Jacobson Hadrianic Architcture

7/27/2019 Jacobson Hadrianic Architcture

1/18

Hadrianic Architecture and GeometryAuthor(s): David M. JacobsonReviewed work(s):Source: American Journal of Archaeology, Vol. 90, No. 1 (Jan., 1986), pp. 69-85Published by: Archaeological Institute of AmericaStable URL: http://www.jstor.org/stable/505986 .

Accessed: 03/12/2012 03:23

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

Archaeological Institute of America is collaborating with JSTOR to digitize, preserve and extend access to

American Journal of Archaeology.

http://www.jstor.org

This content downloaded by the authorized user from 192 168 52 75 on Mon 3 Dec 2012 03:23:10 AM
http://www.jstor.org/action/showPublisher?publisherCode=aiahttp://www.jstor.org/stable/505986?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/505986?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=aia


2/18

Hadrianic ArchitectureandGeometry*DAVID M. JACOBSON

AbstractAllthethreads f evidence oint o the Greekworldofthe Hellenistic eriodas the fountain-headf the"rulerandcompassespproach"odesign, mbodiedn thecen-tralizedbuildings f Hadrian's eign hatrepresentneof thehighwatermarks f the "Roman rchitecturalev-olution."Analysis f theplansof sixofthesebuildingsnRome,Tivoli andBaiae,somehavinganImperial sso-ciation,reveals how importantgeometrical rincipleswere o advanced oman rchitecturalesign.

A number of buildings dated to the reign of Ha-drian, including some well known examples at theEmperor'spalatialresidencenearTivoli, areconspic-uous among the monumentsof classicalantiquity forthe ingenioussymmetryof their ground plans. Thesestrikingcurvilinearcompositionsstood unrivalledfor1500 years until Baroquearchitects, ed by Borromi-ni, scaled new peaks in architecturaldesign.' It hasbeen recognized,however,that Borrominihimselfre-peatedly looked to Hadrian's Villa as a source of in-spirationfor his own masterpieces.2The plans of these buildings have been viewedwithin the perspectiveof the "Roman architecturalrevolution," panningthe centuryand a half betweenthe death ofJulius Caesar and that of Hadrian,whichexploitedthe plastic freedompermittedby concrete.3It has been pointed out that, already in the time ofAugustus, curvedforms were assuming a prominentplace in the domesticarchitecture of Campania. ByNero's reign, curvilinear forms were being treatedmoremethodically n his Domus Transitoria and Do-mus Aurea. A paralleltrend has been discerned n thelayoutof gardensand peristyles.The innercourtyardof Domitian's Domus Augustana,with its symmetri-cal arrangementof curving platformsand channels,representsan advancedstageof this process.4

It is in the architectureof Hadrian'sreignthat thisdevelopmentreachedits apogee,5with a burst of pro-digious inventiveness.Besides the distinctivegroundplans, the architectureof this periodis also noted forwhat appear to be several important innovations.These includetwo typesof segmenteddome,occasion-ally raised on drums with windows-claimed to beanother novel feature-and other experiments invaulting.6 While the origins of these elements aresomethingof an enigma, the same cannot be said ofthe sophisticatedcurvilineardesigns.This study attempts to identify and delineate theroots of this typeof architecturaldesignin the appliedgeometryof the Greeks.Drawing on the writtentesti-mony of Vitruvius,our principalsourceon Classicalarchitecture,I shall stressthe role played by Euclid-ean geometry in Roman architecturaldesign. Con-firming evidence of the application of geometricalprocedures s furnishedby an analysisof selectedcen-trally planned buildings dating from the time of Ha-drian,when curvilineardesignwas in its heyday.ORIGINS OF CURVILINEAR DESIGN

Vitruvius informs us that, in his day,' it was thenormalpracticeto work out the plan of a buildinginan architectural drawing (ichnographia) using astraightedge or ruler (euthygrammum, regula) andcompasses (circinus). The scheme would then bestaked out on the ground using ropes, or cords, andpegs.8The applicationof geometricalprinciplesto archi-tectural design can be traced back, with reasonableconfidence, to the fourth century B.C. architectPytheos.His Temple ofAthena Polias at Prieneis thefirst known Greek temple to have a plan developedsystematicallyon a grid of squares,within which all

* I am especially grateful to Dr. Geoffrey Waywell of King'sCollege, London,for his valuable advice and encouragement. alsowish to thank the respectiveauthors and publishersforpermissionto reproducetheir plans of buildings discussed in this article andBrunilde S. Ridgway is thanked for drawing my attention to twoimportantbibliographicreferences.I H. KAhler,Hadrian und seine Villa bei Tivoli (Berlin 1950)143. See, forexample,the geometricalbasis of the planof Borromi-ni's S. Carlo alle QuattroFontanein Rome, described n H. Sedl-mayr,"ZumGestaltetensehen,"Belvedere9-10 (1926) 57-62.2 A. Blunt, Borromini(London 1979) 37, 70, 99, 116.3J.B. Ward-Perkins, Roman Imperial Architecture(London1981)97-120.4 See Ward-Perkins (supra n. 3) 101-11; Kahler (supra n. 1)

87-106; F.L. Rakob, Die Piazza d'Oro in der Villa Hadriana beiTivoli (Diss. TechnischeHochschule,Karlsruhe1967) 89-96.s J.B. Ward-Perkins, Roman Architecture(New York 1977;unrev. trans. of Architettura romana, Milan 1974) 174.6 See F. Rakob,"LitusbeataeVenerisaureum;Untersuchungenam 'Venustempel' in Baiae," R6mMitt 68 (1961) 138-44; alsoM.E. Blake and D. Taylor-Bishop, Roman Construction in Italyfrom Nerva through the Antonines (Philadelphia 1973) 247, 302.7 Vitr. De arch. 1.2.2 and 1.1.4. On the strengthof internalevi-dence,Vitruvius' De architectura as beendatedbetween 35 and 22B.C. See C. Fensterbusch, Vitruv, Zehn Biicher iiber Architektur2(Darmstadt1976) 3-6.8 W.L. MacDonald, The Architecture of the Roman Empire I:An Introductory Study2 (New Haven and London 1982) 136.

69AmericanJournal ofArchaeology90 (1986)

This content downloaded by the authorized user from 192.168.52.75 on Mon, 3 Dec 2012 03:23:10 AMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp


3/18

70 DAVIDM.JACOBSON [AJA90the structural elements are organized.9The appear-ance of this approach points to the use by Pytheos,perhaps for the first time, of preliminarydrawings.10On the evidence of Bammer, the dimensions of thelater Artemision at nearby Ephesus, begunin ca. 350B.C., were formulatedin terms of discreet modularproportions.11About two hundred years later, we find Hermo-genes of Alabandadevelopingand refiningthis mod-ular system of design in his Temples of ArtemisLeukophryene at Magnesia-on-the-Maeander andDionysos at Teos.12 Hermogenes wrote treatises onthese two temples which exerted a strong influenceon Vitruvius.13For his part,Vitruvius recommendedmodularpro-portionsnot only for the plans of rectangular emples,like thoseof PytheosandHermogenes,but also for thedesignsof circulartemples.14 Here, too, he may havedone no more than reiterate Hellenistic architecturalsources: the fact remains that his rules for circulartemples constitute a unique documentarysource onthe subject. By implication, they are also most rele-vant to our understandingof the developmentof ar-chitecturaltheory appliedto centrally plannedbuild-ings. According to Vitruvius' account, the primary

geometricalelement in the plan of a circulartemplewas the circle of its stylobate, n the sense that the dia-meter across he stylobatecontrolled he dimensionsofseveral other elements of the building. Thus, in theschemepresentedby Vitruvius,fractionalor modulardivisions of the stylobatediameterdetermined he po-sition of the concentriccella wall and, indeed,alsothekey dimensions n the elevationof the building. Pre-sumably,the regularintercolumniations f the encir-cling pteron corresponded o a circumferentialmod-ule.15This idea is also found in a geometricalcon-structiondescribed n detailby Vitruvius,namelythatof theanalemma,a projectionused in the constructionof planar sundials.16Like the design of the circulartemple, the analemma is developedfrom the initialcircle whose diameter determinesthe dimensions ofall subsequentelements of the scheme.A clearpatternin Vitruvius'approachto circular-based architecturaldesign emergesafter also consid-ering his prescriptionfor the Roman theater." Inthis case, the circleof the orchestra ulfills the role ofthe primarycircle. The vertices of an inscribeddeca-gon determine the dispositionof the radiatingstair-ways and the scaenae rons. A length twice the dia-meter of the orchestra ixes the length of the scaena.

9T. Wiegand and H. Schrader, Priene: Ergebnisse der Ausgra-bungen und Untersuchungen in den Jahren 1895-1898 (Berlin1904) 81-86, pl. 9; and more recentlyW. Koenigs,"Der Athena-tempelvon Priene,"IstMitt 33 (1983) 134-75.10 See J.J. Coulton, Greek Architects at Work (London 1977)70-71. A trendtowardgreaterorder in architecturaldesignis to beseen as partof a development n Hellenic culturethat tookplaceinthe 5th-4th cs. B.C., where, in the words of Plato (Phlb. 64E),measure (JeTrpLdrOTq)and commensurability (ro-vjpTrp'a) came tobe identified with beautyand excellence.Anothermanifestationofthis outlook was the canon of Polykleitos,which stipulateda set ofcommensurableproportionsfor the human figure (Galen Placit.Hipp. et Plat. 5 [ed. Miiller 425]). See J.J. Pollitt, The AncientViewofGreekArt (New Haven and London1974) 14-22, 160-62.Koenigs (supra n. 9) 165-68, has drawn attention to an architec-tural sketch of a temple pediment scratched on the surface of anashlar of the templeof Athena Polias, which he associateswith theconstructionof that building.

11A. Bammer,"Zum iingerenArtemisionvon Ephesos,"OJh47(1964/65) 137-39; also Bammer,"Der Altar desjiingerenArtemi-sions von Ephesos,"AA 1968, 416.12On the templeof Artemisat Magnesia, see C. Humann, Mag-nesia am Maeander: Bericht ilber die Ergebnisse der AusgrabungenderJahre 1891-1893 (Berlin 1904) 39-49, fig.30. On the templeofDionysos at Teos, see Society of Dilettanti, Antiquitiesof Ionia,Part the Fourth (London 1881) 38-39, pl. 22; also Y. Bequignonand A. Laumonier, "Fouilles de Teos (1924)," BCH 49 (1925)291-98, pl. 8.13Vitr. De arch.7 praef. 12 and 4.3.1. Scholars are divided overthe date of Hermogenes:vonGerkan and Dreruphavearguedfor afloruit in the mid 2nd centuryB.C. but others,mostrecentlyOzganin the contextof the altar at Magnesia, are of theopinionthat Her-mogenes was active towards the end of the previouscentury.Seerespectively A. von Gerkan, Der Altar des Artemistempels in Mag-nesia am Miiander (Berlin 1929) 24-26; H. Drerup, "ZumArte-mistempel von Magnesia,"MarbWinckProg1964, 13-14; and R.

Ozgan,"ZurDatierungdes Artemisaltars n Magnesiaam Maean-der,"IstMitt 32 (1982) 208-209.14 Vitr. De arch. 4.8.1-3.15The tholos at Epidauros(ca.365-335 B.C.) appearsto provideevidencethat circular ntercolumniationswere partof the modularsystemof design.This tholos was endowed with two concentric ol-onnades,an outerringwith 26 Doric columnsand an inner circleof14 Corinthian columns (see G. Roux, L'architecture de l'Argolideaux IVe et IIje sizcles avant J.-C. [Paris 1961] pl. 38). The interco-lumniation foreach ring is aboutthe same, as can be verified fromthe measurementsof the respectivediameters,19.288 m. and 10.11m. (Roux 153). Thus, the average nter-axial arc lengthis 2.33 m.[= (wx 19.288)/26 m.] for the outer colonnade and 2.27 m. [=(wr 10.11)/14 m.] for the inner one. It is to be notedthat Pausa-nias (2.27.5) attributes his tholos to one Polykleitos.The possiblerelationshipbetween this Polykleitosand his namesake, he famousArgive sculptorand author of the canon of human proportions, sexplored by D. Arnold, "Die Polykletnachfolge,"JdI-EH 25

(1969) 13-17.16 Vitr. De arch. 9.7.2-6. On the analemma,seeJ. Soubiran,Vi-truve, De l'Architecture Livre IX (Paris 1969) 71-73; S.L. Gibbs,Greek and Roman Sundials (New Haven and London 1976)105-107; and T.L. Heath, A History of Greek Mathematics 2 (Ox-ford 1921) 286-87. The manner in which the analemmadescribedby Vitruvius would have been used is explained by Soubiran(220-40) and also by E. Buchner in "SolariumAugusti und AraPacis,"RomMitt 83 (1973) 331-35 (in connectionwith Augustus'greatsundial in the CampusMartius)."7Vitr. De arch. 5.6.1-6. A recentcomparative valuationof theplans of Romantheatersby D.B. Small ("Studies n RomanThea-ter Design," AJA 87 [1983] 55-68) revealed that only a small mi-noritywere designedaccording o the proceduresrecommendedbyVitruvius. Most of the others would seem to follow a variantscheme which is, nevertheless, based on similar geometricalprinciples.



4/18

1986] HADRIANICARCHITECTUREAND GEOMETRY 71Other dimensions,includingthose of the stage eleva-tion, are expressedas fractionsof the diameter of theprimarycircle.Hence, it is possibleto identifyas the essential com-ponents of the Vitruvian method for designing cen-trally planned buildings:a) successiveuse of ruler and compasses;b) employmentof modularproportions.An importantfeature of designs developedby thismethod is that all the key dimensions are geometri-cally related to the diameter of the first circle to bedrawn, accordinglyreferred to here as the primarycircle. It is to be noted that these ruler and compassesproceduresconformto the rules of geometricalcon-struction admittedby the Euclidean school,and theyare to be identified with "the geometricalrules andmethods" hat Vitruvius invokes for solving"difficultproblemsof symmetry.'"18In this context, the considerablespace devotedbyVitruvius to the analemma,where we find a detaileddescriptionof its geometricalderivation, s revealing:it is commensuratewith the importancehe attachestogeometry n the educationof an architect.As a schemeof some complexity,the analemma tells us somethingabout the extent to which an architectmight be ex-pectedto acquirea masteryof Euclideangeometry.Atthe very least, its inclusion in the de Architecturaas-sures us that elaborategeometricaldesignwas withinthe competenceof a trained architect n the periodofthe Principate.As far as surviving buildings are concerned,theround fortress of Herodium in Judaea, constructedsometimearound 20 B.C., furnishes one of the earliestillustrations of the use of extensive ruler and com-passes procedures n architecturaldesign.19A recently

proposed geometricalresolutionof its plan takes asthe primarycircle that describing he perimeterwallalong its inner edge.20 In typical fashion,constituentpartsof the plan correlatecloselyto modulardivisionsof the diameterof this circle.Curiously,the basiclay-out of the palace containedwithin the round walls isthatof a luxuriousRomanvilla,21 andit thereforehascertain featuresin common with Hadrian'scentrallyplannedisland villa at Tivoli, which is examinedbe-low. Elements of circulargeometryare also evident nthe contemporaryenclosuresbuilt by Herod aroundthe Tombs of the Patriarchsat Hebron and the Tem-ple of Jerusalem, whose length-to-breadthratios areboth very close to tan-1600:1.22 It may be demon-strated that the constructionof 600 anglesrequiresaruler and compassesprocedure, ike the one given inEuclid.23The same proportionsseem to have beenused in the Delphineion at Miletus, as rebuilt about334 B.C.24

On a smaller scale are two commemorativemonu-mentsin Ionia,bothapparentlyof Augustandate:theHarbour Monument at Miletus and the Monumentof C. Memmius at Ephesus. Their sides were enliv-ened by being given a concaveshape. Bammer hasfurnished a geometricalbasis for the plans of bothstructures.His derivationemploysa sequentialdevel-opment involving circles of constantradius that ac-cords with the Vitruvian method for designing cen-trally planned buildings as stated above.25 Bammerfurtherpoints out that these belongto a line of whathe calls "konkavenBauten" which culminate in thethirdcenturyA.C. templeof Venus at Baalbek.26The prominentroleplayed by the IonianarchitectsPytheosand Hermogenesin formulatingand codify-ing modular rules of designhas beennoted. Attention

'"Vitr. De arch. 1.1.4. Earlier in this passage,Vitruviusexplic-itly acknowledgesthe service renderedby Euclidean geometrytoRoman architectural design: Geometria autem plura praesidiapraestat architecturae; et primum ex euthygrammis circini traditusumn,e quo maximefacilius aedificiorum in areis expediuntur de-scriptiones normarumque et librationum et linearum directiones.The equally importantrole played by geometryin Roman deco-rative design, applied to mosaics and stonework, is discussed byR.H. Smith, "Decorative Geometric Designs in Stone,"BiblArch46 (1983) 175-86.19On Herodium, see E. Netzer, Greater Herodium (Qedem 13,Jerusalem, 1981) 79-101; also V. Corbo, "L'Herodion di GiabalFureidis,"LiberAnnuusSBF 13 (1963) 219-77; 17(1967) 65-121.20 D.M. Jacobson, "The Design of the Fortress of Herodium,"ZDPV 100 (1984) 127-36.21See Netzer (supran. 19) 109-10 andalso F. Rakob,"DerBau-plan einer kaiserlichen Villa," Festschrift Klaus Lankheit (Cologne1973) 113-25.22 On the Tombs of the Patriarchs, see D.M. Jacobson, "ThePlan of the Ancient Haram el-Khalil in Hebron,"PEQ 113 (1981)73-80; on the enclosure of Herod's Temple, see Jacobson, "IdeasConcerningthe Plan of Herod'sTemple,"PEQ 112 (1980) 33-40.23 Following Euc. Elem. 1.1.

24According to C.A. Doxiadis, Architectural Space in AncientGreece(J. Tyrwhitt trans.anded., CambridgeMass. and London1972; originally published as Raumordnung im griechischenStiidtebau,Heidelberg 1937) 55, fig. 24. Many of the geometricalrelationshipsproposedby Doxiadis are, however,suspect,not leastthe simple proportionsascribed o several Greektemples. CompareDoxiadis Tables 1-3 with Tables 1 and 2 in J.J. Coulton, "To-wards UnderstandingDoric Design: The Stylobateand Interco-lumniations,"BSA 69 (1974) 61-86.25See A. Bammer in Forschungen in Ephesos, VII: Das Monu-ment des C. Memmius (Vienna 1971) 74-79. On the HarbourMonument at Miletus, see also A. von Gerkan,Milet. Ergebnisseder Ausgrabungen und Untersuchungen seit dem Jahre 1899, 1.6:Der Nordmarkt und der Hafen an der Lawenbucht (Berlin andLeipzig 1922) 55-73.26 Bammer (supra n. 25) 77-79. This distinctivetype of "con-cave"structurecan be traced back to the early secondcenturyB.C.in a pair of tower tombs at Punic Sabrathaand Numidian Siga,bothshowing strongHellenisticinfluenceandprobably nspired byPtolemaic Alexandria. See F. Rakob, "NumidischeK6nigsarchi-tektur in Nordafrica," Die Numider. Reiter und Kanige nordlichderSahara(Bonn 1979) 146-54.



5/18

72 DAVIDM.JACOBSON [AJA90has also been drawnto earlyinstancesof architecturalplans utilizingruler andcompassesproceduresdenti-fied in the eastern Mediterraneanregion, includingthreefound in lonia. Furtherpointers n this directionare providedby Vitruvius,especiallyin his two chap-ters on sundials.27 They are peppered with Greekterms like analemmaand manaeus,28 and most of theinventors of the differenttypes of sundial mentionedby Vitruvius were of Hellenic origin. More to thepoint, no less than half the namesquotedcanbe iden-tified with celebratedgeometerswho hailed fromAsiaMinor and the eastern Aegean from about the midfourthto the earlyfirstcenturyB.C.29 On thestrengthof these observations, t is suggestedthat the principalsource of Romanknowledgeof appliedgeometrywasthe East Greekworld.While the inspiration for the mathematicalideascame largelyfromthe easternAegean,their practicalimplications were keenly appreciatedand exploitedby the Romans,whose interest n geometry ay almostexclusively in this direction.ContrastingGreek andRoman attitudes toward mathematicians and theirexpertise,Cicerohad this to say:In summoapudillos [Graecos] onoregeometriafuit, itaquenihil mathematicisllustrius: t nosme-tiendiratiocinandiquetilitatehuiusartis erminavi-musmodum.30Architectureprovidedthe ideal medium for combin-ing Roman engineering talents with Greek accom-plishmentsin geometry.One of the main catalystsforprogresson this frontwas, quite clearly,the replace-ment of the time-honoredbuilding materialstimberand stone by the artificialopus caementiciumor Ro-man concrete.It is generallyappreciated hat this ad-vance freedarchitecture romthe constraints mposedon design and constructionby the traditionalmate-rials and set the seal on the "Romanarchitectural ev-olution."The culminationof this momentouschaptermay be seen in the adventurous buildings of Ha-drian'sreign, and in particular n a series of composi-tions whose chief hallmarks include curvilinearground plans of unprecedented complexity; six ofthem are analyzedhere.

GEOMETRICALANALYSIS OF SIX HADRIANIC PLANSThe "Teatro Marittimo" at Hadrian's Villa

Of the centrally planned edifices erected in Ha-drian'sreign,noneperhapshas a plan as complicatedgeometricallyas does the so-called "TeatroMaritti-mo" on the Imperial estate near Tivoli, which mayaccountfor the fact that, while the structureand itsplan are well documented,3'no detailedgeometricalresolution of the plan has been published hitherto.This ground plan therefore s treatedhere in greaterdetail than the others. The "TeatroMarittimo"hasbeen identifiedas an islandvilla which Hadrianusedas a private retreatwithin his palatial estate. It be-longs to the firstphase of constructionon that site bythe Emperor,between 118 and 125 A.C.The plan of the island villa is reproduced n ill. 1.The complexoccupiesa circularareaalmost43 m. indiameter,boundedby a high concretewall facedwithopusreticulatum.The north-southaxis (Y-Y') is em-phasized in the plan by the entrancevestibule pro-truding northwardsand by a rectangularalcove letinto the enclosurewall on the oppositeside. Fringingthe perimeterwall is a porticus,within which lies aconcentricmoat. The island, which occupies the in-nermostzone, has a diameterof 24.5 m. and containsthe remains of a miniature villa. Its main elementsincludea semicircularvestibule surroundedby a col-onnade which faced the main entranceto the enclo-sure and opened out on to an ornate atrium whichmarkedthe centerof the entire enclosure.Three liv-ing roomstakeup the southside, the largerone in themiddlebeing identifiedwith the tablinum.The west-ern segment of the island retreat contains a smallbathing suite complete with hypocaust and coldplunge,while theoppositesideis takenup by two cru-ciformroomswhich may havehousedsmall libraries.The general arrangementof the rooms aroundthecentralatriumfollows that of a conventionalRomanvilla, but it departsfromthe normalschemein beingcircularratherthan rectangular n shape. Even moreexceptionally,most of the internalpartitionsechothemain outline by tracing circulararcs. The design is

27 Vitr. De arch. 9.7-8.28 See Soubiran(supra n. 16). Vitruviusalso uses a Greekterm,embates,formodule (De arch. 1.2.4 and 4.3.3); see Coulton(supran. 10) 66 and n. 49.29 1) Aristarchos of Samos (first half of 3rd c. B.C.). See RE 2.1(1895) 873-76, s.v. Aristarchos 25) (F. Hultsch);andT.L. Heath,Aristarchus of Samos (Oxford 1913; repr. 1959). 2) Eudoxos of Kni-dos(fl. ca. 370- 350 B.C.). See RE 6.1 (1907) 930-50, s.v. Eudoxos(8) (F. Hultsch); and G. Huxley, "Studies n the Greek Astrono-mers,"GRBS 4 (1963) 83-105. 3) ApolloniosofPerge (secondhalfof the 3rd c. B.C.). See RE 2.1 (1895) 151-61, s.v.Apollonios (112)(F. Hultsch); and T.L. Heath, Apollonius of Perga (Cambridge1896; repr. 1961).4) Theodosios fBithynia (ca. 150-70 B.C.). See

RE 5A2 (1934) 1930-35, s.v. Theodosios(5) (K. Ziegler). 5) Dio-nysodorosof Amisus, mathematician,or Dionysodorosof Melos,geographer,(fl. ca. 200 B.C.). See RE 5.1 (1903) 1005-1006, s.v.Dionysodoros (19) and Dionysodoros (20) respectively (F.Hultsch). The inventorsof the sundials and the instrumentscred-ited to them by Vitruvius are also discussedby Soubiran(supran.16) 240-70 and Gibbs (supra n. 16) 59-65.30Cicero Tusc. 1.5.31Kaihler(supra n. 1) 44-54 and 117-22; Blake and Taylor-Bishop (supra n. 6) 242-43: and E. Salza Prina Ricotti, "VillaAdriananei suoi limiti e nella sua funzionalitA,"MemPontAcc14(1982) 33-35.



6/18

1986] HADRIANICARCHITECTUREAND GEOMETRY 73

yo/ II

0 10 20 M

Ill. 1. Hadrian'sVilla,"TeatroMarittimo,"round lan(afterH. Kihler,Hadrian ndseine VillabeiTivoli,pl.6) withproposed eometricalasisamongthe mostflamboyant n the entirerepertoireofRoman architecture. Its architect surely would nothave arrived at such an elaborateplan unless he hadintentionallybeen engagingin someintricategeomet-rical construction:such an approach was employedmany centuries laterby Borromini.32A geometricalresolution that can account for themain features of the plan of Hadrian's island villa issuperimposedon the plan in ill. 1. The probablestepsby which it was reachedare shown in ill. 2 and theycan be describedas follows:A) Draw circlea of radiusRa centeredat 0. Establish

orthogonalaxes XOX' and YOY',using the con-struction of Euclid's Elementa, propositions 1.1and 1.11 (ill. 2a).33B) Divide the principal diameters into six equalmodularlengths, r, such that Ra = 3r. Draw cir-cles b and b' centeredat points -r and +r from 0

alongthe x-axis, each with radiusRb = 2r. Thendraw circle c centered at 0 throughthe points ofintersectionof circlesb andb'.ItsradiusRc ='/3r(ill. 2b).C) Next, drawthreecirclesof equalradius,Rd = Rb= 2r, about centersat -2r, 0, and +2r alongthe x-axis (XOX').Let these be called circlesd', d, andd" respectively.Join the points of intersectionofcirclesd with d' and d"by a pair of straightlinesparallel to the y-axis (YOY').The pointsof inter-sectionof the two parallel lines with the circle care labelledE1,E2,E3, E4in ill. 2c.D) The lengthsE,E2 and E3E4,whicharebothequalto 2r, define the diameters of two new circles, eand e' of radius Re = r. Draw another circle

through the outer extrema of e and e' from 0,which we shall denote as circlef; radiusRf = ('I2+ 1)r, as shown in ill. 2d.32Sedlmayr(supra n. 1).33Since the "TeatroMarittimo" s not properly alignedwith thepointsof the compass,it is unlikely that the more elaborateproce-

dure for establishingthe axes given in Vitr. De arch. 1.6.6-7, andrepeated n 1.6.12-13, was used.



7/18

74 DAVID M. JACOBSON [AJA 90

Da=144fty, Y'

.-.. ....~ ""."?-

Y a Y by' 4 I t:

Y c

Ci

Y' Y'

y, y0*, 1 x

X X' X X'

Y d Y eIll. 2. Hadrian'sVilla, "TeatroMarittimo," nferredgeometricaldevelopmentof the ground plan



8/18

1986] HADRIANICARCHITECTUREAND GEOMETRY 75E) Then, draw a small circleg , centeredat 0, suchthat it touches circlese and e'; radiusRg = ('& -1)r.The annulargap between circlesg andd fixesthe diameterandthe centersof two morecircles,hand h', of radius Rh = /2(3 -/'2)r, which are de-scribedsymmetricallyaboutthe x-axis (ill. 2e).In relationto the islandvilla:a) circlea corresponds o the inner surfaceof the en-closurewall.b) circle c corresponds o the actual island.c) circle corresponds to the outeredgeof the moat.d) circlese, e',h andh'provide he basis for severalofthe bowing colonnades on the miniature island,namely:i) the four cusped porticoesat the center of theatrium, which coincide with arc sections ofthese circles;ii) other curving porticoes, which are concentricwith these circles. Of special note are the pairof crescentsspanningthe two cruciformcham-bers east of the atrium,basedon circleh', andthe semicircularporticoof the northernvesti-bule, concentricwith circlee'.34The remaining details of the plan are accommo-dated within this geometrical framework and theirform would have been determinedlargely by func-tional needs. As realized, the island villa has a dia-meter of 42.56 m.,35 so that Ra = 3r = 21.28 m. Thislengthcorresponds o 72 Ro'man eet, assumingthat 1Roman foot = 0.2956 m.,36 whence r = 24 feet. Thefact that these values are both simple integer multi-ples of 4 Roman feet suggeststhat Ra, or the equiva-lent diameterDa, was the key dimensioninitially setby the architectwhich determinedall the othermeas-urements of the plan.The plan of the island villa, as interpretedhere,possesses some interesting geometrical properties.Denoting the points of intersectionof E1E3and E2E4with XOX'as A1andA2,those of circleb with b'as B1and B2,andthose of circlea with XOX'as C1and C2,it is seen with the aid of ill. 3 that:a) triangles B1A1A2and B2A1A2are equilateral,with each containedangle equal to 60'. This fol-

lows from the constructionof the circles b and b',centeredat Al(-r) and A2(+r) respectively,whichreproducesthat given in the Elementa, proposi-tion 1.1.b) B1A1and B10trisectthe right angle C1B1A2.This

pattern is repeatedfor the right angles A1B1C2)C1B2A2 ndA1B2C2.The rightangle is one of thefew specific angles that is amenableto ruler andcompassestrisection: t only succeedswhen, as inthis case, the angle of trisection(here300) can beconstructed independently by ruler andcompasses.The "trisection f the angle," ogetherwith the "squaring of the circle" and the"duplication f the cube," n the generalcase,con-stituted the three celebratedproblemsof ancientGreekmathematics.37c) the radii Ra = 3r, Rc =f3 r, and Re = r are incontinuousproportion, .e. Ra/Rc = Rc/Re =N'/3= 1.732.

In reality, Dc = 2(Rc) = 24.50 m.38 and Da =42.56 m.39 so that Ra/Rc = 1.737.Greek mathematiciansmade a clear differentia-tion between the general "discrete"(btyp?rT) )proportionalrelationshipa/b = c/d, a f b c dand "continuous"(o-vvEXs, rvvljtupv7r)propor-tion,40 epresentedbya/b = b/c.

The special case where c = a + b corresponds othe "GoldenSection."41ThePavilionofthe "Piazzad'Oro" t Hadrian's VillaLining the south side of the large peristyleknownas the "Piazza d'Oro"are the remains of a suite ofchambersthat Blake thoughtto be "the most elegantrooms of the entire villa."42Their centerpiecewas aclosed colonnadetracing a sinuous octagonof alter-nating convex and concavesegments.This structurewas framed within a square;the spaces between thediagonalsections of the colonnadeand the cornersofthe enclosingsquarewalls formed denticalniches ter-minating in apses. Bowing out southward from thiscentralpavilionwas a curvednymphaeum,and to the

34Kahlerrecognized hat the colonnadeof the semicircularvesti-bule and the northernsegmentof the atriumporticobelongto cir-cles which are concentric.See Kihler (supran. 1) 118 and fig. 24.35 S. Aurigemma, VillaAdriana (Rome 1961) 68.36For the lengthof the pes or Romanfoot,see K. de Fine Licht,The Rotunda in Rome. A Study of Hadrian's Pantheon (Copen-hagen 1968) 195, n. 29. It appearsto havevariedwithin the range0.2942-0.2958 m. at least.MacDonald (supran. 8) 140, n. 70, tookits value to be 0.295 m., while Rakobhas used a footof 0.2942 m. inhis analysisof several Romanbuildings (see infra ns. 46, 50).37C.B. Boyer,A History of Mathematics (New York 1968) 71;also Heath (supran. 16) vol. 1, 218-70.

38Kahler(supran. 1) 45.39See supran. 35.40 For a discussionof the distinctionmadebetween"discrete" nd"continuous"proportion by Greek mathematicians, see T.L.Heath, The ThirteenBooksof Euclid's Elements22 (Cambridge1925, repr.New York 1956) 131.41 Euc. Elem. 6 def. 3.42Blake and Taylor-Bishop(supran. 6) 247. On the pavilionofthe "Piazzad'Oro," ee, in particular,Rakob(supra n. 4) passim;E. Hansen, "La'Piazza d'Oro'e la suacupola,"AnalectaRomanaInstituti Danici, Suppl. 1 (1960) 1-78; Kdihlersupran. 1) 64-73,132-37.



9/18

76 DAVIDM.JACOBSON [AJA90east and west there were a matching pair of internalcourts surroundedby vaultedrooms.The pavilionit-self appearsnot to havesupporteda roof,according oRakob in recent studies.43We learn from the brickstampsthat the "Piazza d'Oro" ogetherwith the ad-joining structures,including the pavilion, belongs tothe second Hadrianic building phase at the villa,which followed the Emperor'sreturn from his firstlong voyagein A.D. 125.The plan of the pavilion and its proposed geomet-

rical basis are shown in ill. 4. The present interpre-tationof the groundplan differs rom those of Hansenand Rakob.44 n the more recentof these two studies,Rakob treated the existing layout as though it hadbeen faithfully transferredfrom the drawing board.He thereforemade little allowance for errors in thetranslationof the planto the actual site. Detailedcon-siderationof Rakob'splan and supportingmeasure-ments has led me to the opinion that his strict ap-proach is unrealistic.45For example, Rakob draws a

; Y '

I E 2

X A l A 2 X

~I

c i r c l e b / c i r c l e bcircle a

, c i r c l edcircle c

Ill. 3. Hadrian's Villa, "TeatroMarittimo,"geometricalrelationships n the groundplan43F. Rakob, "Hansen, La Piazza d'Oro e la sua cupola,"Gno-mon 33 (1961) 243-50; and also Rakob(supran. 4) 57-74.44Hansen (supra n. 42) 62, 64-65; Rakob(supran. 4) 75-88.45On Rakob's own admission[(supra n. 4) 75-77; (supra n. 6)132-33; and also Rakob,"Das Quellenheiligtumin Zaghouanunddie romischeWasserleitungnach Karthago,"RomMitt 81 (1974)76] his views on Romanarchitecturaldesignare coloredby his op-position to the sizable corpus of metrologicalstudies that are di-

vorced romtheirarchitecturaland historicalcontextand which donot refer to a measurement ystemappropriate o the periodof thebuildingsanalyzed.He is undoubtedly orrect oquestionthe valueof suchstudies,but he overreactsn the sense that he concernshim-self exclusively with the practical aspects of design. He therebyoverlooksaestheticand other considerationswhich must have hadan importantbearingon the choice of the elaborategeometries hatwere occasionallyused, such as those at the center of the present



10/18

1986] HADRIANIC ARCHITECTURE AND GEOMETRY 77

;.:.. ?.?:?;.~'?''?T~:?:??? ''' ""i~i:'''' ''' '?: -???.? ??" V'.:".:r

"'"`-'~~;~-' ?"'? ?; ;r?:%I I

;'?-??rlU I ~ rr/l/ I U \r

I, h I n '?V r

I )I I \ I / I \'I ~\r

i I \ I I I i I In~I \ I / I \ I / I I?-.??.

\u\I r ;?t~-....?

I rz r?r:?. r ??.?;'.. t~`"" z ????? --?

0 10 20 m

Ill. 4. Hadrian'sVilla, pavilionof the south side of the"Piazzad'Oro," roundplan(afterF. Rakob,Die Piazzad'Oro in der Villa Hadrianabei Tivoli, fig. 14) withproposed eometricalasisdistinctionbetween a dimension of 12 ft. and one of12?2 ft., althoughthe 5%and 3%spreadin the meas-urementsidentified with each of these dimensionsre-sults in some overlapof the two sets of values.46Headds to these two modules a third one of 15 ft.Thefundamental simplicity of the plan of the pavilionemerges by relaxinghis undulystringentassumption.Then the circle a of radius 12?2 ft., drawn about thecenter of the area, emergesas the key piece in thejig-saw and the otherelements of the geometricalschemederive in a straightforward ashionfromthis primarycircle as shown sequentiallyin ill. 5.First, the primary circle a, of radius r (ill. 5a) isdrawn. A grid of 36 squares, each of side r, is thenmarked out. The area equal to 6r x 6r establishestheoverall dimensions of the centralpavilion. Using thisgrid, four identicalcircles of radiusr are describedat

Da=25ft-

IaII

/

I I

b

\\

I I

II

'I

Ill. 5. Hadrian's Villa, pavilion of the "Piazza d'Oro,"inferredgeometricaldevelopment

study. See H. Geertman,"AedificiumCeleberrimum: tudio sullageometriadel Pantheon,"BABesch55 (1980) 210:46 Rakob(supran. 4) 81, n. 156; 82, n. 157;on p. 5, n. 11, Rakobassumed 1 Roman foot = 0.2942 m. for the hall of the "Piazzad'Oro,"and also for the apodyteriumand the belvedereof the "Ac-cademia"at Hadrian'sVilla, which were also analyzedin his dis-sertation(78-80).



11/18

78 DAVID M.JACOBSON [AJA90pointsx = +2r, y = +2r (ill. 5b).Then a new circle sdrawn to touch eachof the fourequal circles.Finally,fourequivalentsemicirclesof radiusr areadded,cen-tered on the points of intersection of the previouslydrawncircle with the principalaxes (ill. 5c). The un-dulatingcurve so produceddefines the line of the in-ternal colonnade of the pavilion.The fit of this geo-metrical schemeto the actualgroundplan is indicatedin ill. 4, the value of r havingbeen scaled to 121/2t.,with 1 ft. = 0.2942 m.47 Accordingly,the radius ofcurvatureof the twisting colonnadetakes this samevalue,while the pavilionas a whole occupiesa squareof 75 x 75 ft.48The next three groundplans seemto proceed roma similar grid of "close-packed"ircles. This formulais mostobviouslyrealizedin the firstof these,belong-ing to a chamber n a bathingestablishmentat Baiae,the resort where Hadrian died.The Annex to the "Temple of Venus" at BaiaeThe so-called Temple of Venus is now known tohave formedpart of a large bathingcomplex.49Thisbuildingand its annex havebeenassigneda Hadrian-ic date on stylistic grounds.Certainly,the distinctiveplan of the annex (ill. 6) echoes that of the pavilionofthe "Piazzad'Oro,"with which it is seen to share ele-mentsof a commongeometricalbasis.Thus, theopen-ing stepsin theirdevelopmentarerecognized o be thesame, although differently scaled (ill. 7a, b; cf. 5a,b).50Thereafterthe two designsdiverge,with thesug-gested continuation for the annex being indicated nill. 7c. The designof the upper part of this chamber,with its elegantumbrella-shaped upola,is based on asomewhat different geometrical diagram which isshownin ill. 8.51The square bounding he nineequalcircles that provide the geometrical basis of thegroundplan link it with the plan of the upper stage.This square,of side45 ft., is indicated n ills. 6 and8.

The Apodyterium of the Small Baths at Hadrian'sVillaThe Small Baths were apparently begun before

. . ..... ...................

r ~~sas~assa~d 110

Ill. 6. Baiae,annexofthe"TemplefVenus," round lan(afterF. Rakob,RbmMitt 8 [1961] ig.9) withproposedgeometricalevelopmentHadrianleft Italy in A.D. 121.52As their name indi-cates, they are not the most spaciousof the bathinginstallations on the Imperial estate but, as Rivoirapoints out, they "are remarkable or the singularde-sign and shape of the rooms."53 articularlystrikingis the ruined apodyterium,which has a plan in theform of a Greek cross with roundedcorners. Withgreat ingenuity,this chamberwas made to supportasecondtype of segmenteddome,having sections thatwere alternately latand concave.A geometrical esolution spresented n ill. 9 fortheground plan of the apodyteriumwhich differsin im-portant essentials from the one proposed by Han-sen.54 The presentscheme,rather,has its rootsin thegrid of touching circles that also underlies the twoprevious plans, as has been suggested.In this case,however,the foursecondary irclesof radius r drawnsymmetricallyabout the origin of the grid are cen-teredat the pointsx = +2r, y = 0 andx = 0, y = ?2r(ill. 10a, b). These circles would appearto establishthe four curvedwallsof the chamber.The positionsofthe alternatingstraightsides are then determinedby

47See supra n. 46.48Rakob suggested that the outer dimensions of the buildingwere obtainedusing a moduleof 15 ft; thus 75 ft = 5 x 15 ft. Butthen his schemerequiresa separatemoduleof 12?2 t. to account orthe curvatureof the colonnade.49For the "Templeof Venus"at Baiae, see Rakob (supra n. 6)114-49; also Blake and Taylor-Bishop(supran. 6) 268-69.50In this case, the diameter of the primarycircletakesthe valueof 15 ft. (1 ft. = 0.2942 m., followingRakob[supran. 6] 132).51Here, I largely concur with Rakob'sresolution,(supra n. 6)fig. 13. WhereasI take the idealizedgeometrical chemeasthebasis

of the plan, since I believe it governed he originaldesign,Rakob'srepresentationof the scheme accommodates he distortions ntro-

duced when the building was executed(and also perhaps subse-quently).This is in accordancewith his approach o Roman archi-tecturaldesign;see supra n. 45. Cf. the resolutionof this plan of-feredby Bammer supran. 25) 79 and fig. 70c.52For the Small Baths,or "PiccoleTerme,"see especiallyBlakeandTaylor-Bishop(supran. 6) 247-49 and Hansen (supran. 42)47-49, 51. On theirdate,see also A.C.G. Smith,"The Date of the'GrandiTerme' of Hadrian'sVilla at Tivoli,"BSR 46 (1978) 78.3 G.T. Rivoira,Roman Architecture nd its Principles of Con-structionunder the Empire, trans. G. McN. Rushforth (Oxford1925) 135.54Cf. Hansen (supran. 42) 45-47.



12/18


FDa=15t-

! i

a

I I

b

!i I (

:I

I --

/C

% I

Ill. 7. Baiae, annex of "Temple of Venus," inferredgeometricaldevelopmentof the groundplan

//i/

I I\I' \i I1

\--"--

It\

I

',,,

u

tt/

/

I t \

\` \\,

' l- - Io

Ill. 8. Baiae,annexof "TempleofVenus,"planof theupperstage(afterF. Rakob,RimMitt 68 [1961] fig. 10) with pro-posedgeometricalbasisthe points of intersection of each of these circles withlines drawn from their centers to the adjacent circlesat points where these are cut by the main axes(ill. 10c). The radius r of the primary circle is, in thiscase, 16 Roman feet.55The Belvedere of the "Accademia"at Hadrian's VillaAnother structure organized on a central plan onthe lines of the apodyterium graced the "Accademia"or "Piccolo Palazzo," a semi-autonomous residentialcomplex situated at the southern end of Hadrian'sVilla which, on the evidence of the brick stamps, wasbuilt in A.D. 123.56 The ruins occupy land that haslong been in private ownership, and have never beenmethodically excavated. Kahler and Hansen, how-ever, have judiciously pieced together the plan of thisremarkable structure from the visible remains and thedrawings executed by leading antiquarian scholars ofthe seventeenth and eighteenth centuries.57 It wouldappear that the building in question was a sumptuousgarden pavilion or belvedere which, like that of the"Piazza d'Oro," had a serpentine colonnade as its cen-

55Assuming1 ft.= 0.2942 m.,after Rakob(supran. 46). Accord-ingly, the innerwidth of the apodyteriumakenacrossthe straightsides is 35.1 ft. This compareswith the value 35.0 ft. assignedbyRakob (supra n. 4) 78, the differencebetweenthese figuresbeingwell within the limitsof precisionof the groundplan.56 For the belvedereof the "Accademia,"ee Kahler(supran. 1)81-84, 129-32; Hansen (supran. 42) 50-51; also Blakeand Tay-lor-Bishop(supran. 6) 252.57Kaihler supran. 1) 81-84, 129-32; cf. Hansen (supra n. 42)50-51.



13/18


i ~ ~ ~ 7e ~,, t4... .... . .0 I 20

Ill. 9. Hadrian's Villa, Small Baths, apodyterium,groundplan (after F. Rakob, Die Piazza d'Oro in der VillaHadriana bei Tivoli, fig. 15) with proposed geometricalbasisterpiece: the enclosed space was almost certainly like-wise open to the sky.58The plan of this belvedere, as reconstructed byKdihler, and its suggested geometrical basis are shownin ill. 11. The present resolution differs from that ofRakob,59 following instead the development postu-lated for the apodyterium so that the preliminarystages of the design, represented by ill. 12a and b, re-peat ill. 10a and b. The square defined by the four cir-cles of radius r drawn about each of the main axesseems to have determined the subsequent stages, forother geometrical elements in the actual plan that canbe readily identified are the circle inscribed in thissquare (ill. 12c) and another obtained via the circlethat circumscribes it (ill. 12d). Here, the radius of theprimary circle is scaled to a round value of 25 Romanfeet.60The Pantheon in Rome

The last of the buildings chosen for consideration isthat great masterpiece of Roman architecture, thePantheon as reconstructed by Hadrian between 118and 128 A.D. It comprises a rotunda with a cylindri-cal wall and a hemispherical cupola, onto which is

HDa=32t

, -

I I

a

b

,/

C'-C

I I

I !

,,

,'

S \I i

Ill. 10. Hadrian'sVilla, Small Baths,apodyterium, nferredgeometricaldevelopmentof the groundplan

58 See Rakob in Gnomon (supra n. 43), contra Hansen (supran. 42).59For Rakob'sresolution,see (supra n. 4) 78-80 and fig. 16.60Where 1 ft. = 0.2942 m., following Rakob(supran. 46).



14/18

1986] HADRIANICARCHITECTUREAND GEOMETRY 81grafteda trabeatedrectangularporch.The organiza-tion of the plan is treatedin somedetail in two recentstudies, namely those of de Fine Licht and Geert-man.6' Their analyses are conflicting,but both offerilluminating points of contactwith the design proce-dures deduced for the other Hadrianic buildingsabove.In the resolutionof de Fine Licht (ill. 13) the keycircle is that enveloping ts interiorspace,which has aradius Ra1 = 74 ft.62 This, the primarycircle of hisscheme, supports a multitude of architectonic fea-tures. Amongthe more evidentones are the alternat-ing openand closednichesspacedat equal intervals n

- '- .

j '1, / '

A ,

' I

0 o Im

0 10 20MIll. 11. Hadrian'sVilla, "Accademia,"elvedere, roundplan (after H. Kdihler,Hadrian und seine Villa bei Tivoli,pl. 13)withproposedeometricalasis

the circumferentialwall: their positions are deter-mined by the regular 16-sided polygon inscribed inthe primarycircle andalignedwith the principalaxesof the building,which virtuallycoincidewith the car-dinal points. De Fine Licht has highlightedthe im-portanceof the equivalentpolygonrotatedby half thebase angle of 221/2 (= 11?), so that the vertices ofthe two interlockingpolygonsdivide the circle into32equal arcs. Accordingto this scholar the second 16-sided figure defines the widths of the eight large re-cessesopening fromthe interiorof the rotunda.Fur-thermore,he suggeststhat the extrapolationof a pairof sides of this polygon in a northward direction(asindicatedin ill. 13) determinesthe depth of the en-tranceporticoandthat of the adjoiningvestibule. In alike manner,de Fine Licht is able to account for thedepthsof the eightrecessesandfor the outer radius ofthe rotunda using geometrical constructionsbasedsolely on the two 16-sidedpolygons.63Rememberingthat 11o1/4and 221/2 are an eighthand a quarterof aright angle respectively, t can be assumedthat thesepolygonswere obtainedfromcircleaI by repeatedbi-sectionusing compassesand following procedures etdownin the Elementa.64The alternative interpretationof the plan of thePantheon offered by Geertman relies on a differentprimarycircle and has a more extensivegeometricaldevelopment.The main features of his scheme areshown in ill. 14. Geertmanobtains his primarycirclea2 from the overall length of the building, from themeasureddistancebetween the frontof the porchandthe center of the rotunda,and from the principaldi-mensions of the porch itself: all these dimensions hesees as having been geometricallyderivedfrom thatcircle.6' A second circle of the same radius, Ra2, isdrawn abouta pointon the circumference f the first,where it is cut by the principalaxis YOY'.The tan-gent to this new circle,perpendicular o YOY'at E inill. 14, corresponds o the front of the porch. More-over, the three naves of the porch line up with axesdrawn through the points of intersection of the twosquares inscribed in the primary circle a, and ori-entedat 45' to one another. These squares appearto

61On the designof the Pantheon,see de Fine Licht (supran. 36)194-98, Geertman(supra n. 45) 203-29, MacDonald (supran. 8)94-121 and The Pantheon. Design, Meaning and Progeny (Lon-don 1976) 44-75; also Blake andTaylor-Bishop(supran. 6) 42-48.62 See de Fine Licht (supran. 36) 195. This authorhassuggestedthat Hadrian's architectschose 148 ft. (where 1 ft. = 0.2958 m.) forthe internal diameterof the rotundaof the Pantheon, n preferenceto the moreexpectedfigureof 150 ft., so as to reproduce he lengthdimension of its predecessor.63Thus, circleb, of radius Rb,, corresponding o the extrema ofthe large recesses,passes through the points of intersectionof theaxes of eitherpolygon produced,with the sides of the samepolygon,

as shown in ill. 13; i.e. Rb, = Ral/(2 cos 221/2'- 1). The radiusdrawnfrom the centerof therotunda,0, to the verticesof a 16-sidedpolygoncircumscribing he circle b1 in turn, approximatelycoin-cides with that taken to the outer edge of the rotunda wall. Thisradius, labelledRc,, is given by RcI = Ra /[cos 221/'(2 cos221/2 -1)].That Rb1andRc, are directlyproportional o Ra,, throughtheabove trigonometricalexpressions, stems from the fact that thesedimensions are totally dictatedby the primary circle a,, and theinscribed16-sidedpolygonswhich contribute he factorcos 2212.64See, forexample,Heath (supra n. 40) 111.6sGeertman(supran. 45) 205, 210-11.



15/18


HDa=5OftA

*b

, ,,I'

II

I

a b

%d

I

I I? --'. .

IIo

aj'r \ re '

II

t f\ In\

CIdI , I

%I .

? dIll. 12. Hadrian'sVilla, "Accademia," elvedere, nferredgeometricaldevelopmentof the ground plan



16/18


0 10 50MIll. 13. Rome,Pantheon, eometricalasis of the groundplan accordingo K. de Fine Licht.(Afterde FineLicht,TheRotundanRome, ig.202)fix the positionsof the pillars in the main niches, asshown in ill. 14.Geertman'sresolution s at variancewith thatof deFine Licht on a number of important points. Whilethe geometrical constructions differ in these cases,they do, however,producevalues that closely agree.66In fact,from the pointof view of precisionof fit, thereis little to choose between the two schemes. Geert-man's scheme commends tself by being able to pro-vide a morecomprehensive eometricaldescriptionofthe plan of the Pantheon.It also offers a closerparal-lel with the plansof the Hadrianicbuildingsanalyzedabove.Thus, the pair of interlocking quaresforminga regular octagonwithinthe primarycirclea2 s a geo-metrical devicefound also in the designsof the upperstage of the annex at Baiae, as notedby Geertman67(cf. ill. 8) and for the belvedereof the "Accademia" tHadrian's Villa (cf. ill. 12). Moreover,the repetition

of circle a2, translated a distance Ra, along one of theprincipal axes, echoes the design procedure proposedearlier for the "Teatro Marittimo". A major weaknessof Geertman's hypothesis, however, is that hisprimary circle does not correspond with a visiblefeature of the plan; nor does its radius or diameterassume a neat number of Roman feet."8By contrast,de Fine Licht's proposal is based on the internal dia-meter of the rotunda.

Being in an almost complete state of preservation,

I lo !iN I2to 6o-m

IZ2

/ i N , 2_4r

o 10 50 mIll. 14. Rome, Pantheon,geometricalbasis of the groundplan to H. Geertman. AfterGeertman,BABesch55 [1980]fig. 4, courtesyauthor). The dimensions are expressedasfactors of the radius Ra, of the primary circle a, ofGeertman'sscheme

66For example, the relativedistancesfromthe centerof the ro-tundato the front of the porchaccording o thegeometrical chemesof Geertman and de Fine Licht may be shown to be X,/X =

2Ra2/(17.1+iITRa,) = 1.006, where Ra, = 24.18 m. and Ra =

21.89 m.; 17.1 m. is half the measuredwidth of the porch:seeGeertman(supran. 45) 211. Also, the respectivevaluesof the radii

taken to the outer surface of the rotunda wall are in the ratioRc,lRc, = [Ra,/(cos2 221/2')]/[Ra,/(cos 221/2(2 cos 221/2' - 1)] =1.014.67Geertman(supran. 45) 205, n. 9.

68 Ra, = 814 Roman feet, denotedby R in Geertman(supran. 45) 2-11.



17/18

84 DAVIDM.JACOBSON [AJA90TABLE. Diametersof "PrimaryCircles" n Six HadrianicGroundPlans

Building Diameter Text IllustrationDa, Romanfoot*Tivoli, "TeatroMarittimo":nclosure 144 1, 2

"Piazzad'Oro": outhpavilion 25 4, 5Small Baths:apodyterium 32 9, 10"Accademia":elvedere 50 11, 12

Baiae, "Templeof Venus":annex 15 6, 7Rome, Pantheon: otunda 148t 131 Romanoot = 0.2956m.forthe "TeatroMarittimo"= 0.2958m.forthe Pantheonseen.62)

= 0.2942m. forthe otherbuildingsseens.46,50)- afterde Fine Licht seen. 62)the Pantheon affords a detailed comparisonof theground plan with the elevation. What emerges is astrikingcorrelation69:he plan shows a close relation-ship with the verticalsection,the heightof the rotun-da being equal to its internal diameter. This inte-grated approach to the design of centrally plannedbuildings appears to represent standardpractice inRoman architectureof the Imperial period,being at-tested in Vitruvius'descriptionsof the designof roundtemples and the Roman theateras notedearlier.70Asimilarsynthesisof groundplan and elevationoccursin the Dome of the Rock in Jerusalem, completed nA.D. 691.71Few todaywould doubtthat, froman ar-chitecturalpointof view, the Dome of the Rock has itsroots in the Graeco-Romanbuilding tradition. It isstrikingthat the designof this monument, ike that ofthe Pantheon,can be accounted orby an elegantgeo-metricaldevelopmentfrom a regularpolygondrawnwithin a circle, in this case an octagon.The dearth ofother comparableexamples, one suspects, has to doprimarilywith the rarityof buildingsof centralsym-metrythat havesurvived ntact fromClassical times.

The above examples serve to demonstrate hat se-quential ruler and compassesprocedures,on the Eu-clidean method, were used in the draftingof the re-spectiveplans. In everycase the primarycircle,drawn

about the centerof the design, can be readily identi-fied:its radius,or diameter,is the controllingdimen-sion of the entiregroundplan. No doubt,for this rea-son, the diameterwas chosento be an integermultipleof four or five Romanfeet.72The Table lists the val-ues of this diameter,Da, appropriate o the six build-ings considered n this study.Not all the geometricalschemespresentedprovidea perfect fit to the actual groundplans. A degree ofmismatch is particularlynoticeable n ill. 4, showingthe pavilionof the "Piazzad'Oro,"andin ills. 6 and8,depictingthe two levels of the chamberat Baiae;suchdeviations are to be expected, bearing in mind thesomewhat primitivemethodsused in Classical anti-quity for layingout planson the ground.In a studyofGreektempledesign,Coultonhaspointedout that thetwo principal devicesavailable for this purpose, themeasuringcordandthe measuringrod,were pronetoerror.73Cord or rope is susceptibleto shrinkageorexpansion through stretching.On the other hand, ameasuringrod, being madeof wood, has a more lim-ited length and the Greeks and Romans commonlyfixed it for convenience o a standardof 10 ft.: impre-cise calibrationand misalignmentof rods laid end-to-end could easily generate substantialerrors.Circlesand arcs,which would have been markedout on theground using a cord (or rope) tied at one end to a

69Comparede Fine Licht(supran. 36) fig.201 with fig.202, andGeertman(supra n. 45) fig. 11 with fig. 4.70See supra ns. 14 and 17.71 See J. Wilkinson,"ArchitecturalProcedures n ByzantinePal-estine,"Levant 13 (1981) 165-70. On the Dome of the Rock andits

architecturalorigins, see K.A.C. Creswell, Early Muslim Archi-tecture2 1 (Oxford1969) 65-131, 658-60.72MacDonald (supran. 8) 140 furnishesadditionalexamples.73J.J. Coulton, "TowardsUnderstanding Greek Temple De-sign: GeneralConsiderations,"BSA 70 (1975) 90-91.



18/18

1986] HADRIANICARCHITECTUREAND GEOMETRY 85stake,could also become distorted f, forexample, theanchoringwas not firmor the cord allowedto slacken.In the case of the building at Baiae, irregularitiespresent in the plan geometry may have an additionalcause, namely ground movement.74 The Bay of Na-ples is notorious for seismicdisturbance,and we havedocumentaryevidence that the great earthquakeof1538 causeddamageto the "Templeof Venus".75HADRIAN S PERSONAL ROLE

The fact that someof the mostaccomplishedexam-ples of Roman architecturaldesign employingcurvi-linear forms are to be found at Hadrian'sVilla indi-cates that at the least this distinctivetype of designenjoyedImperialpatronage.On this pointwe can ob-tain some useful guidance from the remarkson Ha-drianpreserved n the ancienttexts.Two of our prime sourceson the Emperorconcurthat geometryrankedhigh among his intellectual ac-complishments.76From the passage in Dio Cassiusdescribingthe downfall of Trajan'sarchitectApollo-dorus we also learn of Hadrian'sexceptionalinterestin architecturalmatters.77Dio appearsto equateHa-drian's drawings with architecturalplans since bothare mentioned n the Apollodorusepisode.Inthis pas-sage we are also given to understandthat Hadrianwas personallyinvolved n the planningof the temple

of Venus and Rome,oneof the majorClassicalmonu-ments in Rome.78Whateverthe true extent of Hadrian'scommitmentto architecturaldesign,his well attestedpenchantforgeometrymust surely have some connectionwith thesophisticatedplans that have formedthe focus of thisstudy. It is a strikingfact that many of the buildingscommissionedby Hadrian emphasizethe qualitiesofgeometricalorder and refinement,and there can belittle doubtthat they reflecthis personaltaste. Brownhas suggested hat Hadrianwas the author of the seg-mented domeswhich featurein buildingsdatedto hisreign, includingsome of those discussed above.79Heidentified these distinctive domes with Hadrian'sdrawings of "pumpkins" (KOAOK;v'vra)which wereridiculedby Apollodorus,as we are told by Dio Cas-sius. Brownventuredas far as to claim that Hadrianwas the inventorof these unusual domes, suggestingthat he was fascinatedwith undulatingshapesanden-joyed experimentingwith convolutedstructures. Inthe absenceof firmerevidence,however,the ideathatHadrian played an activeand creativerole in archi-tecturemustremainan intriguingriddle.

DEPARTMENT OF CLASSICSKING'S COLLEGE LONDONLONDON WC2R 2LSUNITED KINGDOM

74See supra n. 51.75 Rakob(supra n. 6) 115.76 S.H.A., Hadr. 14.8;Epit. de Caes. 14.2.77 Dio Cass. 69.4.2-3.78 On the question of Hadrian's authorshipof the design of thetemple of Venus and Rome, see MacDonald (supra n. 8) 135-37.

This authoralso considers he broader ssue of Hadrian'sinvolve-mentin architecture,buthe doesnotcommenton thepossibilityofalink betweenthe Emperor'sarchitecturalnterestsandhis learningin geometry.79 F.E. Brown, "Hadrianic Architecture," Essays in Memory ofKarl Lehmann (New York 1964) 55-58.

Jacobson Hadrianic Architcture

Documents

Transcript of Jacobson Hadrianic Architcture