Contents:



The Place of a Hidden Pavement


An Accident Reveals a Cover-up

The Lineage of Geometric Pavements


The Laurentian Geometric Pavement


The Fifteen Panels of the Pavement


The Medici Panel #2

Ellipse #

#1

#2

#3

#4

#5

#6

#7

X Axis

5:3

9:5

5:3

9:5

8:4

9:5

9:4

Y Axis

3:1

21:8

2:1

9:5

9:5

9:5

9:5


The Incommensurable Panel: Panel #7


The Lambda Panel: Panel #14


In Conclusion


Books and Buildings


A New Public Library


The Programmatic Needs of the Reading Room

The Size of the Collection

Alternative Floor Plans that would reveal the Geometric Pavement

Modifying the Basilical Form

Which scheme?


A Codex for Mannerism


The Artist's Text

The Author

Real Bookworms

Figures

Fig. I The Laurentian Library geometric pavement revealed beneath the desks (montage)

Fig. 2 The architectonic weight of the vestibule. (photo: Alinari PIN1906)

Fig. 3 Reading Room with furniture. (photo: Bib. Laur. #22299a)

Fig. 4 The passageway to the Rotunda (photo: Contardi pl.135)

Fig. 5 The Reading Room without furniture, 1928 (photo: Bib. Laur. #b15606)

Fig. 6 Biscioni's trapdoors in the dais (photo: Nicholson)

Fig. 7 Biscioni's engraving of the pavement (Biscioni, Pl IV)

Fig. 8 Plan of the lateral pavement from the Scholtz Sketchbook (photo: Met.N.Y. # 49.92.90.Recto)

Fig. 9 Plan of Laurentian Vestibule, from Rossi, Pl. I (photo: Art Institute of Chicago)

Fig.10 Fallaceous pavement designs of Stegmann & Geymuller, Band VIII, Bl.8 (photo: Art Institute of Chicago)

Fig.11 Photographs of the pavement from the Laurentian Library archive.

Fig.12 The desks being removed during WW II (photo: Bib. Laur.)

Fig.13 Durer's studies of tiled pavements. (Netherlands Sketchbook, 13 verso)

Fig.14 Ceiling and garden designs, (Serlio, S. On architecture Bk.IV)

Fig.15 The Sacred Cut revisited: The pavement of the Baptistery of San Giavanni, Florence by Kim Williams

Fig.16 The Shrine of the Holy Sepulchter, Cappella Rucellai, S. Pancrazio, Alberti (photo: Borsi, Pg.82)

Fig.17 The fifteen geometric panels in the attic order of the facade of S.M.Novella, Alberti (photo: Borsi, Pg.70)

Fig.18 Tomb marker of Cosimo de 'Medici in S. Lorenzo, Verrocchio (photo: McKillop, fig.14)

Fig.19 The Cosmatesque pavement in the Sistine Chapel

Fig.20 The Sistine Chapel pavement (Camesasca & Ettore)

Fig.21 The fifteen goemetric pavement panels on the west side. Photo: Bib. Laur. 43101-43112, 43098-9, 33100)

Fig.22 Panel 2. Painting by Blake Summers (photo: Gerry Henderson)

Fig.23 Rosette design in the Florence Baptistery: the geometric construction (photo: Alinari No 1888)

Fig.24 Panel 2: geometric construction. (Drg. Hisano & Wibisono)

Fig.25 Panel 7. Painting by Blake Summers (photo: Ralph Schopen)

Fig.26 Geometric panel in the Lower church of St. Francis in Assisi.

Fig.27 Geometric Construction of Panel 7, by Wayne Bock

Fig.28 Panel 14. Painting by Blake Summers (photo: Gerry Henderson)

Fig.29 Geometric construction of Panel 14, by David Tsevat)

Fig.30 A figure and proportional scale, after Michelangelo, related to the geometric structure of the Panel 14 (Nicholson)

Fig.31 The Platonic Lambda (S.Georgio, G. Riesch)

Fig.32 A Durer, 'Body of a Child' Dover Books.

Fig.33 The 4 gold rings of the Medici Coat of Arms. (photo: Alinari PIN 1910)

Fig.34 San Marco Library, Florence, 1440.

Fig.35 San Marco: catalog system (Nicholson)

Fig.36 The Malatesta Library at Cesena 1477. (L.Baldacchini, pg.88)

Fig.37 Studiolo in the Urbino Ducal Palace, Urbino.

Fig.38 The Laurentian Library within the church complex at S. Lorenzo, Florence

Fig.39 Plan of San Lorenzo complex (after W. and E. Paatz)

Fig.40 The Latin and Greek Libraries of the Imperial Forum, 107-113 AD (drawing: Rome Blue Guide pg.102)

Fig.41 Composite of three early drawings showing how the library might have been planned at an early stage.

Fig.42 Wooden Dias beneath the desks of the Cesena Library (L.Baldacchini pg.95)

Fig.43 Drawing of interlocking desks (photo: Casa Buonarroti 94A)

Fig.44 The desks being removed during WWII (photo: Bib. Laur.)

Fig.45 A proposal for the Reading Room utilizing three passageways and two lines of desks (montage Nicholoson)

Fig.46 A library desk for one book, fabricated in the 19th century (photo: Bib.Laur.)

Fig.47 The book security system of the Laurentian Library (Clark, 144.5)

Fig.48 Laurentian Library catalog system, circa 1589. (Nicholson)

Fig.49 Reading Room, interior elevation study (photo: Casa Buonarroti 42A)

Fig 50 Mineralogical analysis of the geometric pavement in the Laurentian Library. (photo: Spampinato)

Fig.51 The desks being removed for safe keeping during WWII (photo: Bib.Laur.)

Fig.52 Top: Worm pilings from active woodworm in the Dias.
Bottom: Worm damage to original ash desks and 20th century pine subflooring (photo:Potz)

 

Notes

1 Biscioni, A.M. Bibliotecae Ebraicae, Graecae, Florentinae: Bibliothecae Mediceo (Florence 1752-7), 34-35. Biscioni's introduction to his catalog of the book collection gives a good history of the formation of the Library and includes the story of his discovery of the lateral pavements.

2 Rossi, G.I. La Libraria Medicea Laurenziana, Architettura di Michelangelo Buonarotti (Florence 1727-39).

3 Stegmann, C.M.R.von, & Geymuller, H.von Die Architektura der Renaissance in Toscana (Munich 1904), vol.VIII, see Plate 8.

4 Schiavo, A. Michelangelo Architetto (Rome 1949), fig.36. "This motive, bearing the Medecean arms in the center, anticipates Michelangelo's drawing for the pavement of the Piazza del Campigdoglio. Goldscheider, L. Michelangelo: Paintings, Sculpture, Architecture (London 1962), Plate XII. The plate includes panel 2, the Campigdoglio, and extant rosette pavement designs and pavements.
De Angelis d'Ossat, G. The Complete Works of Michelangelo (New York 1964), Pg.363-365 "I cannot resist drawing a connection between this contaminated representation of circles and crosses, and the intricate design of one of the late pavement panels of the Laurentian Library (Fig. 193), in which the same design of the plan is effectively geometricised.

5 Catalano, M.A. Il Pavimento della Biblioteca Mediceo Laurenziana (Florence 1992), Pages 28-31. An argument is put foreward stating that Tribolo designed the panels, and suggests that they are based upon engravings found in The Five Books of Architecture of Sebastiano Serlio.

6 Wittkower, R. Michelangelo's Biblioteca Laurenziana, in Idea and Image (London 1978) Pg.55, reprinted from The Art Bulletin, Vol XVI, 1934.

7 I am deeply grateful to the directors of the Laurentian Library who have helped this project in every possible manner. Dott. Morandini generously permitted extraordinary access to the pavement and Dott. Lenzuni has permitted further extensive measuring privileges. Together, with Dott. Dillon and Dott. Viccario, they have been invaluable critics who have advanced and countered every foray into this investigation with great patience and exactitude.

8 Alberti, L. trans. by Rykwert, J. (1988), On the Art of Building in Ten Books, pg.220, Bk.VII Ch.10 v124-126

9 I am endebted to the late Robin Evans who pointed out the similarities between the Pavement and Serlio's plates in 1987.

10 For fear of the smell, it might be wiser to follow his footsteps, for the story goes that Michelangelo had the reputation of sleeping in his boots. His servant once pulled them off and the skin of his feet came with them! Rolf where is this story?

11 "According to Bocchi in 1571, later repeated by Richa and Lalande, the pavement of the choir of S.M. Fiore was done from a design form Michelangelo". Salmi, Mario and Guglio De Angelis D'Ossat, The Complete Works of Michelangelo, Novara, 1967, pg.513

12 The plan of the walls and pavement frame layout has been found to accord to the Sacred Cut. Williams, Kim, "The Sacred Cut Revisited: The Pavement of the Baptistery of San Giovanni, Florence" The Mathematical Intelligencer Vol.16 #2 1994 pp.18-24. See also Evans, Robin "Translations from Drawing to Building", A.A.Files 12 1986, pp.11-14, for an examination of Philibert de l'Orme's pavement of the Royal Chapel, Anet.

13 Borsi, Franco, Leon Battista Alberti, The Complete Works, New York 1989, pg.74 & 79.

14 Ames-Lewis, F. ed: Cosimo 'il Vecchio' de' Medici, 1389-1464. Essays in Commemoration of the 600th Anniversary of Cosimo de' Medici's Birth. McKillop, Susan, "Dante and Lumen Christi: A Proposal for the Meaning of the Tomb of Cosimo de' Medici" OAP1992 pp 245-291. The Tomb has designs in it that are similar to Laurentian Panels #13 and #15.

15 Bartoli, M.T., Un pavimento Neoplatonico, in C. Acidini Luchinat, Benozzo Gozzoli, La Cappella dei Magi, 1994, pp.25-28.

16 Hutton, Edward, The Cosmati: The Roman Marble Workers of 12th Century, London, 1950.

17 Check with Kim Williams to see if she has published this.

18 Rolf, any ideas?Camesasca, Salvini & Ettore, Roberto, The Sistine Chapel, xxxx, 1965, also check Steinmann, Ernst, Die Sixtinische Kapelle, 2 vols, Munich, 1901.?

19 An investigation was made by students of the College of Architecture at IIT, Chicago in 1992 to determine whether a system of proportioning was evident in the Laurentian Library. Nate Lindsay identified The Golden Mean to be present in the north wall of the Reading Room, and Linda Liegh developed the idea, investigating the presence of the Golden Mean as an ordering system that Michelangelo used extensively in his works.

20 The Panels are numbered, starting at the south end of the Reading Room. Each Panel is also named by the author to make them easy to identify; the name relates to the dominant theme expressed in the design.

21 In the center of the Medici panel is an emblemata of Duke Cosimo de Medici's insigna. Cosimo 1 assumed power in 1537 and took for his insigna the six Medici palli. The upper center palli is inscribed with the Fleur de Lys given to Piero di Cosimo in 1465 by Louis XI of France. Above the crown is a five pointed Ducal Crown and below the Palli, on the white ring, is the Order of the Golden Fleece that Cosimo received in July 1545. The two curved forms, composed of C shapes to the left and right of the palli might be the Medici Laurels (broncone), dolphins, the chain for the Golden Fleece, or an amalgam of all three.

22 I am endebted to David Farrel Krell for pointing the presence of the Tectractys in Panel 5.

23 Cox Rearick, Janet Pearson, Dynasty and Destiny in Medici Art, Princeton, 1984, pg.179.

24 Catalana's spends much time on making the link between the masks in Tribolo's sculpture and those of the central pavement in the Laurentian Library. She makes no reference to the mask in Panel 13, whose physiognamy is closer to Michelangelo's mask than it is to Tribolo's.

25 The Florentine Braccio measures .5836 meters. It is divided into 20 soldi and each soldo is divided into 12 dinari, thus the braccio is divided into 240 parts which permits the decimal and duodecimal system to operate. The braccio has the advantage over both the decimal and duodecimal systems as it can express in whole number measurement 1/2 (10 soldi), 1/3 (6 soldi 8 dinari), 1/4 (5 soldi), 1/5 (4 soldi), 1/6 (3 soldi 4 dinari), 1/8 (2 soldi 6 dinari), 1/10 (2 soldi), & 1/12 (1 soldo 8 dinari). This permits ratios and measuration to have a common mean which otherwise would have to be expressed in irrational divisions of measurement; for example a ratio of 20:21 can be expressed as 4 braccia by 4 braccia 4 soldi (4 1/5th braccia). A measurement of 4 braccia 19 soldi and 11 dinari is written as b4 s19.11 (the point is not a decimal point but shorthand for dinaro).

26 During the past decade there has been a renewed interest in architectural geometries and their cosmological sigmificance. Kieth Kritchlow reopened the field of Islamic geometries and the late Robin Evans dedicated his time to investigating Western Architectural Geometries. More recently Kim Williams is preparing a book on Italian pavements, and Steven Wander has been investigating the great Westminster Abbey Sanctury Pavement.

27 The Medici Panel has been co-investigated by 6 students during the past eight years. I am endebted to Karen Taylor, Brandon Diamond, Timothy Burke, Veronica Parvaz, Songjin Choi, and Melanie Langwort whom have advanced every aspect of the panel's geometry.

28 The difference in the ratios are slight but significant. Great care has been taken to differentiate masons error from geometric errancy. The team has taken into account three variables when proposing a 'pure' measurement handed down from the architect. They are: 1) mason's error, 2) settling of the building, 3) obstacles & peculiarities of the site. The archaeological standard of a 2% error has been adhiered to when making a statement without recourse to a footnote, but the critical dimensions have varied by less than 1%. The proposed and actual dimensions, with percentage errors, of the two panels are as follows; the stretching of the long axis may be due to the spreading of the floor.
Long axis Short axis Proposed design b4 s5 d0 b3 s18 d10 West Panel b4 s5 d4 (+0.6%) b3 s19 d3 (+0.5%) East Panel b4 s5 d10 (+1.0%) b3 s18 d10 (0.0%)

29 The only known method of doing this is to wrap a flexible measuring stick around the circumference, straighten the stick, subdivide it, then rewrap the stick and transfer the divisions onto the arc.

30 Serlio, op.cit. Book 1, Chapter 1 Folio 8v, 10v

31 I am endebted to Julie Wheeler, who helped interrogate Panel 7 (and 12) at the S.O.M. Foundation, Chicago, and George Krassas (U. of Illinois) and Wayne Bock (IIT).

32 The proposed measurements have been taken from a 20% sample of one panel, conducted by Wayne Bock of IIT.

33 Compare with the method of exhaustion, described in Euclid Book VII, in which the area of a circle is successively inscribed with polygons. Kline, M., Mathematical Thought from Ancient to Modern Times Vol.I, pg.83, 1972

34 The size of a 13:14 frame ratio is within 1/2% of a frame composed by bisecting the hypotenuse of the star's triangular point. Over the 4 1/4 braccia length of the panel, the 13:14 frame is only 6d (13mm) longer than a frame composed by bisecting the extreme sides of the star

35 Choulant, L. History and Bibliography of Anatomic Illustration Trans. Mortimer, Frank, New York 1962. pg.**

36 Plato, The Timeaus pg.1172, 43c - 43e, of Hamilton, E., Plato, The collected Dialogues. Previous to this, section 42e -43b discusses the making of the body out of fire, earth, water and air, which is then welded with "little pegs too small to be visible......so that the whole animal was moved and progressed irregularily however and irrationally and anyhow, in all the six directions of motion...." These values are also present in the design.

37 Condivi, A. (1553) The Life of Michelangelo trans. Wohl, A.S. and edited by Wohl, H. Baton Rouge 1976. Pg. 97-98. ' It is quite true that when he [Michelangelo] gave it [anatomy] up he was so learned and rich in knowledge of that science that he has often in mind to write a treatise, as a service to those who want to work in sculpture and painting, on all manner of human movements and appearances and on the bone structure, with a brilliant theory which he arrived at through long experience... I know very well that, when he reads Albrecht Durer, he finds his work very weak, seeing in his mind how much more beautiful and useful in the study of this subject his own conception would have been. And to tell the truth, Albrecht discusses only the proportions and varieties of human bodies, for which no fixed rule can be given, and he forms his figures straight upright like poles; as to what is important, the movements and gestures of human beings, he says not a word'.

38 During the investigation of the fifteen panels, it has been found that the form of the Cross is invariably composed from interconnecting grids, ratios and irrational numbers.

39 O'Gorman, F. The Architecture of the Monastic Library in Italy 1300 -1600 (1972), see plate 13.

40 Leo X made a provision that books should be examined by local religious bodies before approval, but only in 1548 (Council of Trent) was this made stringent: Paul IV ordered a catalog of forbidden things to be drawn up, and this was first published in 1559. Dee, D. "Index of Prohibited Books", New Catholic Encyclopaedia, VII, Pg. 434-5. (Washington 1967).

41 The inventory of the San Marco collection was completed in 1450. Ullman, B. & Stadter, P.A. The Public Library of Renaissance Florence: Niccolo Niccoli, Cosimo de' Medici and the Library of San Marco (Padua 1972)

42 Cheles, L. The Studiolo of Urbino: An Iconographic Investigation (Penn State 1986).

43 Spencer, J. Filarete's Treatise on Architecture (Yale 1965), Vol I, Pg.325.

44 I am indebted to Mr. Kimball Brooker for directing me to the specifics of the pictorial catalog.

45 See pg.6 of The Biblioteca Medicea Laurenziana, Florence 1983.

46 Masson, A. (1972) The Pictorial Catalogue, pg.12-14.

47 Wallace, W. Michelangelo at San Lorenzo (Cambridge 1994), Pg.9.

48 Salmon, F. 'The Site of Michelangelo's Laurentian Library', J.S.A.H. Vol.XLIX, No.4, Dec 1990, Pgs.407-429.

49 Salmon, Pg. 420 note 55.

50 This drawing is made to the scale of 1 1/2 braccia (b1s10) to 1 soldo (1:30). On the narrow side of the drawing the center to center dimension between the white bands, that represent the roof beams set above pilasters in the wall below, is 8 3/4 braccia (b8s15). At this stage of the design process, if the length of the Reading Room was the same as the built dimension (B79 S1.4), then the bay system in the drawing divides the Reading Room into almost exactly nine bays, the difference between the two dimensions is only S6.4 (18.5cms) over the length of the Reading Room. This drawing could have been the one referred to by Fattucci in his letter of 13 April 1524, in which he comments that he considers the span of the bay was too wide to be practical, and therefore unbuildable. The possibility of building a nine bay library would not have been unusual at that time. Medieval libraries had used Basilical form structures, separated into three aisles and there are examples of libraries built before 1520 that are 6,7,9,10,11 and 12 bays long. The Laurentian Library belongs within this tradition and could perfectly well have used a 9 bay system.

51 Il Carteggio di Michelangelo,ed. P. Barocchi and R. Ristori, 5 vols., Florence, 1965-1983, vol.III, p.95, DCLV, 2 Aug.1524 (Fattucci to Michelangelo)

52 Carteggio, vol. III, letter DCXLV.(The three aisled letter.) <

53 The archival researches for the project have been undertaken by Dr. Rolf Bagemihl, who is developing an independent but parallel research on an overview of Renaissance Library Organisation. Dr.Bagemihl is trying to establish subject areas and dates within which acquisitions mushroomed during the formation of the Laurentian Library collection.

54 For Piero's Library: F. Ames-Lewis The Library and Manuscripts of Piero di Cosimo de' Medici, NY, 1984.

55 See note 10.

56 M. Lenzuni, "Dalla Medicea privata alla Libraria di S. Lorenzo," in G. Cavallo, ed., Il Luoghi della Memoria Scritta: Manoscritti, incunaboli, libri a stampa di Biblioteche Statali Italiane (Rome 1994), p.124. She notes that a copy of the inventory was once in the Palazzo Vecchio; the extant copies are in the Vatican (ms. Barbn. lat. 3185, lat. 7134). The importance of this ms. was recognised independently, and R. Bagemihl transcribed the Greek list, totaling 420 volumes, in 1993. For the redacter of the inventory, see M.-H. Laurent, Fabio Vigili et les bibliotheques de Bologne (Vatican City,1943).

57 Alvisi, E., ed., Index Bibliotecae Medicea (Florence 1882)

58 Rondinelli, N. Manuscript of the inventory made on 21 August 1589. Ms.Laur. plut. 92-94.

59 Bandini, A.M. Catalogus codicum Latinorum Bibliotechae Mediceae Laurentianae (Florence 1774-78) vols. 1-5.

60 Biscioni, A.M. Bibliothecae ebraicae, graecae, florentinae: sive Bibliothecae mediceo-laurentianae catalogus. (Florence 1752-57)

61 BNCF, Magl. II.III.354, ex Magliab. xxv.84.

62 Vitrivius, The Ten Books of Architecture (New York 1960), Bk. VII Ch.I.4. Vitrivius describes the method of giving a burnt brick pavement its final grinding.

63 Catalana. Note 159. Catalana suggests that the dais might have been a socle, (presumably like the example in Cesena).

64 See note 17 (The three aisled letter).

65 The tread widths of the spiral staircases that link the book galleries to the reading room in Bibliotheque Nationale, Paris are about 65 cms. wide.

66 Rolf,was this noted in Bandini?

67 I am grateful to David Farrell Krell for having pointed this out, as well as a host of other acute observations.

68 Dr. Rolf Bagemihl is of the opinion that the visitor enters the Reading Roon at the crux of a U shaped progression of knowledge, rather than at the beginning of two parallel sequences.

69 I am prompted by Andrew Morrough to come to terms with this issue.

70 Dott. Angela Dillon was kind enough to show me the present method of storing the books that were formerly in the desks.

71 Greenaway, P., director of Prospero's Books (1991).Get from Arizona the title of greenaways book on the making of the movie

72 Medici Account Book 'B' (1548-52) , Archivo di Stato, Florence. The account book details the weeky payments to workers as well as the tasks they were performing. For a period of three weeks, between Nov. 16th 1549 and Dec. 7th 1549, preparations for the laying of the side pavements were made by masons, stonecutters, and laborers. On Monday Dec. 9th 1549 work began on installing the pavement for a perion of 21 weeks until Saturday May 2nd 1550. Payments were made during this time to two masons, two stone cutters, and two laborers: this indicates that there was propably a three man team working on each length of pavement and, in effect, they paced each other until the two sides were completed.
The acccounts then document a perplexing occurance that poses questions concerning the relation of the middle and lateral pavements. The middle pavement was constructed almost immediately after the side pavements were finished. In fact building materials, in the form of clay, were ordered for the middle pavement on April 26th 1550 (CVIII.4), a month before the last record is entered for work done on the side pavements. By June 7th, 1550 work had begun in ernest on the middle pavement, when 'masters in clay' were added to the work team (121.4). Payments for the middle pavement were concluded on Feb 9th, 1555 (Book D, XCVII.1). It is curious that as soon as the side pavements were completed, work began so soon on the middle pavement. This may suggest that at sometime between 1548 and 1550 a decision was made not to use the side pavements.

73 Had the Laurentian Vestibule included sculptures in the tabernacles, as was planned, then the visitor would have had some clue as to what to expect from the building, for there is little doubt that they would have had all the allegorical trappings appropriate to this domain of scholastic revelation. The frieze of famous men in the upper part of the Studiolo of Urbino serves as a model for this proposal (see Cheles, pp.35-52).

74 The Old and New Testiment Bibles (desks 1-5) and the Greek Metaphysicians (desks 85-87) are positioned over the Cross Panel (#1) and the Cosimo Panel (#2). Books on Greek and Latin Astronomy (desks 28-30) are almost on top of the Horoscope Panel which is positioned beneath desks 30-32. The Latin poets are situated on top of Panel 3, which has a pair of curious grimacing masks on it, a traditional symbol for the theatre. There are also a surprising number of categories still in existence in the 1571 layout that use three desks - the width of a panel. Hebrew, Astronomy, Medicine, Greek Grammar & Oratory, and Letters are all allocated three desks; this represents six of the sixteen categories that were present in 1571. These alignments may be the remnants of an earlier layout that considered the pavement as a response to the categories of books in the collection.

75 Sample measurements have been made of the East and West Panels #2 and #14, and it appears that their geometric structure differs slightly between the panels of these two pairs.

76 Wittkower, Rudolf, 'Michelangelo's Biblioteca Laurenziana'. Art Bulletin, XVI, 1934, pp.123-218. Reprinted in Idea and Image, London, 1978, see pp.58-67.

77 Summers, David, Michelangelo and the Language of Art, Princeton, 1981.

78 Serlio's opening sentence of the First Book of Architecture, entreating Geometry, stresses the importance of the Secret Art of Geometry. "How needful and necessary the most secret Art of Geometry is for every Articifer and Workman, as those that for a long time have studied and wrought without the same can sufficiently witness, who since that time have attained unto any knowledge of the said art, do not only laugh and smile at their own former simplicities, but in truth may very well acknowledge that all whatsoever had been formerly done by them, was not worth the looking on." Serlio, Sebastiano The Five Books of Architecture, 1611. Reprint, New York, 1982, Book 1, folio1r.

79 This is a term developed by Mies Van Der Rohe, "Just as we acquainted outselves with materials and just as we must also understand the nature of our goals, we must also learn about the spiritual position in which we stand. No cultural activity is possible otherwise; for also in these matters we must know what is, because we are dependent on the spirit of our time". Inaugural Address as Director of Architecture at Armour Institute of Technology , 1938, Mies van der Rohe. Neumeyer, Fritz, The Artless Word, 1991.

80 Alberti, Leon B. On Painting, translated by J.Spenser, New Haven, 1966.

81 Leonardo Da Vinci, The Notebooks of Leonardo da Vinci Reprint New York, 1970. See Vol.1 pp.242-254. I. Moral Precepts for the Student of Painting.

82 Durer, Albrecht, The Painter's Manual 1525, Edited by W.Strauss, New York, 1987.

83 Serlio, op.cit. Book II, frontspiece v.

84 Don Bates recently held a symposium On Geometry at LOPSIA, Briey en Foret, France 1994.

85 Condivi, op.cit. note 67.

86 Rolf is this strictly true? Catalano missed the mask present in Panel 13, which would have aided her argument that Tribolo authored the pavement, however Michelangelo has his own tradition of incorporating the mask into his sculpture and freize decoration.

87 This reference was made and kindly translated by James Ackerman. Vasari,G. Le Vitae. Ed. Milanesi vol. I p.88, note 1 p.92.

88 A chemical analysis was conducted on particles of a red and a white tile from Panel 10, which established that the tiles were made of terra-cotta. (Fortunately an electrician has punched a hole in the pavement for a steel conduit - a familiar story and the microscopic analysis was performed on fragments of the electrician's handiwork!

89 Pirina, C. Art Bulletin Sept 1985 Vol. LXVII #3 pp 370-382. 'Michelangelo and the Music and Mathematics of his Time'. Linda Liegh, of IIT, has a far more thorough and well reasoned proposal for Michelangelo's 'proportional gyroscope' based upon the Golden Mean. She argues that it permiates all his work and, because it is not present in the pavement, proves that Michelangelo had no hand in its design.

90 The Laurentian Library administration has permitted measurements, in the form of frottage rubbings, to be made on three separate occasions. Panel 2 is the only panel for which we have both the long and short dimensions of the east and west panel frames. Due to the extreme practical difficulty of making the measurements, it has only been possible to take partial dimensions of 9 of the 30 panels and, excepting the panel in front of the Sala D'Elesi, the frottages never exceed more than 20% of the area of the panels.

91 This is especially the case in the subflooring on Panel 2 east.