1 Mirandola, Pico dell, Opera Omnia (Basle, 1557), p. 40 Google Scholar, f. 2 as translated in A. Koestler, The Roots of Coincidence (London, 1972), p. 106.

2 Serlio, S., Tutte l’opere d’architettura et prospettiva (Venice, 1584), III (first published, separately, in 1540), pp. 18–19 Google Scholar, and Palladio, A., I Quattro Libri dell’ Architettura (Venice, 1570)Google Scholar, iv, ch. 17, both honoured the Tempietto by including it alongside ancient examples of good architecture. There are arguments for dating the building as early as 1502 (E. Rosenthal, ‘The Antecedents of Bramante’s Tempietto’, Journal of the Society of Architectural Historians, 23 (1964), pp. 55) but a later date seems more likely, see A. Bruschi, Bramante architetto (Bari, 1969), p. 481.

3 P. Delorme, Le premier tome de l’architecture (Paris, 1567), v,I, fol. 131; Coffin, D. R., ‘Pope Marcellus II and architecture’, Architectura, 9 (1979), p. 12 Google Scholar.

4 Jones, M. Wilson, ‘Principles of Design in Roman architecture: the setting out of centralised buildings’, Papers of the British School at Rome, 57 (1989), n. 8 and n. 38CrossRefGoogle Scholar; Vagnetti, L., ‘Architettura e Metrologia’, Quaderni del Istituto di Elementi di Architettura e Rilievo dei Monumenti, 6 (Genoa, 1971), pp. 69–126 Google Scholar.

5 Lotz, W., ‘Sull’Unità di misura nei disegni di architettura del Cinquecento’, Bolletino del Centro Internazionale di Studi di Architettura, 21 (1979), pp. 223–32 Google Scholar; Zervas, D. F., ‘The Florentine braccio da panna’, Architectura, 9 (1979), pp. 6–11 Google Scholar; Fernie, E., ‘Pegolotti’s cloth lengths’, The Vanishing past: Studies of Medieval Art, Liturgy and Metrology presented to Christopher Hohler (British Archaeological Reports International Series, III (1981), pp. 13–28.Google Scholar

6 Serlio, Tutte l’opere, III, 18v; Cataneo, P., L’Architettura (Venice (2nd ed.), 1567), III, ch. xi, pp. 72–73 Google Scholar. For the sake of clarity Cataneo drew out the relevant piede (296 mm in length) in the margin. Usually he gave measurements in Florentine braccia or piedi half as long, i.e. of 292 mm.

7 Günther, H., Die Memorialanlange der Kreuzigung Petri in S. Pietro in Montorio, Rom (Diss. Munich, 1973)Google Scholar; idem, ‘Bramantes Hofprojekt um den Tempietto und seine Darstellung in Serlios dritten Buch’, Studi Bramanteschi (Rome, 1970), p. 483 ff; Tiberi, C., ‘Misure e contemporaneità di disegno del Chiostro di S. Maria della Pace e del Tempietto di S. Pietro di Montorio’, ibid., 437ff; Bruschi, Bramante architetto, p. 465, Fig. 307.Google Scholar

8 Tiberi chose a braccio of 2½p even though the Roman braccio is equated to 3p by authorities such as Martini, A., Manuale di Metrologia (Rome, 1976), p. 396 Google Scholar, and Doursther, H., Dictionnaire universel des poids et mesures anciens et modernes (Amsterdam, 1965), p. 72 Google Scholar. The Tempietto does yield some multiples of 2½p, but no more than might reasonably result from measurement inpalmi and a preference for numbers such as 10, 20 and 50. Tiberi derives his unit in part from a supposed parallel with the mensuration of Leonardo da Vinci’s famous man in a circle and square. The logic of this idea escapes me completely.

9 Vitruvius, III, 3; III, 5; iv, 1; iv, 3; iv, 8; v, 9.

10 Günther, H., ‘Die Rekonstruktion des antiken römishen Fußmasses in der Renaissance’, Kunstgeschichtliche Gesellschaft zu Berlin. Sitzungsberichte, 30, (1981-82), pp. 8–12 Google Scholar; Jones, M. Wilson, ‘Palazzo Massimo and Baldassare Peruzzi’s approach to architectural design’, Architectural History, 13 (1988), pp. 64–65 Google Scholar. See also Thoenes, C., ‘Proportionsstudien an Bramantes Zentralbau-Entwurfen’, Romisches Jarbuch für Kunstgeschichite, 15 (1975), p. 57.Google Scholar

11 Compare also the height above the floor of the springing of the cupola, that of its crown, and the same measured from the floor of the crypt, each 32 units (respectively palmi, piedi and columnar modules). For the source of these and all other dimensions cited, see the Appendix.

12 The same subdivisions are common to both units, with the piede and palmo divided into either 16 and 12 digiti of 18½mm, or 12 and 9 oncie/digiti of 24¾mm. The possibility that Bramante intended ancient (that is slightly shorter) as opposed to contemporary values for palmi/piedi remains an open question, as the measurements of the Tempietto suggest unit lengths that fall between the norms for each version (see the Appendix).

13 The system of squares is highlighted by Bruschi, Bramante architetto, p. 513, Fig. 335. However not all his proposals are borne out; for example the internal radius of the cella is not 6M and nor is the cella wall 2M thick (p. 465, Fig. 307).

14 Ideal ratios such as these were sometimes modified if there was a conflict of intentions. Consider the following possibilities: (i) that the height of the dome’s springing be 24P (32p), ¾ the total height of the interior (32P), (ii) that the part heights of the interior elevation are simply related to other significant dimensions in the building as follows:

These produce a total of 24⅓ for the height of the springing, rather than the ideal 24P of the first premise. It seems that 24P was achieved by reducing the pedestal height to 2P, 14dg and the attic height to 6½P.

15 Rosenthal, ‘Antecedents’, pp. 55–56. Judging by the section in the Codex Coner, the present dome is probably about o. 5m thicker than the original.

16 As Günther, (‘Hofprojekt’, pp.490, 498 and Figs 12, 13 and 18) has shown, a circular court 100 palmi in diameter centered on the Tempietto would fit snugly into the dimensions of the original quadrangular courtyard.

17 The actual ratios between these pairs of measurements are respectively 1.404 and 1.408. For the first pair a ratio of 225/160 follows if the intended dimensions were 25p (14^1/16M) and 10M. For the second pair a ratio of 7/5 follows if the external radius of the cella was intended as 10P, the interaxial radius of the colonnade intended as 10M (13⅓P), and the radius of the columns intended as 2/3P, thus making the radius to the column faces 14P.

18 On the heritage of the use of √2 see Gros, P., ‘Nombres irrationels et nombres parfaits chez Vitruv’, Mélanges de l’Ecole française du Rome: Antiquité, 88 (1976), pp. 669–704 CrossRefGoogle Scholar, and references cited in Wilson Jones, ‘Palazzo Massimo’, n. 5.

19 The following are averages (author’s survey). See also Basso, P., Cappella, E., Il Chiostro di S. Maria della Pace (Rome, 1987)Google Scholar, and Letarouilly, , Edifices de Rome moderne, (Paris, 1869-74), 1. pp. 63–66 Google Scholar:

Bruschi, Bramante architetto, p. 246 ff. notes such interrelations as 1:1, 1:2, 1:3 and 3:4. On the use of √2 in other projects of the period by Bramante see Thoenes, ‘Proportionsstudien’.

20 Letarouilly, P., Le Vatican et la Basilique de St.-Pierrede Rome (London, 1963, facsimile of the Paris 1882 edition), pl. 123 Google Scholar. A separate study of this structure is being prepared by this author.

21 Comparable floors are found in the chapel of the Cardinal of Portugal in S. Miniato in Florence, the Sistine chapel, Raphael’s Stanze, and the palace attached to SS Apostoli in Rome. See Bruschi, Bramante architetto, p. 473, n. 15, and Rizo, A. Vanegas, ‘Il Palazzo Cardinalizio della Rovere ai SS. Apostoli a Roma’, Quaderni dell’Istituto di Storia dell’Architettura, 139 (1978), pp. 3–12.Google Scholar

22 Bramante may have been aware that the ratios 1:1, 4:3 and √2:1 were frequently used in the original Cosmati designs, see Glass, D., ‘Studies on Cosmatesque pavements’, British Archaeological Reports (1980), p. 40 ff..Google Scholar

23 Appendix, compare RP and f5. For ancient precedents for this 2:1 relationship, see Wilson Jones, ‘Principles’, n. 20.

24 Similarly the interval 5:2 between the 50p diameter of the steps and the 2op interior diameter of the cella is made up of the progression 4:3-4:3-√2:1, or alternatively 4:3-√2:1-4:3, via the external diameter of the cella and the diameter of the colonnade, measured in the first case to column centres and the second case to their faces. 5:2 is in fact matched exactly if 225:160 is used as an approximation for √2:1.

25 Bramante would have had to check that the dimensions chosen produced satisfactory rhythms around the circumference. The external circumference of the cella (to the face of the pilasters/frieze) works out at 84p assuming a diameter of 26⅔ (20p) and 3.15 for π; this produces 5¼p per bay and approximately a 1:2 rhythm between the width of the pilasters and the distance between them. Similarly the interaxial circumference of the colonnade works out as 112p, and this produces 7p per bay and an approximate rhythm of 1:3 between the columns and the intercolumnations. The resulting circumference of the external frieze of the colonnade nearly approaches 7½P per bay and thus almost 2½p intervals for the triglyphs and a (suitably Vitruvian) rhythm of 1p.1½p between the width of the triglyphs and metopes (my thanks to David Hemsoll for this observation). None the less, the fact that none of these relationships are accurately realized, confirms the primacy of the radial dimensions.

26 The following are centralized spaces 20 braccia wide, or thereabouts (20br equals 11.68m given a unit of 0.584m, see Zervas, ‘The Florentine braccio’).

The sources for these measurements are:

a-h: author; Stegmann, C. v. and Geymuller, H. v., Die Architektur in der Toscana, 12 vols (Munich 1885-1907)Google Scholar. See also for a: D’Ossat, G. De Angelis, ‘Brunelleschi e il problema delle proporzione’, in Filippo Brunelleschi, La sua opera e il suo tempo (Florence, 1977), p. 222ff.Google Scholar; for b: Saalman, H., ‘The New Sacristy of San Lorenzo before Michelangelo’, Art Bulletin, 67 (1985), pp. 199–228 CrossRefGoogle Scholar, esp. p. 212; for d and e: Benevolo, L., Chieffi, S., Mezzetti, G., ‘Indagini sul S. Spirito di Brunelleschi’, Quaderni dell’Istituto di Storia dell’Architettura, 85 (1968), pp. 1–52 Google Scholar; for g: Bartoli, L., ‘L’Unità di Misura e il modulo proporzionale nell’Architettura del Rinascimento’, Quaderni del Istituto di Elementi di Architettura e Rilievo dei Monumenti, 6 (Genoa, 1971), pp. 127–37 Google Scholar; for h: Papini, R., Francesco di Giorgio Martini architetto (Florence, 1946), 3 volsGoogle Scholar and Millon, H., ‘The Architectural Theory of Francesco di Giorgio’, Art Bulletin, 40 (1958), pp. 257–61 CrossRefGoogle Scholar (clearly related to 20br are the depth of the transepts, 15br (8.77m), the overall internal width, 50br (29.25m), the external width of the arms, 28br (16.34-16.40m) — note that 28.20 is approximately V2:i), the width of the main door-frame, 10br (5.86m) and the height of the crossing’s cornice, 40br (23.40m); for i: Morselli, P. and Conti, G., La chiesa di Santa Maria delle Carceri in Prato (Florence, 1982), p. 38 ff.Google Scholar, who note ratios such as 1.1, 1:2 and 3:2 between dimensions such as 10, 20, 30 and 40br.

27 Metternich, F. Wolff, ‘über die Massgrundlagen des Kuppelentwurfes fur des Peterskirche in Rom’, Essays in the History of Architecture presented to Rudolf Wittkower (London, 1967), p. 40 ff.Google Scholar

28 Wurm, Baldassarre Peruzzi Architekturzeichnungen (Tubingen, 1984), figs 229 and 291. For other comparable dimensioned schemes see 9, 11, 164, 205, 292, 293 and 345).

29 The average width of the arms (to pilaster faces) of S. Eligio is 5.94m or 20 piedi of 0.297m (author). The plan thus resembles a half-scale S. Maria delle Carceri, with principal dimensions transposed from braccia to piedi. See Valtieri, S., ‘Sant’ Eligio degli Orefici’, in Raffaello architetto, ed. Frommel, C. L., Ray, S. and Tafuri, M. (Milan, 1984), pp. 143–56 Google Scholar. especially Fig. 2.4.5.

30 Tavernor, R., Concinnitas in the theory and practice of L. B. Alberti (Cambridge University PhD, 1985), pp. 66 ff. and 135 ff Google Scholar. illustrates this argument with S. Andrea in Mantua, the nave of which measures 40 by 120 Mantuan braccia, to wall faces (see also Rykwert, J. and Tavernor, R., ‘Sant Andrea in Mantua’, Architects’ Journal (1986), xxi, pp. 36–57 Google Scholar. Millon, ‘Architectural Theory’, n. 14, has also observed that Francesco di Giorgio’s grid lines coincide with walls rather than pilasters.

31 Kings, 1, 6 and 7.

32 Vitruvius, especially 1, 2; in, 1; vi, 2. On difficulties of interpretation see Gros, P., ‘Vitruve et sa theorie, à la lumière des études récentes’, Aufstieg und Niedergang der Römishen Welt, 30.1 (1985), pp. 660–95 Google Scholar, and references in Wilson Jones, ‘Palazzo Massimo’, n. 24.

33 Les Traités d’Architecture de la Renaissance, Actes de la Centre d’Etudes Supérieurs de la Renaissance, Tours, ed. J. Guillaume (Paris, 1987 (1981)); Vitruve, De architecture Concordance, ed. L. Callebat, P. Bouet, P. Fleury and M. Zuinghedan, (Hildesheim, 1984), with comprehensive bibliography, 11, vii-xli; P. N. Pagliara, Vitruvio da testo a canone, Memoria dell’antico nell’arte italiana, 3 (1986).

34 See Wittkower, R., Architectural Principles in the Age of Humanism (London, 1949)Google Scholar; Hersey, G. L., Pythagorean Palaces: Magic and Architecture in the Italian Renaissance (Ithaca and London, 1976)Google Scholar and references in Wilson Jones, ‘Palazzo Massimo’ n. 27–30.

35 10 is the base of the Roman/Arabic system of counting, the hands and feet have 10 digits, and 10 is 1 + 2 + 3 + 4 while 10² = 100 =1³ + 2³ + 3³ + 4³. On the almost mystical significance for the Greeks of the decad, a triangle made up of 10 points in rows of 1,2,3 and 4 points, see Pollitt, J. J., The Ancient View of Greek Art: criticism, history and terminology (New Haven, 1974), pp. 14–22 Google Scholar. As Tavernor, Concinnitas, p. 182, has pointed out, Vitruvius’s value for the circumference of the earth, 3,150,000 passi (I, 6, 9) was no doubt calculated from an assumed diameter of 1 million passi or 10,000 miglia (miles) and 3.15 as an approximation to π.

36 Frankl, P., ‘The Secret of the Medieval Masons’, Art Bulletin, 27 (1945), p. 46 ff Google Scholar. See also Fernie, E., ‘Historical Metrology and Architectural History’, Art History, 1 (1978), pp. 383–99 CrossRefGoogle Scholar. However, for Bucher, F., ‘Medieval Architectural Design Methods 800–1560’, Gesta, xi (1972), pp. 48–49 Google Scholar, ‘measurements are dirty within the context of geometry which is an affair of the mind’. He argues that the paucity of medieval standard units of measure supports his interpretation — but this also renders it more difficult to detect whole dimensions if they were used.

37 The following measurements have been taken by the author:

It has also been noted that the plan of the Old Sacristy is the same width (some 11 ½m plus) as the Trecento Baptistry of Padua which it resembles in other ways (see Battisti, E., Filippo Brunelleschi (Milan, 1976), p. 355 Google Scholar and Saalman, H., ‘Carrara Burials in the Baptistry of Padua’, Art Bulletin, 69 (1987), p. 386 CrossRefGoogle Scholar). However this not to say that the Florentine braccio must have been used in setting out of the earlier building.

38 The designer of the fourth century B.C. Monument to Lysicrates in Athens, like Bramante here, may have more than one unit in mind — the width of the podium is 2.94m, or 10 Attic feet of 0.294m, while that of the tholos platform is 3.275m, or 10 Ionic feet of 0.326m. See Wilson Jones, ‘Principles’, Appendix 11.

39 In Wilson Jones, ‘Principles’, the plans were analysed of a comprehensive group of centralized buildings that are large, free-standing, well-preserved and constructed in or near Rome between 200 B.C. and 500 A.D. Selected measurements are as follows:

40 Davies, P., Hemsoll, D. and Jones, M. Wilson, ‘The Pantheon: a triumph of Rome or a triumph of compromise?’, Art History, 10 (1987), pp. 133–53 CrossRefGoogle Scholar. For proportional studies of other Roman buildings, see P. Gros, ‘Vitruve et sa theorie’, p. 689.

41 Wilson Jones, ‘Principles’; Panofsky, Ë., ‘History of the Theory of Human Proportions’ in Meaning and the Visual Arts (New York, 1970), pp. 83–138, esp. n. 19.Google Scholar

42 Günther, H., Das Studium der antiken Architektur in den Zeichnungen der Hochrenaissance (Tubingen, 1988)Google Scholar; Wilson Jones, ‘Palazzo Massimo’, pp. 64–65.

43 G. Vasari, Le Vite dei piú; eccellenti Pittori, Scultori e Architettori, ed. Milanesi (Florence, 1878–85), p. 146.

44 See notes 23 and 39 supra.

45 Jones, M. Wilson, Designing the ‘Corinthian Order’, Journal of Roman Archaeology, 2 (1989), pp. 35–69 CrossRefGoogle Scholar. Furthermore, the Doric columns of the Theatre of Marcellus — particularly important models for the Tempietto — are about 24P (6.95m or 23.6P) tall, see Saponieri, F., Visconti, A. and Feoli, V., Teatro di Marcello (Rome, 1822).Google Scholar

46 Bruschi, Bramante (1973), p. 143.

47 For perspectives on this issue before modern times see Serlio, Tutte l’opere, iv, fols 33r, 34V and 37V; Herrman, W., The Theory of Claude Perrault (London, 1973), p. 31 ff.Google Scholar

48 Sinding-Larsen, S., ‘Some functional and iconographic aspects of the centralized church of the Renaissance’, Acta ad Archaeologiam et Artium Historiam Pertinentia, 2 (1965), p. 236.Google Scholar

49 Wittkower, Architectural Principles, p. 7; L. B. Alberti, De re aedificatoria, vi, 2.

50 See, for example, of the last chapter of Hersey, Pythagorean Palaces; Ritz, A., The Supreme Creation of the Past, Present and Future: The Everlasting Temple of S. Stefano Rotondo in Rome, the New Jerusalem and the Book of Revelation (Rome, 1980)Google Scholar; Brunes, T., The secrets of Ancient Geometry (Copenhagen, 1967)Google Scholar, and other publications on ‘sacred geometry’; and F. Tiberi, ‘Misure e contemporanietà’ on the Tempietto in particular. These tend towards unnecessarily clever, complex or abstruse interpretations; inaccuracies can be also quite considerable.