixed and far distant position. This makes it possible to grasp instantly the over- all plan of Florence and its relationship to the surrounding countryside, but forces the viewer to lose tactile contact with the individual details that so delight all the senses when he walks through the city. The unity of the Renaissance view has replaced the diversity of the mediaeval one.

One of the few contemporaneous documents we have concerning Toscanelli is a laudatory verse from a long biographical poem, De illustratione Florentiae, written by Ugolino Verino toward the end of the Quattrocento:

Quid Paulum memorem? terram qui norat et astra, qui prospective libros descripsit, et artem, egregius medicus, multos a morte reduxit.13

What is meant by "books on perspective" (prospective libros) ?

In the fifteenth century the word "prospectiva" had not yet been accepted as the term for the artist's construction in painting. It most often referred to the mediaeval science of optics. This traditional body of knowledge was founded by the ancient Greeks, particularly Euclid and Ptolemy, by ap- plying the laws of geometry to the physical and physiologi- cal processes of seeing. According to ancient beliefs, visual impulses came into the eye in the form of a cone with its apex falling on the optic nerve in the posterior part. Before converging on this special conduit to the brain, the visual rays, which collectively made up the cone and which were subject to Euclidian rules, passed through the crystallinus, or what is understood today as the dioptric lens. The crys- tallinus sits in the anterior part of the eye and, as we now know, is a tractable lens focussing the entering light rays onto the retina. In the Middle Ages and the Renaissance however, it was believed that the crystallinus acted as. a sensitive mirror. On its anterior surface a point-for-point image of the seen object was displayed by the converging visual rays. The image was thus rendered small enough on the intercepting crystallinus to be in turn transmitted to the optic nerve and then to the brain14 (Fig. 3).

This mechanical operation of the eye according to medi- aeval optics was further justified by the Euclidian proposi- tion concerning similar triangles.15 The triangle formed

o -----AKX-S

VtSUALIS

A po. . .

Fig. 3. The eye as conceived by mediaeval optics (author).

within the eye between the apex of the visual rays at the optic nerve and the height of the small-scale image on the crystallinus would be in exact proportion to the triangle formed between the viewer's standpoint and the height of the actual object before his eyes. Alberti's own theory of the "intersection" through the "visual pyramid" is based on these same mediaeval optical and geometric principles. So also was Brunelleschi's first perspective demonstration. It is a touch of irony that linear perspective in picture making, often described as "scientifically correct" by modern physi- ologists and perceptual psychologists, was originally de- duced from a quite erroneous understanding of how the eye functions.16

Another aspect of mediaeval optics which had great im- port for the advent of Renaissance linear perspective was the notion of the centric visual ray. This concept was first worked out by the Alexandrian Greek Ptolemy. According to this theory, all but one of the rays making up the visual cone either enter or leave the eye obliquely. They are thus refracted, causing their power of conveying visual informa- tion to be weakened. The centric ray, however, makes per- pendicular contact with the surface of the optic nerve, the surface of the crystallinus, and the surface of the object seen. Hence it is the shortest, meaning that impulses of sight not only travel most directly along its path but cover the shortest distance to the optic nerve and the brain. Therefore, the old optical scientists all agreed that this ray alone among the others brought the clearest visual message. Christian casu-

13. Ugolino Verino, De illustratione urbis Florentiae, in Carmina illus- trium poetarum italorum (Florence, 1724), x, 347.

14. Edgerton, Renaissance Rediscovery. 15. J. L. Heiberg and H. Menge, eds., Euclidis opera omnia (Leipzig,

1896), vi, 179; Proposition Twenty-one.

i6. Concerning the "scientifically accurate" theory of linear perspective see M. H. Pirenne, "The Scientific Basis for Leonardo da Vinci's Theory of Perspective," The British Journal for the Philosophy of Science, III (i952- 1953), 169-185; G. Ten Doesschate, Perspective; Fundamentals, Contro- versials, History (Nieuwkoop, Holland, 1964); and James J. Gibson, "The Information Available in Pictures," Leonardo, Iv (1971), 35, fn. 34. See also Decio Gioseffi, Perspectiva artificialis; per la storia della prospettiva spigola- ture e appunti (Trieste, 1957).

278

istry added a moral imprimatur." Dante applied the notion to the belief that you only know an honest man when he looks you straight in the eye.18

It seems certain that Brunelleschi applied the principle of the centric ray to his first realization of the "vanishing point." He observed that for a person looking straight ahead in a mirror the centric ray defines the level of the reflected

"horizon"; that is, the place where parallel edges of things receding from sight seem to converge. Alberti applied the same principle-he called the centric ray the "prince of

rays"-in his own definition of frontal, centric point per- spective which became the norm in Italian painting. Believ-

ing that painting should be didactic and inspire only noble

thoughts in the minds of the viewers, Alberti preferred that the center of meaning in a picture be congruent with the

point where the centric ray strikes the picture surface, thus

insuring that its moral message would be conveyed most

directly and without interruption to the brain.19 These ideas also permeated church architecture. In Bru-

nelleschi's Sto. Spirito and S. Lorenzo (Fig. 4), the viewer

facing the apse is conscious that all the horizontal edges of the architectural members, like orthogonals in a perspective picture, seem to converge toward a centric "vanishing

point" on his own eye level. This is the position of the altar, the spiritual message of which Renaissance architects wanted to impress upon the beholder's imagination. Al-

berti seems also to have applied the doctrine of the morally

superior centric visual ray to city planning. Straight and

wide avenues, he averred, enhanced the dignity of the upper

classes, while lower-class artisans and shopkeepers were more suitably located on winding or oblique streets.20

If Ugolino Verino is right that Toscanelli himself wrote

"perspective books," or treatises on optics, they have not

survived, but it is probable that Paolo was versed in the sub-

ject. Such learning was compatible with the medical educa- tion he received at the University of Padua.21 He graduated in 1424, the year in which it is thought he met Brunelleschi.22 Brunelleschi's own schooling did not include university training, only the fundamentals of grammar and arithmetic as taught in the public abaco; so, it is reasonable to ask from

whom did he learn about optics? How could he have de-

vised his linear perspective experiments without some

knowledge of the science? Circumstantially, it seems that

the kind of "geometry" Vasari reported Brunelleschi and

Toscanelli discussed had to do with optics, which then

formed the basis for Brunelleschi's experiments in linear

perspective. But Toscanelli knew about another science, which may

have been of even more catalytic importance to Brunel-

leschi's and Alberti's contributions to the art and architec-

ture of the Renaissance. This was contained in Ptolemy's

Cosmographia, or Geographia, which first came to Western

Europe by way of Florence about the year 1400. This classi-

cal world atlas had been known for centuries to the Arabs

and the Byzantine Christians, but had made no apparent

impact upon Western Europe. Then, about 1395, a number

of leading Florentine intellectuals and businessmen, in-

cluding Palla Strozzi the banker, Leonardo Bruni the hu-

manist and future chancellor of the commune, Antonio

Corbinelli the merchant, Coluccio Salutati the statesman, Roberto de' Rossi the magnate, and Jacopo d'Angiolo da

Scarperia the papal secretary, organized a seminar for the

study of Greek. They hired the gifted Byzantine scholar

Manuel Chrysoloras. He so charged his students that they

quickly outran their meager supply of Greek books, re-

quiring Chrysoloras and Jacopo d'Angiolo to travel to

Constantinople for more texts. They returned about 1400, after a nearly disastrous shipwreck off Naples. Their sal-

vaged library included a wholly unexpected dividend: the

Ptolemaic world atlas.23

17. The English Franciscan Roger Bacon, for instance, wrote in his Opus majus, in the section on optics: "Since the infusion of grace is very clearly illustrated through the multiplication of light, it is in every way expedient that through the corporeal multiplication of light there should be manifested to us the properties of grace in the good, and the rejection of it in the wicked.

For in the perfectly good the infusion of grace is compared to light incident

directly and perpendicularly, since they do not reflect from them grace nor

do they refract it from the straight course which extends along the road of

perfection in life.... But sinners, who are in mortal sin, reflect and repel from

them the grace of God. .. ." Robert Belle Burke, The Opus majus of Roger Bacon (Philadelphia, 1928), II, 238-239; also Edgerton, Renaissance Re-

discovery. 18. Dante Alighieri, II Convivio, eds. Moore and Toynbee (Oxford, 1924),

pp. z61-z6z: "E qui si vuole sapere, che avvegnache pi1u cose nell' occhio a un'ora possane venire, veramente quella che viene per retta linea nella punta della pupilla, quella veramente si vede, e nella imaginativa si suggella sola- mente. E questo e, perocche il nervo, per le quale corre lo spirito visivo, e

diritte a quella parte; e per6 veramente l'un occhio l'altro occhio non puo guardare, sicche esso non sia vedute da lui; che siccome quello che mira riceve la forma nella pupilla per retta linea, cosi per quella medesima linea la

sua forma se ne va in quello cui mira ...." 19. Samuel Y. Edgerton, Jr., "Mensurare Temporalia Facit Geometria

Spiritualis; Some Fifteenth Century Italian Notions About When and Where

the Annunciation Happened," in Irving Lavin and John Plummer, eds., Studies in Late Medieval and Renaissance Painting in Honor of Millard Meiss (New York, forthcoming in 1975).

zo. On this point, as it seems to have been expressed through Alberti's

follower Bernardo Rossellino, see Torgil Magnusson, Studies in Roman

Quattrocento Architecture (Stockholm, 1958), pp. 65-97. 21. On the role of mathematics, optics, and astronomy in mediaeval medi-

cal education, especially at Padua, see Antonio Favaro, "I lettori di mate-

matiche nella universita di Padova dal principio del secolo XIV alla fine del

XVI," Memorie e documenti per la storia della universit•a

di Padova, I

(19zz), 1-70. zz. Parronchi, Studi su la dolce prospettiva, pp. 24zff.

23. For the story on how Ptolemy's atlas first came to Western Europe,

see Joseph Fischer, S.J., Claudii Ptolemaei Codex Urbinas Graecus 82, 4

vols. (Leipzig, 193z), I, I3Iff.

1 url~a%~c~~(l~4~rf~arsl, ,aggg ii r~ d , ??: ;i I: ?, i I

i ~~p~dl~aleed ii i" ~e"l bd~d II L9ril f~ 1

-----' ~a ~a~%bPL$if~b ~1IiS~!

'Sa*ljea~iillsl~fB~Bi ,i P: ~~~&g~Bl~yLI ---?-- Is~8isi~.aPP?;att?surlr~ : ~; ~

tr~PI~Ir~ ~a~r ~ ts~t $.. i;? i 'I ?;; ' :?i i: !li I~

1~II :i F

1.1 ; i

L?1~~ r r ;tl

j'?

?:: i; ii;'' iii I:

r; :

; I:

i-;.-.--

xie

~-ht~~~~:?~, :-~~:g- ~?-ii ib~i

Fig. 4. Brunelleschi, S. Lorenzo, Florence, ca. 1440. Interior (photo: Alinari-Art Reference Bureau).

This Greek edition of the Geographia is not extant, but

very likely it was similar to several handsome versions, writ-

ten and illuminated in the fourteenth century, which are

now in the Vatican and Laurentian libraries.24 Ptolemy's treatise consisted of eight books illustrated by twenty-seven

maps including a two-page mappamundi. When Jacopo

d'Angiolo and Chrysoloras first discovered Ptolemy's atlas

among the wares of the Byzantine booksellers, they were

not exactly ignorant of its usefulness beyond a mere lan-

guage text. They may or may not have known about

Ptolemy's optics, but they most certainly knew of his Alma-

gest, the standard treatise on astronomy during the Middle

Ages. A casual thumbing through the pages of the Geo-

graphia would have revealed that Ptolemy had applied to

the study of the Earth's surface the same mathematical

principles he had applied to the heavens in his Almagest.25 Chrysoloras began to translate Ptolemy's work into Latin

almost immediately after his return, which indicates that the members of the Greek seminar recognized its universal

importance. This translation was interrupted and then re- sumed about I405 by Jacopo d'Angiolo and finished per- haps in the next year. Annotated Latin copies of the colored

maps were not added however until the following decade, when two distinguished young Florentine gentlemen named Francesco di Lapacino and Domenico di Lionardo Bonin-

segni undertook the task.26 These men were not artists but scions of important Florentine families; Domenico was sub-

sequently to occupy several high posts in government. I stress this because it shows the impact which Ptolemy's atlas made upon the wealthy, intellectual, and highly influential

z4. Paul Duise-Kiel, "Die handschriftlichen Ptolemaiuskarten und ihre

Entwicklung im Zeitalter der Renaissance," Zentralblatt fuir

Bibliotheks- wesen, xxx (I913), 379-404.

z5. K. Manitius and 0. Neugebauer, eds., Ptolemdus; Handbuch der Astronomie, z vols. (Leipzig, 1963).

z6. Fischer, Claudii Ptolemaei . . , I, 191.

z8o

IN/

--V-ilv?"11111.tott lilt 44 , ?f oft olt ;~lv

x ??~c - -e- iltbr

~i,,,tb t? ~A 2- trfn rfit

cJR*,~1. !?L9d h'

-.~, k

'"? ;i-5

i~/

Fig. 5. Petrus Vesconte, Portolan chart, ca. 1320 (photo: Vatican Library).

laymen who now set the cultural tone in the city. Vespasiano da Bisticci, writing many years later about his genteel biblio-

phile friends, mentioned the Geographia in four separate biographies and, incidentally, referred each time to the maps as pitture.27 Furthermore, a scriptorium for the reproduc- tion of these Ptolemaic atlases seems to have been set up in Florence to supply a steadily rising demand. As we shall see, it was not so much Ptolemy's knowledge of geography prop- er that was so captivating, but his system for mapping the surface of the Earth.

This system allowed for easy corrections, and already by 1424, improved maps of Northern Europe began to be added." Florence was becoming a center of cartographic study as well as a scriptorium. The Portuguese under Henry the Navigator began to beat a path to the city. Henry's brother Dom Pedro was there in 1428, perhaps also to purchase maps."9 Dom Pedro's own son became the Cardi-

nal James of Portugal, now buried in Florentine splendor at San Miniato. Incidentally, Toscanelli was one of Cardinal James's personal physicians at the time of his death.30 Not only Florentine maps but Florentine gold soon stimulated the Portuguese to make their spectacular expeditions down the African coast. Knowledge of Ptolemy's atlas also perme- ated the august ecclesiastical councils on schism and heresy going on in Pisa, Rome, and Constance during the second decade of the Quattrocento.31 The French cardinal Guil- laume Filastre, antagonist of John Hus, was sufficiently in- terested to purchase a copy from Florence in 1417 and an- other with updated maps ten years later.32 His friend Cardi- nal Pierre d'Ailly was himself a learned geographer and had

already composed a long compendium on the subject, the

Ymago mundi, when he heard about the new Ptolemaic atlas while attending the council. Around 1412, he wrote two commentaries on the Geographia. Pierre d'Ailly's Ymago mundi and the commentaries eventually found their

27. Ptolemy's Geographia is mentioned in the biographies of Francesco di Lapacino, Boninsegni, Palla Strozzi, and Alessandro de' Bardi; see Vespasi- ano da Bisticci, Le vite di uomini illustri del secolo XV, eds. Paolo d'Ancona and Erhard Oeschlimann (Milan, i961).

z8. This first "correction" was made by a Danish cartographer named Claudius Clavus; see Lloyd Brown, The Story of Maps (Boston, 1950), pp.

I5zff. 29. Francis M. Rogers, The Travels.of the Infanta Dom Pedro of Portugal

(Cambridge, Mass., 1961).

30. Frederick Hartt, Gino Corti, and Clarence Kennedy, The Chapel of the Cardinal of Portugal, 1434-1459 (Philadelphia, 1964), p. 29 and passim.

31. Thomas Goldstein, Fifteenth Century Geography Against the Back- ground of Medieval Science (Salem, Mass., 1964); also his "Geography in 15th Century Florence," in John Parker, ed., Merchants and Scholars (Minneapolis, 1965), pp. I -32.

32. Fischer, Claudii Ptolemaei, 1, 191.

z81

t~l

"

aB

b?,~ :::i

J, i! i; ~::~:::-

~ ~rrrpCleo -~i~iBL~ Ili~W~** :i- B~a- ~k~SB" 66"8 U~? ilGI~V~-~

e~r~ps ~WIIIPaa~~l: ~~e~u~

i-ni:

i_ n i 1 Ir

B I

.ili

r, : i!'

E Fig. 6. Giotto, Expulsion of Jo- achim from the Temple, ca. 1305. Arena Chapel, Padua (photo: Ali- nari-Art Reference Bureau).

way to the library of Christopher Columbus, where they made his principal "bed-time reading," as Samuel Eliot Morison has written.33

Should anyone have doubts about the prestige of these Ptolemaic atlases in Florentine intellectual life, let him in-

spect the magnificent Latin copies in the Laurentian Library, and most particularly the great edition prepared for the

condottiere Camillo Maria Vitelli now lying in relative ne-

glect in the National Library in Florence. This work of the

late fifteenth century was not only updated with the latest

geographic information but was lavishly decorated with

gold leaf and brightly colored miniatures in the style of

Ghirlandaio.34 The huge Vitelli atlas represents the culmina-

tion of a whole industry fostered in Florence during the

Quattrocento, an industry that brought together scientists, artists, and patrons. The city, as if it had not already con- tributed enough to the Renaissance, was the most important center in Europe for the study and production of the revolu-

tionary new Ptolemaic system of geography and map- making.

In spite of what little is known about the life of Paolo dal Pozzo Toscanelli, it is generally acknowledged that his

greatest accomplishment was in being the most outstanding authority on Ptolemaic cartography. As we shall see, there were certain remarkable aspects of the Ptolemaic system which would have been of great interest to someone with the artistic, technical know-how of Brunelleschi, if they had been interpreted to him by someone with the theoretical

knowledge of Toscanelli. Before examining the Ptolemaic system we should take a

brief look at another method of mapmaking in practice since the thirteenth century, especially in the seafaring Medi- terranean region. This was the harbor-finding or "portolan" sea chart, the earliest example of which may have been pro- duced in Tuscany (the "carta Pisana," now in the Biblio-

33. Samuel Eliot Morison, Admiral of the Ocean Sea, z vols., (Boston, 1942), I, 1IZI-IZ5.

34. Bibl. Naz., Cl. xIII, 16, Lat. The title page states that the maps were drawn by Henricus Martellus Germanus. The decorations around the charts were done by Gherardo and Monte di Giovanni da Firenze, probably the same Gherardo del Fiora (1444/5-1497) who with his brother Monte

(1448-?) is listed by Ulrich Thieme and Felix Becker (Allgemeines Lexikon der bildenden Kuinstler [Leipzig, 1920], xIII, 525-526) as painters and minia- turists in Florence working in the manner of Domenico Ghirlandaio.

z8z

thique Nationale, Paris, ca. Iz75). Certainly by the early Trecento portolan charts were in general use by Italian sea- men for negotiating the Mediterranean, and as late as 1700 were still the best means for plotting sailing voyages across the Atlantic Ocean. Figure 5 shows a Genoese portolan chart of about 1311 by one Petrus Vesconte, whom art his- torians might consider the "Giotto" of cartography.35

When a portolan chartmaker like Petrus sat down to draw such a map, he first laid in a stretch of shoreline he had either sketched himself or learned about from other sailors. He then added place names, always carefully set inside the coastal boundary so as not to obscure the important con-

figuration of the shore as seen from the ship. Different col- ored inks were employed in order to distinguish the best

harbors, and sometimes the chartmaker added little flags to denote the arms of ruling princes. Finally and most im-

portantly, he superimposed on top of his coastal contour a

compass rose, containing sixteen points interconnected by fans of radiating lines. Each of the four cardinal compass points he labelled with the traditional names of the four winds. When the ship's navigator put the portolan chart to

use, he opened it upon a table, took a rule, and laid it down

upon the map between his own port and his eventual desti- nation. He then took a pair of dividers to find the nearest

compass rose line, called a "rhumb," which ran parallel to his proposed course. When the proper rhumb was found, he traced it to its direction point on the compass rose, set his own course accordingly, and sailed away. Sometimes these

portolan charts showed a scale of miles or a superimposed grid for reckoning distance, but usually portolan charts were not so effective in giving accurate distances as they were in showing precise directions. What a sailor could

instantly determine from a portolan chart was the direction

of his destination and the sequence of landmarks to be

passed along the way. But the rhumb line system per se did

not provide him ready information concerning distances

between landmarks. At this point we might compare our portolan chart by

Petrus Vesconte to a nearly contemporaneous painting by Giotto, a scene from the Arena Chapel of 1306 (Fig. 6). Al-

most the same limitations as well as advantages character- istic of the portolan chart are also characteristic of Giotto's

painting. In Giotto's art one always has a clear idea of which objects are in front of others and which direction the

eye should follow to reach the fictive depths of the picture. There are no clues about the distance between painted ob-

jects or the depth of foreshortened surfaces. In other words

Giotto's painting, like a portolan chart, gives information about direction but not distance. The use and purpose of the portolan chart was still based on the same mediaeval

perceptual and psychological attitudes of seeing, that is, in

empirical combination with touching and moving around, which also inspired Giotto's painting.

The Ptolemaic system of mapmaking, on the other hand, was based on quite another psychological, perceptual atti- tude. In Book One of the Geographia, Ptolemy described two methods for mapping the Earth in the form of conic sections. Later, in Book Seven, he described a third method which is very like Renaissance linear perspective. All three methods have in common the aim of mapping on a flat plane the curving longitudes and latitudes of the globe. Ever since ancient times certain scientists had conceived of the world as abstractly divided into evenly spaced meridians (longi- tudes) converging at the poles and intersected by parallels (latitudes) crossing at right angles. We need not concern ourselves with the history and mathematical calculation of

this longitude-latitude system, but in mediaeval Europe no

one had yet presented a satisfactory way to project a reticu- lated spherical surface onto a flat chart. Ptolemy's three

methods showed how to project the coordinates of any geo-

graphical location and how to compensate for the distor-

tion of the spherical surface when stretched out on a two-

dimensional plane. The world that Ptolemy would map, however, was only

the oikumene or that part known to men of ancient times. It

began with the Fortunate Islands, probably the modern

Canaries-the "Greenwich" of Ptolemy's longitudinal reck-

oning-and stretched eastward through China. While it

showed Scandinavia and Russia, it extended southward

only slightly below the equator. The rest of the world was

terra incognita, although Ptolemy's longitude-latitude sys- tem was equally extendable around the whole of the globe, which he realized was much larger than the oikumene.

Ptolemy offered three separate mapping solutions be-

cause he knew there must always be some distortion no

matter how his spherical surface was unfolded on a plane. The first two were attempts at preserving the spherical char-

acter by having meridians converge, thus the oikumene ap- pears in the shape of a curved trapezoid36 (Fig. 7).

Neither of these methods was a projection from the eye.37

35. Roberto Almagia, Planisferi carte nautiche e affini dal secolo XIV al

XVII esistenti nella Biblioteca Apostolica Vaticana, 4 vols. (Vatican City,

1944), I, 13-16. For further on how portolan charts were used, see E. G. R.

Taylor, The Haven Finding Art (New York, 1957), pp. 109-III.

36. A full explanation of these first two mapping methods is given in Hans

V. Miik and Friedrich Hopfner, "Das Klaudios Ptolemaios Einfiihrung in

die darstellende Erdkunde," Klotho, v (1938).

37. J. G. Lemoine ("Brunelleschi et Ptolmeme;

les origines geographiques de la 'boite d'optique'," Gazette de Beaux-arts, LI [I958], 281-296) asserted

that Ptolemy's second method was similar to linear perspective and included

a diagram showing the convergence point of the meridians as an "eye." This

is incorrect. The author has misunderstood Ptolemy's cartographic projec- tion and gives a misleading case for Brunelleschi's application of it.

z83 B

??? ~~

u, t* ;o~. : ?; ,? \f *? Cr Z~ 1? .R?

?,i r b; ir r,' r

2: ~?; ~ f-. \6- v

s,~ t F "s. `Y. t ? t

ii. ?i.,?

u ,, i c--??r? + 4' r? i vL 71~ " j ~i~71b i

i ik I~e r1\ \?~: ~L. : ?'?

?r h ..2 fl C.K:?ZI~* 1~Y

t?1~5~C I .i, .r ~ S

3 I~ ~""r~il~ x?? ?. ?,. :&?.

1?;? :"?-? . i rL: -s

?:*. ;c'-??;~ -* w ~( .?;. i g i ~-~~ Ih?~~ ?ur-;~ i-- ,i- rri i

i.i I

I ;i "~ Y 7

Y!? f-:; ?c; ?t~?-.?- .. ~~~pt~?il -'5 t? r. i. I$

cC ̂ `2i 8"~:~: ??~i ,'Eli"e~i:) ?=

\~?I ?:, -:i ?r. -~" " t ""~~ :i-n

? . 3 :i CI~t -r i J

i - :I; i %i 8

3 ~~ ~Cc' i

:liCIIIF~~Z~F~7~Le~ - ' ~san~~~ r~,~-- U "r :s

i "O: i * ii; ~?II ,-? ?r~? "" r 5 i:

:i "' k~_ a

z ;-d .i i: "if ., i ;b. le s~ ,;h-gp-:~i

~s iip: :...," z a

f'~ ~rri, ~1 :::::~ :r ?:313~r. b:"c? ::?~-. ~

:;e " `??'~~ ;'" '"p" t- 1

~74

r 1-~t~3 o-:

sn

i

C r~ : liir_ a

??:~? ~CUsc-r r"L II

Fig. 7. Ptolemy, Oikumene, double-page map from a Greek edition of the Geographia, ca. 1405, owned by Antonio Corbinelli

(Laurentian Library, Florence, Plut. 28.49, fols. 98v-99r).

However, the second, which Ptolemy himself preferred, did take the eyepoint into consideration by what amounts to an

application of one of his optical theories. Just before intro-

ducing this second method, Ptolemy asked his reader to hold a globe motionless before his eyes and locate the particular parallel marked on it which passed through Syene (modern Aswan). This line, just twenty-four degrees north of the

equator, marked the exact center between the northern and southern halves of the oikumene.38 The viewer was then to direct his visual axis toward the internal center of the sphere in such a way that the axis would pass through the external surface of the globe at just that point where the parallel through Syene crosses the meridian directly in the middle of the viewer's visual field (Fig. 8). In other words Ptolemy was

saying that the viewer, before he does any mapping at all, should have a firm optical impression of how the oikumene would look if it were the base of the visual cone with his axis visualis certifying the precise geographical center.39 The

t

1 I

Fig. 8. How Ptolemy wanted the globe to be seen prior to mapping by his first and second methods. Hatched area is the oikumene

(author).

viewer was to observe the centermost meridian in such an

image of the oikumene as a perfect vertical, while the other meridians would appear bending concavely as they con-

38. For a mathematician like Ptolemy it was important that his halfway latitude have astronomical significance. Syene was selected because at that

place the sun can light up a well at high noon at the summer solstice. In other words, the sun stands near the zenith there about z21 June every year.

39. M.ik

and Hopfner, "Das Klaudios Ptolemaios Einfiihrung," p. 70.

The Ptolemaic atlases are not illustrated at this point (Book ii, Chap. 24). My Fig. 8 is an adaptation from Ptolemy's text based on the reconstruction in Miik and Hopfner.

284

verged on either side. However, the actual mapping ac-

cording to Ptolemy's second method did not follow from this point of sight but by another mathematical method for

preserving as much as possible the true distances between the northern latitudes. His optical directions served here

merely to give the mapmaker a clearer picture of the oiku- mene in his mind's eye before submitting it to the charting scheme.

After detailing his first two methods in the second book of his Geographia, Ptolemy went on to discuss more topo- graphical questions, but he was not finished with the prob- lem of projection. He raised it again in Book Seven, almost

apologetically, as if he felt there was still another alternative to representing the globe not covered earlier. This time he

presented a method much closer to an artist's approxima- tion. Again, he asked his reader to position his eyes at a

specific location vis-d-vis the globe, with the visual axis

lying in the plane of the latitude through Syene; that is, so

the latitudinal rings around the earth would be parallel rather than at angles with the visual axis.40 He intended the

whole three-dimensional "Earth" to be positioned frontally before the eyes in the conventional manner of looking at a

picture (Fig. 9). What Ptolemy now proceeded to explain is probably the

first recorded instance in which any scientist or artist gave instructions about making a picture based on a projection from a single point representing the eye of an individual.

This third system is in fact the direct ancestor of Renais-

sance linear perspective. The manner in which Ptolemy de-

scribed his own perspective procedure, however, seems to

imply that it was well known, at least among mathemati-

cians, in ancient times. The details derive from optics, the

geometry of conic sections, and the cartographic theory of

his own day. But Ptolemy was one Greek mathematician

who had a consistent interest in the arts. There are several

passages in his Optics where he makes reference to painting and sculpture, and in the Almagest there is a charming pas-

sage in which the author writes with almost craftsmanlike

sensitivity about constructing and painting a model of the

celestial globe.41 Ptolemy sounds there like some Alexan- drian Alberti, an all-around genius, and it is not surprizing that he of all the classical philosophers involved in problems of optics, astronomy, and geography should want to visual- ize the world like a perspective picture.

Nonetheless, the Geographia was hardly intended to serve artists. It was written for cartographers and mathema-

< -- dm ago

Ap

Fig. 9. How Ptolemy wanted the globe to be seen prior to his third method (author).

-

2:

- ...... S: -

8 . _

Fig. io. Ptolemy's third method using linear perspective (author).

ticians, and the perspective explanation is couched in the

most abstruse terminology. Furthermore, the original dia-

gram which accompanied the text in Book Seven is lost. In

the subsequent Greek and Latin copies of the fourteenth and

fifteenth centuries there is no explanatory diagram at all.

The method in fact was apparently so difficult that no

mediaeval or Renaissance cartographer understood it. Nev- er to my knowledge was this third method employed for the

making of Ptolemaic maps.42 Professor Neugebauer has recently published a recon-

struction of Ptolemy's linear perspective map projection without acknowledging its importance to the history of

art.43 Figure io is a diagram which explains how Ptolemy worked out his perspective picture. First he would draw

two concentric circles, the smaller representing the Earth, the larger the outer "sphere" of the heavens. Then following astronomical practice, he marked on the great circle of the

heavens where the northern and southern solstitial rings crossed (ZH and BA). IHP represents the meridian on the

40. See O. Neugebauer, "Ptolemy's Geography, Book vii, Chapters 6 and

7," Isis, L (I959), zz-z9. 41. Manitius and Neugebauer, Ptolemaus; Handbuch der Astronomie, II,

72 (Book viii, Chap. 3).

42. The earliest Ptolemaic atlas that I have seen in which there is an at-

tempt to reconstruct the third method is the Marco Beneventano edition,

Rome, 1507. 43. Neugebauer, "Ptolemy's Geography."

285

Earth which runs through the poles. On this meridian he next marked the point 2 where the parallel through Syene crossed. This point, it will be remembered, also marks the

place where the observer's visual axis contacts the surface of the globe.

Next, Ptolemy extended a line from this point of sight at

2; to Qt. From Q2 he then drew lines to B and Z, and through 1H and A to where they touched the central meridian. He thus established eight points around which he could construct two perspective ellipses. In other words, he devised a linear

perspective construction from a "distance point," 2. The theoretical observer stands with his visual axis extending to Z, distance Q2; away. The northern solstitial ring appears as an ellipse, ZH, seen from below, while the southern

ring, BA, is seen from above. The circle through Syene therefore appears as a straight line since its plane is exactly on level with the observer's own eyes. Ptolemy's perspective did not depend, as did Brunelleschi's Renaissance construc- tion, on the centric vanishing point.44 Nonetheless, a van-

ishing point is implicit at 2, and one could construct exactly the same result by projecting the ellipses from that center.45 Ptolemy went on to describe how the ends of the ellipses should be drawn as rounded.46 This is interesting, because as anyone knows who has looked at pictures from late an-

tiquity, circular objects were then often drawn as ovals with

pointed ends, more like American-style footballs than true

perspective ellipses.47 The Alexandrian geographer also

suggested that brighter colors be used to define those parts of the depicted sphere nearest the viewer while fainter colors be used for parts further away.48

It is amazing how many passages of the Geographia, espe- cially in Book One, contain ideas that seem relevant to Florentine artistic thought in the early fifteenth century. In the first paragraph, Ptolemy makes a cogent analogy be- tween geography and painting as he attempts to separate his subject from chorography-his word for the decoration of maps with topographical details:

The end of chorography is to deal separately with a part of the whole, as if one were to paint only the eye or ear by itself. The task of geography is to survey the whole in its just proportion, as one would the entire head. For in an entire painting we must first put in the larger features and afterwards those detailed features which portraits and pictures may require, giving them proportion in relation to one another so that their correct distance apart can be seen by examining them, to note whether they form the whole or part of the picture.49

After detailing his longitude-latitude system and explaining his first two cartographic methods, Ptolemy continues:

We are able therefore to know the exact position of any particular place; and the position of the various countries, how they are inte- grated in regard to one another, how situated in regard to the whole inhabited world.50

Ptolemy's classical geography thus confirms the basic tenet of classical art; the whole must express the sum of all its parts. What impetus these words must have given to men like Brunelleschi, Alberti, Toscanelli, and Columbus!

Figure ii shows one of the maps from a fourteenth-cen- tury Greek Ptolemaic atlas which may have been a copy purchased by the influential Antonio Corbinelli, a charter member of the Florentine Greek academy.51 Of the twenty- seven charts in this and similar editions, only the first, the mappamundi showing the whole oikumene, was ever pro- jected by Ptolemy's first or second cartographic method. All the other maps were strictly rectilinear grids on which were shown the separate regions of the oikumene. Ptolemy's world still centered on the European-North African-West Asian land mass. Not until the sixteenth century did maps include broader reaches of the surrounding oceans. But Ptolemy's text did explain, and his perspectival third pro- jection made even more explicit, that the oikumene occu-

44. Edgerton, "Brunelleschi's First Perspective Picture"; Renaissance Rediscovery.

45. That is by the method described by Alberti in which an ellipse is in- scribed in a foreshortened square projected to a centric vanishing point.

46. Neugebauer, "Ptolemy's Geography," p. 24. Ptolemy's text on this reads as follows: "At the design of the rings, one has to watch that each goes through the said four points, in an egg-shaped form and not ending sharply where they meet the outermost circle, in order not to give the impression of a break, but it should be given a consistent direction even if the convexities which end the ellipse fall outside the circle which encompasses the figure; this also appears to happen with the real [rings]."

47. The figures Ptolemy described are linear perspective ellipses rather than true geometric figures. The difference is that in linear perspective, the major axis of the ellipse does not divide it exactly in half. In perspective, the "leading half" of a circle appears illusionistically to be fatter than the re- ceding part. Also, as Ptolemy noted, the figure appears to widen before the major axis instead of being at its widest at just those points where the major axis touches the ends of the ellipse. It is interesting that Paolo Uccello, in his famous drawing of a chalice now in the Uffizi (Fig. iz here), did not apply linear perspective rules. The individual circular turns of the chalice were not drawn as perspective but as true geometric ellipses, nor were these figures projected to a single centric vanishing point.

48. Neugebauer, "Ptolemy's Geography," p. 24. Ptolemy's text continues: "One must also take care that the circles are not merely [represented by simple] lines but with an appropriate width and in different colors and also

that the arcs across the earth [be given] in a fainter color than those near the eye; and that of [apparently] intersecting parts those which are more distant from the eye be interrupted by the nearer ones, corresponding to the true position on the rings and on the earth .

49. See Miik and Hopfner, "Das Klaudios Ptolemaios Einfuihrung," p. 13, fn. 3. This and the other passages quoted in my text are reasonably correct renditions of the original Greek and most subsequent Latin copies. They are based on Edward Luther Stevenson's English translation (after the Latin) of Ptolemy's Geographia (New York, 1932). The cited quotation is from Book I, Chap. i.

50. Miik and Hopfner, "Das Klaudios Ptolemaios Einfuihrung," p. 61. The quotation is from Book I, Chap. 19.

5i. Plut. 28.49, Laurentian Library, Florence, fol. 51V

is 60M T ui '>p 6044

a" '"04W aw r. - .t rwm

l_. 7$L t

V. A& AO er" v al 0 cy SI/4-4 -i 1* p, r >iY~WI *'('

; CI [Al~~p I~ Ic Mt0 Kc

cVve. ''Zr;YI46Y xY1 IQ~JU60I~6 I~

0% At; A

0

Al H

ELfL 'C r? (O f1OII if

Cl~r f?' 01?J~o~r ~ oI-?? j d'

r cr~?-Zj"I1?n~n ~ ~ ~ A

IF,

kO~no

Fig. II. Ptolemy, single-page map from the Geographia (Laurentian Li- brary, Florence, Plut. 28.49, fol. 51v).

pied only a part of the whole sphere. If one could determine

longitudes eastward from the Fortunate Islands, one could

also, at least theoretically, determine them westward as far as Cathay.52 This is clear from another of Ptolemy's state- ments:

From the ratio of any given arc to the total circumference of the great circle, the number of stadia [between places on the Earth] can be calculated from the known number of stadia in the circuit of the whole Earth.53

Of course this was much easier said than done, even though Ptolemy had made a reasonably good estimate of the cir- cumference of the globe. From the moment the Ptolemaic atlas appeared in Florence, however, the gauntlet was down, waiting for some would-be Columbus to pick it up. To be

sure, the actual geography of Ptolemy's book left much to be

desired, as is obvious from the shape and location of the delineated lands on the mappamundi. His contribution was not to this kind of topographical knowledge, but to the science of measurement.

Ptolemaic maps were not intended originally for the use of seafarers and did not until late in the eighteenth century supplant the portolan sailing charts. Instead, the new grid technique of mapping was of greater importance to land-

lubbing intellectuals, and in this sense helped shape the

52z. John Kirkland Wright, "Notes on the Knowledge of Longitudes and Latitudes in the Middle Ages," Isis, v (19zz), 75-98; also O. Neugebauer, "Mathematical Methods in Ancient Astronomy," Bulletin of the American Mathematical Society, LIV (1948), 1013-1014.

53. Mzik and Hopfner, "Das Klaudios Ptolemaios Einfiihrung," p. zo. The cited text is from Book I, Chap. 3, Part i.

287

Renaissance attitude about man and his world. The portolan sailing chart, while useful for direction finding at sea, did not furnish a uniform framework for perceiving the Earth as a whole. The Ptolemaic grid on the other hand gave instant geometric continuity. The most far-flung places could, at least theoretically, be fixed precisely in relation to one another by absolute coordinates so that their propor- tionate distances apart, as well as their directions from one another, became instantly apparent. At just the time when much new information was becoming available about the outside world, the Ptolemaic system gave Western Euro- peans the power to catalogue, collate, and correct geo- graphic knowledge. Above all, it seemed to indicate that the Earth was subject to the same principles of harmony and proportion that people expected of the moral and social order.

Brunelleschi's great achievement in architecture and Al- berti's in the theory of painting were that they understood this relationship and could apply the grid metaphorically and aesthetically in their art. Alberti's perspective rules, in- volving a projected checkerboard pavimento, were intended not to provide merely "realism" but rather a rational stage setting for the noble subject of the picture, or istoria. For Alberti, the purpose of painting was to teach moral lessons. Linear perspective therefore provided a pictorial matrix symbolic of a world in which everything has its ordained place and man himself is in harmony with God's master plan of the universe. This same concept also pervades Brunel- leschi's architecture. In S. Lorenzo (Fig. 4), the gridded floor is no mere decoration. Rather, it gives the module for the entire architectural conception. The didactic purpose of Brunelleschi's church, like Alberti's istoria, was to show man how to live in harmony with God. Mathematics seemed to be the chief instrument of the Divine Will, and the geometric grid was its earthly metaphor.

In truth, the grid was not new to Western Europeans. It had already been applied to land measure by surveyors, cartographers, and even architects since the beginning of the Middle Ages.54 Indeed, the grid must have something to do with the primal structuring power of the human brain itself. The modern Swiss psychologist Jean Piaget has dis- cussed what he calls the "space structuration" process in

little children; how they develop a sense of a priori, abstract, horizontal and vertical coordination in their surrounding space.55 No matter how a gridded surface is shrunk, en- larged, twisted, warped, curved, or peeled from a sphere, the human observer learns never to lose his sense of how the parts of the surface articulate, even when the grid squares themselves have become distorted. Whatever the configura- tion of a grid-divided surface, the observer is able to comprehend all of its continuity as long as he can relate to the side of at least one undistorted, modular square which represents the true unit of measurement for judging the whole.

The Ptolemaic grid was not new to Western Europe, but it reappeared at a particularly opportune moment when the intellectual climate of Florence was ideally prepared to take advantage of it in new and creative ways. The fact that it reappeared in the guise of an ancient Greek manuscript, just when Greek studies were obsessively fascinating to Floren- tine intellectuals, that it arrived at a time when mathematics generally were being appreciated with a new moral as well as practical fervor, served to give impetus to Ptolemy's grid as no similar notion had ever enjoyed before. It seems clear that there could have been no appreciation or application of linear perspective in pictures and no appreciation or appli- cation of Brunelleschi's modular system of architecture without the kind of space structuration Ptolemy's atlas now encouraged in the Renaissance mind.56

That Florentines were beginning to think according to the Ptolemaic system is evident in the mid-fifteenth-century writings of Giovanni Cavalcanti. In his Istoria Fiorentina of about 1440, Cavalcanti described a territorial dispute be- tween his home city and Milan during the wars of the 1420s, and mentions that a longitudinal line was to be established as a boundary between the two states. This may be the first instance where an imaginary geometric line rather than a physical landmark was to be recognized as a territorial limit to a political power:

And thus the eye is the ruler and compass of distant regions and of longitudes and abstract lines. Everything is comprehended under the geometric doctrine, and with the aid of the arithmetic art, we see that there is a rule for measuring with the eye. . ...

54. See D. J. Price, "Medieval Land Surveying and Topographical Maps," The Geographical Journal, cxxi (1955), I-io; also Richard Krautheimer and Trude Krautheimer-Hess, Lorenzo Ghiberti (Princeton, N.J., 1956), p. 237, fn. zz. The oldest surviving portolan chart, the so-called Carta Pisana, ca. Iz275, in the National Library, Paris, shows a simple grid device over the compass rose. Also the famous psychotic cartographer Opicinus de Canis- tris applied a grid to his weird, erotic map of Pavia (ca. 1336-1337): Richard G. Salomon, "Aftermath to Opicinus de Canistris," Journal of the Warburg and Courtauld Institutes, xxv (i962), 141-146.

55. See, for instance, Piaget's short work on Psychology and Epistemol- ogy, trans. Arnold Rosin (New York, 1971).

56. Parallels between Ptolemy's geography and Renaissance ideas about architecture have already been suggested by Dagobert Frey, Gotik und Renaissance als Grundlagen der modernen Weltanschauung (Augsburg, 1929), pp. zoff.; and Joan Gadol, Leon Battista Alberti: Universal Man of the Early Renaissance (Chicago, 1969), pp. 70-74.

57. Giovanni Cavalcanti, Istoria Fiorentine (printed edition; Florence, 1838), I, ix, zo: "E cosi l'occhio e regolo e sesta dei paesi lontani, e delle longitudini e linee incorporee. Ogni cosa si comprende sotto la dottrina geometrica, e con l'ajuto dell'aritmetica arte noi veggiamo che ci e una regola a misurare... coll'occhio...."

z88

*"'-~ ?'C~ ~.!.*---1.. r ? sJ-;

r- ~ r t ?T1---- 1( -rrs*r- ii- I Fi ? i ir i - t ..

3 -. r

i ?1~- r- \ L I

- ---- ~ ;U-- - `Ct;' .i L.- i;`?I.L~r??t;7 ~~cl"C f ~'-l----CI-- L".--*? --?-- -q_-,~;, C-- \t~P~L. .t

.i?--c~- ,~c i" * I -L *- i _2~1Z1~1--~i~;=Yt-=;I~T~'?\r? II`~, il.?'`~bJ

c-. ~~*"X? L- :I r \

I t `u? 1.1 ; JZ: 1,.

4J - "?- f- ?- ??+-- .",-- ^1- ?t c~ * t

t

'i 7 i L i.-ii..?i i

..1. t ?f ? it ~ I-~ , ?--- i , t c?-: :? C--?e

~?t~? 1-t-r-l'-~ ~ ~?d?, /7~'-t' " ft 21~~

r _7 -I-- t :. ~~-J '-'-\ r i ?? 3 1, -. -?,

.i: F" --t~-i-t ?-Id: -~s :* tS ?i~" ~ I~i`r~

~~fT: ~ ?r r?- *'i r: : ?;

*-1_ i Li ?- i;' itl i IC,. t i?r;

;1?-I. + t i i e??"i t :/i T' 1- i?

'' f"t--- t. -I--L1 h,--- i ,-ft-f~-i t -?-

r i-i-- ~ ,i 1 t t -' i? ?? ? t-- f ?- .F"-!':'L v

I; - ?:, ~-(. r + (?? : "c- rS :c-~.-+ ~ -? :r i r? i .. (i i ".rz~ ?- ~n~R""~ ? i c-? C.. i ?r I* -t

.?~ ??C\ ̀ 4/ L Y il~F t c. ----r-.- -.C--)-?--~

:t "" &- '" ~

~, .,.tl""' ;t x;r? " a,

.. -

Fig. iz. Paolo Uccello, Chalice, ca. 1440 (photo: Gabinetto dei disegni, Uffizi, Florence).

Moreover, it may be no coincidence that the grid was also

being applied, by Masaccio for example, to the craft of fresco painting. Just when Ptolemy's Geographia was being copied and disseminated from the scriptoria of Florence, Masaccio seems to have abandoned the traditional sinopia method for laying up his Trinity fresco in Sta. Maria No- vella in favor of a grid for transferring details from his sketches tooled into the intonaco surface.58 Another ex-

ample of this fascination for the grid among Florentine artists, even as applied to the surface of a sphere, is seen in the well-known drawing of a chalice attributed to Paolo Uccello (Fig. iz).

Antonio Manetti, Brunelleschi's biographer, tells how his hero and Donatello, after Brunelleschi failed to win the

Baptistery door competition, went to Rome to study ancient architecture. In so doing, Manetti writes, they made plans and elevations by means of drawings on grid paper, ". .. on

strips of parchment graphs with numbers and symbols which Filippo alone understood."59 In other words, he drew charts, squared like those in the Ptolemaic atlas, including a similar system for numbering and lettering the parallels and meridians at the sides. Brunelleschi not only employed the

grid for copying ancient buildings to scale, but also in-

corporated this concept as a modular system for his archi- tecture.

Alberti also became quite interested in cartography and worked out a mapping technique of his own which he ap- plied to a new plan for the city of Rome. His scheme was not quite the same as Ptolemy's but certainly derived from it. Alberti explained it carefully in a brief treatise entitled

Descriptio urbis Romae, written about 1450. The original map is lost, but a recent reconstruction has been published by Luigi Vagnetti (Fig. 13).60

Alberti started with a circle he called a "horizon" and divided it into a number of equal parts or degrees, each num- bered and connected to the center by radii. These radii acted as meridians. Then equally spaced, concentric circles were drawn from the center, like parallels. Thus, the whole looked like the Ptolemaic globe with its point of sight at one of the poles. Each of the radii (meridians) and concentric circles (parallels) was given a number. Alberti then con- structed a mechanical measuring device of this same shape and set it up on the Capitoline Hill, which was to be the exact center of the circular map. With the instrument lined

up so that o', that is, radius #48, pointed north, he devised a

small ruler (also called by him a "radius") fixed with one end at the center of the disk and rotatable so that he could site different landmarks by looking along its edge. With this instrument he could fix the location of various buildings in the city in relation to each other along the "horizon" by determining their meridians. Next, by pacing off the dis- tance each building was away from the center, he would be able to locate these places on the proper parallels. Thus, he had devised a very simple system for fixing a set of coordi- nates to every landmark in Rome. He then provided a table listing all the sites and their coordinates so they could be found on the map. To this day street guides constructed on the same principle are mounted in the public squares of

58. See Joseph Polzer, "The Anatomy of Masaccio's Holy Trinity," Jahr- buch der Berliner Museen, xiii (1971), 18-59; Ugo Procacci, The Great Age of Fresco; Giotto to Pontormo, Metropolitan Museum of Art Catalogue of an Exhibition of Mural Paintings and Monumental Drawings (New York, 1968), p. 29; and Millard Meiss, The Great Age of Frescoes; Discoveries, Recoveries, and Survivals (New York, 1970), pp. 124-127.

59. Life of Brunelleschi, pp. 52-53, also p. 132, fn. 34. The Italian reads as follows: "... in su striscie di pergamene che si lieuano per riquadrare le carte con numero d'abaco e caratte che Filippo intendeva per se medesimo."

6o. Luigi Vagnetti, "La 'Descriptio Urbis Romae' di L. B. Alberti," Quaderno n. i, Universitai degli studi di Genova; Facoltai di Architettura ..., October 1968, pp. z5-8i; also Giovanni Orlandi, "Nota sul testo della 'Descriptio Urbis Romae' di L. B. Alberti," ibid., pp. 81-91.

289 SEPTENTRIO

47 48

48 20

245 46 2

44 4

43 5

42 •6

41 / 7

4O' ," /-"ll-•C=-. \-'i;b~A\\\i~ \ 8

39 / i

OCCIDENS 36 "AT 12 ORIENS

35 13

34 14

ii

7 21

2 20

AUSTER

Fig. 13. Alberti, Map of Rome, from the Descriptio Urbis Romae, ca. 1450 (reconstruction by Luigi Vagnetti). The thin line represents the walls of the city established by aerial survey in 195o by the Istituto Geografico Militare; the thick line follows Alberti's calculations. The numbered circles are Alberti's locations for monuments; their actual locations established by the I.G.M. survey are indicated by squares.

many cities in France, and tourists find their destinations

merely by twisting a dial according to the coordinates listed

on an accompanying alphabetical chart.61

But certainly the most interesting adaptation of Ptolemaic

grid-thinking to the art of painting in the fifteenth century was Alberti's velo, which he described in Book Two of the

Treatise on Painting:

It is like this: a veil loosely woven of fine thread, dyed whatever color

you please, divided up by thicker threads into as many parallel square sections as you like, and stretched on a frame. I set this up between the eye and the object to be represented, so that the visual pyramid passes through the loose weave of the veil.62

For the author of the Treatise on Painting however the grid- formed velo was not merely a device for transferring a scale

drawing, but a means for organizing the visible world into a

geometric composition, structured on evenly spaced grid coordinates. Alberti then admonished his artist-readers to

learn to see in terms of such grid coordinates in order that

they develop an intuitive sense of proportion:

A further advantage is that the position of the outlines and the boundaries of the surfaces can easily be established accurately on the

painting panel; for just as you see the forehead in one parallel, the nose in the next, the cheeks in another, the chin in one below, and

everything else in its particular place, so you can situate precisely all the features on the panel or wall which you have similarly divided into

appropriate parallels. Lastly, this veil affords the greatest assistance in executing your picture, since you can see any object that is round and in relief, represented on the flat surface of the veil.63

How similar Alberti's attitude is to Ptolemy's, especially as

the Alexandrian described the purpose of chorography in

the opening pages of the Geographia. Some idea of how 61. Alberti also described a similar surveying device in his treatise on

practical mathematics, the Ludi matematici, and again in his De statua. In the latter, the companion piece to his Treatise on Painting, Alberti applied the same principle to a device for copying statues.

6z. Cecil Grayson, ed., Leon Battista Alberti On Painting and On Sculp- ture (London, 1972), pp. 68-69. The cited text is Grayson's translation from the original Latin.

63. Ibid.; for more on this idea, see Erwin Panofsky, "The History of the

Theory of Human Proportions as a Reflection of the History of Styles," in

Meaning in the Visual Arts (Garden City, N.Y., 1957), PP. 55-107.

z90o

~* .~~ -

r.

...

-

Fig. 14. An artist drawing a picture using the Albertian velo, ca. IS3I (from Duke Johann II of Bavaria and Hieronymous Rodler, Eyn schon ntitzlich bzchlein und unterweisung der kunst des Messens, '53').

Alberti's velo might have been put into practice is seen in

Figure 14, a 1531 woodcut from a German treatise on the "art of measurement.6"" Albrecht Diirer also adapted the same idea to his own Underweysung der Messung.65

It is also no coincidence that Pius II was more than cas-

ually interested in Ptolemy's Geographia. It was during his

papacy (1458-1464) that the official nihil obstat of the Ro- man Church was granted to the new atlas. He himself wrote a lengthy Cosmographia (as part of his Historia rerum

ubique gestarum) full of references to the Alexandrian ge- ographer including a chapter on longitudes and latitudes.66 In fact Columbus owned an annotated copy. Certainly Ptolemy lurks in the background of the planning of the

square in Pius's Pienza (Fig. 15).67

Since ancient times, the mathematically related sciences have had a role in the lives of Western peoples different from that in contemporaneous civilizations to the east. Western- ers saw mathematics as serving two functions: as the model

by which God ordered the universe, and as a practical tool for secular gain. No matter that these two concepts were often in philosophical conflict, this symbiosis between God and mammon has remained a peculiar Western accomplish- ment. Only in the West did there develop the kind of psycho- logical "mental set" which could rationalize capitalism as an extension of moral law. Only in the West was there a

propensity to understand mathematics simultaneously as the key to the mystery of God's Will and as the tool for man's conquest of the physical world. It is interesting that both the

Empire of China and the states of Islam possessed carto-

graphic systems based on the grid long before it became known in the West.68 The Mohammedans had exploited the Ptolemaic method for centuries, but neither of these two

great civilizations, both ahead of the West in nearly all mat- ters of science and technology at the beginning of the Renais- sance, ever made the psychological connection between a

conception of a mathematically ordered world and practi- cal, empirical visual perception as did the Western Chris- tians. No Chinese or Muslim artist ever devised a method of linear perspective based on projecting a grid plane to a

single vanishing point. Similarly, no Chinese or Muslim sailor ever applied such a conception of the world to the

possibility of sailing around it to reach land from the other side.

Was there never a Chinese or Muslim Toscanelli? It does seem clear that even if there were, he would not have had a

community like Florence in which to exert his influence. The

68. Joseph Needham, Wang Ling, and Lu Gwei-Djen, Science and Civilisation in China (Cambridge, Eng., 1959),

II, 525-591.

Awl

IV

, aaB

~kb

Fig. i5. The Square, Pienza, ca. 1465 (from E. Carli, Pienza, 1967).

64. Johann II of Bavaria, Eyn scho6n niitzlich btchlein und unterweisung der kunst des Messens ... (Simeren, Germany, 1531). This has frequently been attributed to the duke's secretary, Hieronymous Rodler. The picture is illustrated and discussed by Joseph Meder, Die Handzeichnung; ihre Technik und Entwicklung (Vienna, 1923), p. 475.

65. Erwin Panofsky, Albrecht Durer, z vols. (Princeton, N.J., 1948), I, z52zff.

66. Aeneae Sylvii Piccolominei postea Pii II Papae opera Geographica et Historica (printed edition; Helmstadt, Germany, 1699/I700), Chap. 4, pp. 10-11.

67..Enzo Carli, Pienza, la cittd di Pio II (Rome, 1967).

291

Fig. I6. Antonio Pollaiuolo, Pro-

spectiva, ca. 1493. Detail of the tomb of Sixtus IV, S. Pietro in Vincoli, Rome (photo: Alinari- Art Reference Bureau).

s:lo~-"ii"i~ ""; ; .. ~s.?c i Lie,, c c. c- L, 4 t

aB~- ill ""--s I i la -eY ~~C ~ld~r

/ ~C"~ s~? J

r?l.

*

sfttl-a Q, a~z~-i~F ~ ~F i I~PI\ ?

5;?- f~'i~"?~Y;~! ~T a

i:. ;9 ::i?:;;?

~-~"L~ert?~ k ;d c--t

;k~r:Llu\L;i?J~ ~`c~-?~~* r~ ~.c`?~`r??l"z;~.i~~Llir:~5 .

J. ta: ;? f -- a i-t

imperial and bureaucratic policies of China and Islam dur-

ing the Middle Ages did not encourage the kind of first-

name, everybody-knows-everybody-else camaraderie of the small-scale Italian communes. Such "interdisciplinary" en-

couragement is perhaps Florence's greatest contribution. We might sum up by looking at a bronze relief cast in 1493

by the Florentine Antonio Pollaiuolo for the tomb of Sixtus

IV (Fig. i6). The subject shows a svelte, allegorical figure of

Prospectiva, as one of the artes liberales surrounding the

effigy of the pontiff. We should not be surprised to find the

science of optics now elevated to the heretofore exclusive

seven, but it is odd that the artist chose to include an astro-

labe, the ancient tool for determining latitude, as one of

Prospectiva's attributes.69 The astrolabe, of course, was well

known to astronomers and geographers, but normally had

no significance for optical scientists. The reason for its in- clusion must be that Pollaiuolo recognized optics as the

basis for all sciences of measuring. Prospectiva also holds in

her hands the oak branch symbol of the pope's della Rovere

family and a copy of a book open to a page inscribed with

scattered phrases from John Pecham's Perspectiva com-

munis, the most popular book on optics throughout the

Middle Ages and Renaissance.70 Pollaiuolo probably never

--? R VI Z- ,*

r L.;r

:3if. =,~-:~$6

;;"

-?i ?; 8

.I-:.t

- a ~:

?9V':~`tii;?k?, ~~Q~ ?i?: ~x~;4-c;r

~I ;- ?d ~5 k ~i"

i -~~;: ~

:? i r

Fig. 17. Leonardo da Vinci, Prospettografo, ca. 1480-1482 (Codex Atlanticus, fol. Ibisr-a; photo: Elmer Belt Library).

lucis in rectum semper porrigitur nisi curvetur diversitate medii / Incidentiae et reflectionis anguli sunt aequales." These are unconnected phrases from Pecham's Perspectiva communis. It is tempting, of course, to think that Pollaiuolo actually intended to represent painters' perspective in his alle- gorical rendition of Prospectiva. Most recently, Gadol (Leon Battista Al- berti, p. 132) has suggested, "She [Prospectiva] is no longer the theoretical science of optics ... she became an applied mathematical science in the course of the fifteenth century, and as such drew painting into the circle of the liberal arts." In the light of the widespread interest in theoretical optics all over Europe at this time and its increasing influence in intellectual circles, it is hard to believe Pollaiuolo intended, much less would have been allowed to decorate the pope's tomb with, what amounted to only a workshop subscience under the more exalted aegis of optics. Nevertheless, the fact that Pollaiuolo had his Prospectiva carry an astrolabe implies that, since she had finally raised herself to be included among the liberal arts, she ought now to be considered the "mother" of all the arts of measurement. Cartog- raphy, therefore, and no doubt painting and sculpture too, could be

thought of as Prospectiva's "handmaidens."

69. L. D. Ettlinger, "Pollaiuolo's Tomb of Pope Sixtus IV," Journal of the Warburg and Courtauld Institutes, xvi (I953), z58-z6i.

70. Ibid., p. 258; also David C. Lindberg, John Pecham and the Science of Optics; Perspectiva communis (Madison, Wis., 1970), p. 32. The Latin in- scription in Prospectiva's open book reads as follows: "Sine luce nihil videtur / Visio fit per lineas radiosas recte super occulum mittentes / Radius

292

heard of Christopher Columbus, and the date of his relief is only a happy coincidence. Nevertheless, it is no coinci- dence that architecture, painting, science, and technology were remarkably congruent in the fifteenth century. Pol-

laiuolo's notion of Prospectiva seems to have been very much in the mind of Leonardo da Vinci (Fig. 17), who was

writing at this time:

The eye is the master of astronomy, it makes geography, it advises and corrects all human arts ... the eye carries men to different parts of the world, it is the prince of mathematics ... it has created archi- tecture, and perspective, and divine painting . . . it has discovered navigation.7n

Too bad Leonardo's notion of knowledge has not carried over into the curriculum of the modern college of liberal arts. What has happened to the once lively Renaissance fusion between the sciences and the humanities ? Perhaps only in a small community like mediaeval Florence was it

possible for a good idea to get from the bottom to the top in a short time, and so many different "disciplines" in the

pursuit of both God and secular gain fuse together with such creative results. Perhaps also it is poetic justice that Amerigo Vespucci the Florentine, rather than Christopher Columbus the Genoese, gave his name to the great continents newly discovered through the transformed visual power of the Italian Renaissance.

71. For a contextual discussion of this passage, see Vassily Zubov, Leonardo da Vinci (Cambridge, Mass., 1968), pp. I3Iff.; concerning Leo- nardo's own applications of Ptolemaic geography, see M. Baratta, ed., I

disegni geografici: Leonardo da Vinci (Rome, 1941); also L. Heydenreich, Leonardo da Vinci (New York, 1954), T, 86-89.