VITRUVIUS ON MODULE
TINE KURENT, LOJZE MUHIC
Faculty of Architecture, Ljubljana
The reintroduction of m odular coordination in m odern architecture1 
revived the Vitruvian theory2 on m odular composition.
Vitruvius (1.2.2) teaches th at "O rder is a suitable disposition of m em bers 
of a building and the coordination of m odular sizes3 implying proportion 
for the single elem ent and for the whole. I t consists of dim ensions, which 
are called posotes in Greek. Dimension itself is the determ ination of m odules4 
from the building p ro p er and from individual parts of m em bers which
results conveniently to the whole build 
A detailed description of w hat is a 
in the following passage: “M odular 
of m em bers of the w ork itself and the
1 A short history of modular coordi­
nation since the Vitruvian commodulatio 
find in the paper by Mark Hartland 
Thomas, ’ Modular coordination Hind­
sight and Foresight’ (The Modular 
Quarterly No 3, London 1967). See also 
Enzo Frateili, T tempi profetici e sag­
gistici della coordinazione modulare 
(Prefabbricare XI/1, Milano 1968).
2 There are many modem transla­
tions of Vitruvius. Though linguistically 
correct, they obscure the Vitruvius’ 
modular and proportional theory with 
the use of terms which have changed 
or lost their original meaning, with the 
misinterpretation of the generic singu­
lar, and with the not understanding of 
the system of the Roman standard sizes.
3 Comparatio ad symmetriam is 
equivalent to our "coordination of sizes”. 
See note 5.
4 Modulorum sumptio means “deter­
mination or selection of modules”. Note
m odulus is offered by Vitruvius (1.2.4) 
sizes5 are a convenient coordination 
corresponding appearance of the whole
the plural! There are many modules to 
be determined in a building. Compare 
with the notes 6 and 8.
5 Symmetria means "modular sizes”. 
cf Graeci... modulorum mensuras auji- 
[ìETpiav... appellaverunt meaning "Modular 
sizes were called symmetria by Greeks". 
The quotation is from M. Ceti Faventini, 
De Diversis Fabricis Architectonicae, in 
the text of Valentine Rose’ s Large Edi­
tion, published in Hugh Plommer, Vi­
truvius and Later Roman Manuals 
(Cambridge, 1973). A module in Roman 
architecture is equivalent to a whole 
multiple of a standard Roman unit of 
length (see illustration 1). Modern trans­
lations offer for symmetria terms "sym­
metry”, "symetrie”, "Symmetrie”, "sim­
m etria”, "simetrija”, etc. This is lingui­
stically correct, but it obscures the most 
important passages of Vitruvius. Sym­
metria is not what is understood with 
"symmetry” today.

figure arising from the selection of the unit of m easure6 for every single 
part. As in the hum an body the system of m easures appears in the eurhythm y 
between cubit, foot, palm , finger, and other particles (illu stration 2), so it is 
in the perfect buildings (illu stration s 1, 3, 12, 13). The selection of standard 
m odular units7 can be found in tem ples either from the thickness of a 
column, or from the triglyph, or from any other rhythmically repeated unit 
(illu stration s 4, 5, 6, 7 ); in the ballista, from the bore or peritreton, as called 
by Greeks (illu stra tio n 8) ; in the ship, from the space between two tholepins, 
two cubit apart (illu stra tio n 9 ); and in other works, from their com ponent 
m em bers ” (illu stra tio n s 10, 11, 12, 13, 14,15, 16).
The m ost strongly emphasized Vitruvian praecept is in the following 
paragraph (3.1.1): “Composition of buildings depends upon m odular sizes,5 
the ratios of which m ust be m ost diligently observed by architects. It arises 
from proportion, called analogia by Greeks. Proportion is the selection of a 
u nit of sizes8 for every m em ber and for the whole of the building and their 
coordination, from w hich appears the ratio of m odular sizes.5 For w ithout 
m odular sizes5 and proportion there is no rational com position for any 
building;9 * * it m ust folow the ratio of m em bers of a well shaped m an” 
(illu stration 2, 3).
The Vitruvian m odular theory was used in practice.1 « Dimensions of 
building components w ere m odular, expressible w ith the whole m ultiples of 
one of the units of the standard system of m easures (illu stra tio n 10). The 
Roman buildings, as com positions of com ponents, were m odular toou > 1 2 (and
6 Ex partibus separatis ratae partis 
responsus means "coordination of mo­
dules selected from single parts”. The 
singular ratae partis is a generic geni­
tive, meaning “of every calculated part” 
or "of all coordinated modules”. See 
notes 4 and 8. The generic singular is 
misleading, hence the simplistic belief in 
modem modular coordination that only 
one module is sufficient. Since a module 
is mathematically a common denomi­
nator of two or more quantities, the ab­
surdity of only one module in a com­
position is evident. Number one is a 
universal common denominator only for 
prime numbers.
7 Symmetriarum ratiocinatio means 
“selection of modular units”. A modern 
attempt to calculate a system of com- 
ponible units resulted in a series of 
numbers in a ratio equal to the ratio of 
standard Roman units of length. See 
note 14.
8 Ratae partis commodulatio means
"coordination of selected modules”. The
generic singular is misleading. One
element only can not be coordinated; the
term commodulatio implies more than 
one module. Compare the notes 4 and 6.
9 More about modules and proportion 
in: Tine Kurent, 'Proportio and Commo­
dulatio after Vitruvius Compared to 
Proportion and Modules of Diocletian’ s 
Palace in Split’ (Živa antika XXI/1, 
Skoplje 1971).
1 0 Tine Kurent, 'The Roman Modular 
Way’ (Official Architecture and Planning 
12, London 1971).
1 1 Tine Kurent, Franc Možek, Janez 
Lapajne, Poskus rekonstrukcije emonske 
inzule VII (Varstvo spomenikov XII, 
Ljubljana 1967); — Tine Kurent: The 
Modular Eurythmia of Aediculae in 
Šempeter (Dissertationes Musei Nationa- 
lis Labacensis, Ljubljana 1970); — Tine 
Kurent, ’ The Modular Analogy of the 
Roman Palaces in Split and Fishbourne 
(Archaeometry 12/1, Oxford University 
1970); — Tine Kurent, ’ The Modular 
Composition of Diocletian’s Palace in 
Split’ (Živa antika, Skoplje 1970); — Ti­
ne Kurent, 'Avgustov tempelj v Pulju' 
(Arheološki vestnik XXIII, Ljubljana 
1972).

illu stra tio n s 12, 13). Finally, the Roman new towns were m odular1 2 - 2 1 (and 
illu stra tio n 14).
U nfortunately, after the fall of Rome, the Roman standard sizes were 
replaced by a host of system s of m easures, having only a local validity 
(illu stra tio n 1). Therefore, the architects of the Gothic style ressorted to 
geom etrical proportioning ( quadratura, triangulatura). Renaissance m eans 
the reb irth of th e m odular method, b u t w ithout its coordinating and com­
positional pow er (see the text at the illu stra tio n 6). The aesthetic role of 
the Renaissance m odule1 3 was of a lim ited application and the introduction 
of m etre one hundred years ago obscured the role of the system of com ponible 
anthropom etric sizes in the architectonic com position. Therefore m odern 
architects do not "m ost diligently” observe the ratio of m odular sizes as 
postulated by Vitruvius. M odern efforts are still generally ignored or mis­
understood1 4 and the only civilisation w ithout standard com ponible sizes 
( = preferred sizes = selected modules ) is the present one.
The m odular principle,1 5 the oldest known account of which is V itru­
vius, has been adopted by architects since tim e im m em orial all over the 
w orld.1 6 The neolithic Stonehenge (note 23) and the (illu stra tio n 17) and 
the old Chinese architecture (illu stra tio n s 15, 16) are good examples for 
m odular com positions of civilisations far away in space and time.
1 2 Tine Kurent. ’ The Analogy in Mo­
dular Composition of Roman Fortresses 
at Caerleon and at Mogorjelo’ (Živa an­
tika XX/2, Skoplje 1971); — Tine Kurent, 
’ Silchester the Vitruvian Octagonal town’ 
(Živa antika XXII, Skoplje 1972); — Tine 
Kurent, 'La Composition Modulaire de 
la Ville Romaine de Lambaesis’ (Živa an­
tika XXIV/1—2, Skoplje 1974).
1 3 O. B. Scamozzi, Le fabbriche e i di­
segni di Andrea Palladio (facsimile edi­
tion by Alec Tiranti, London 1968); — 
Vincenzo Scamozzi, L’ idea della Archi­
tettura universale (facsimile edition by 
The Gregg Press Inc., Ridgewood, N. J., 
U.S.A., 1964); — Giacomo Barozzi da Vi­
gnola, Gli ordini di Architettura (Fratelli 
Vallardi, Milano 1810).
1 4 Tine Kurent, Izbor preferencialnih 
modularnih mer za dimenzioniranje 
gradbenih elementov (Univerza v Ljub­
ljani 1961); — Tine Kurent, Preporuka 
za dimenzioniranje građevinskih eleme­
nata s komponibilnim modularnim me­
rama (Dokumentacija za građevinarstvo 
i arhitekturu, DGA — 1189 sveska 227, 
Beograd 1972); — Tine Kurent, Priporo­
čilo za dimenzioniranje gradbenih pre- 
fabrikatov s komponibilnimi modularni­
mi merami (Kompozicija modularnih 
mer, Univerza v Ljubljani 1974).
1 5 Tine Kurent, Tl principo modulare' 
(Belfagor XXX/II, Casa editrice Leo S. 
Olschki, Firenze 1975); — Tine Kurent, 
'Modularni princip’ (Sinteza julij 1976, 
Ljubljana).
1 6 Tine Kurent, 'Modularna kompozi­
cija v Stari Egiptovski arhitekturi' (Ka­
talog: Spomeniki starega Egipta, Narod­
ni muzej v Ljubljani 1974); — Tine Ku­
rent, 'Proportions modulaires dans la 
Composition du monument des Lacédé- 
moniens à Delphes’ (Živa antika XXII, 
Skopje 1972).
1 7 F. Hultsch, Griechische und römi­
sche Metrologie (Berlin 1862); — H. Nis­
sen, Metrologie, Handbuch der Klassi­
schen Altertums-Wissenschaft (München 
1892); — T. Kurent, L. Muhič, 'Pertica 
nova’ (Arheološki vestnik XXIV, Ljub­
ljana 1973).

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Illustration 1
The system of Roman standard sizes.1 7 Units of length, called for mnemonic 
reason after the parts of the human body, are in the ratio of small integers. Hence 
their componibility.1 8 They, or their simple multiples, were used as modules in the 
Roman architectural composition. Modular sizes of Roman building components,1 0 
buildings1 1 and new towns,1 2 vases,1 9 weapons and other tools, can be expressed with 
Roman standard sizes, called with the Greek name symmetria by Vitruvius.

ITEM SYMMETRIA EST EX IPSIUS OPERIS MEMBRIS CONVENIENS CON­
SENSUS^. EX PARTIBUSQUE SEPARATIS AD UNIVERSAE FIGURAE SPECIEM RATAE
PARTIS RESPONSUS UTI IN HOMINIS CORPORE E CUBITO PEDE PALMO
I
DIGITO C E T E R iS Q U E P A R T IC U L IS S Y M M E T R O S EST E U R Y T H M ÌA E Q U ALITAS , SIC 
EST IN OPERUM P E R F E C T IO N IB U S . ET P R IM U M IN A E D IB U S SACRIS AUT E 
C O LU M N AR U M C R A S S IT U D IN IB U S AUT TRIG LYPHO AUT ETIAM E M B A T E R E , BAL- 
FO R A M IN E i QUOD GRAECI PERITRETON VOCITANT ( N A V IB U S IN T E R - 
I QUAE D IPEC H YAIA D IC ITU R '| ITEM CETERORUM OPERUM E M E M B R IS
’ ■ I 4
LISTA E 
SCALMIO
P E S
NAMQUE NON POTEST AEDIS ULLA SINE SYMMETRIA ATQUE PROPOR­
TIONE RATIONEM HABERE COMPOSITIONES | NISI UTI HOMINIS BENE FIGU­
RATI MEMBRORUM HABUERIT EXACTAM RATIONEM . L . Ill | C. I | 1
ERGO SI ITA NATURA COMPOSUIT CORPUS HOMINIS i UTI PROPOR­
TIONIBUS MEMBRA AD SUMMAM FIGURATIONEM EIUS 
SA CONSTITUISSE VIDENTUR ANTIQUI | UT ETIAM IN 
SINGULORUM MEMBRORUM. AD UNIVERSAM FIGURAE
MENSUS EXACTIONEM L • III | C. I
RESPONDEANT , CUM CA- 
OPERUM PERFECTIONIBUS 
SPECIEM HABEANT COM-
Illustration 2
As in the human body, from cubit, foot, palm, digit and other small parts comes 
the eurhythmic quality of modular sizes,5 so it is in the completed building (1.2.4.).

AEDIUM COMPOSITIO CONSTAT EX SYMMETRIA , CUIUS RATIONEM DILIGENTI­
SSIME ARCHITECTI TENERE DEBENT . EA AUTEM PARITUR A PROPORTIONE , QUAE 
GRAECE ANALOGIA DICITUR . PROPORTIO EST RATAE PARTIS MEMBRORUM IN OMNI 0- 
PERE TOTIUSQUE COMMODULATIO , EX QUA RATIO EFFICITUR SYMMETRIARUM .
NAMQUE NON POTEST AEDIS ULLA SINE SYMMETRIA ATQUE PROPORTIONE RATIONEM 
HABERE COMPOSITIONIS | NISI UTI AD HOMINIS BENE FIGURATI MEMBRORUM HABUE­
RIT EXACTAM RATIONEM . CORPUS ENIM HOMINIS ITA NATURA COMPOSUIT | UTI O S 
CAPITIS A MENTO AD FRONTEM SUMMAM ET RADICES IMAS CAPILLI ESSET DECIMAE 
PARTIS i ITEM MANUS PALMA AB ARTICULO AD EXTREMUM MEDIUM DIGITUM TANTUNDEM ,
CAPUT A MENTO AD SUMMUM VERTICEM OCTAVAE | CUM CERVICIBUS IMIS AB SUMMO 
PECTORE AD IMAS RADICES CAPILLORUM SEXTAE , ( A MEDIO PECTORE I AD SUM­
MUM VERTICEM QUARTAE . IPSIUS AUTEM ORIS ALTITUDINIS TERTIA EST PARS AB 
IMO MENTO AD IMAS NARES | NASUM AB IMIS NARIBUS AD FINEM MEDIUM SUPER­
CILIORUM TANTUNDEM | AB EA FINE AD IMAS RADICES CAPILLI FRONS EFFICITUR 
ITEM TERTIAE PARTIS . PES VERO ALTITUDINIS CORPORIS SEXTAE , CUBITUM QUAR­
TAE i PECTUS ITEM QUARTAE . RELIQUA QUOQUE MEMBRA SUAS HABENT COMMENSUS 
PROPORTIONES | QUIBUS ETIAM ANTIQUI PICTORES ET STATUARII NOBILES USI MAG­
NAS ET INFINITAS LAUDES SUNT ACSECUTI . SIMILITER VERO SACRARUM AEDIUM 
MEMBRA AD UNIVERSAM TOTIUS MAGNITUDINIS SUMMAM EX PARTIBUS SINGULIS 
CONVENIENTISSIMUM DEBENT HABERE COMMENSUS RESPONSUM . ITEM CORPORIS CEN­
TRUM MEDIUM NATURALITER EST UMBILICUS . NAMQUE SI HOMO CONLOCATUS FUE­
RIT SUPINUS MANIBUS ET PEDIBUS PANSIS CIRCINIQUE CONLOCATUM CENTRUM IN 
UMBILICO EIUS ! CIRCUMAGENDO ROTUNDATIONEM UTRARUMQUE MANUUM E T PEDUM 
DIGITI LINEA TANGENTUR . NON MINUS QUEMADMODUM SCHEMA ROTUNDATIONIS IN 
CORPORE EFFICITUR , ITEM QUADRATA DESIGNATIO IN EO INVENIETUR . NAM SI A 
PEDIBUS IMIS AD SUMMUM CAPUT MENSUM ERIT EAQUE MENSURA RELATA FUERIT 
AD MANUS PANSAS , INVENIETUR EADEM LATITUDO UTI ALTITUDO , QUEMADMODUM 
AREAE QUAE AD NORMAM SUNT QUADRATAE . ERGO SI ITA NATURA CONPOSUIT COR­
PUS HOMINIS , UTI PROPORTIONIBUS MEMBRA AD SUMMAM FIGURATIONEM EIUS 
RESPONDEANT , CUM CAUSA CONSTITUISSE VIDENTUR ANTIQUI , U T ETIAM IN 0 - 
PERUM PERFECTIONIBUS SINGULORUM MEMBRORUM AD UNIVERSAM FIGURAE SPECIEM 
HABEANT COMMENSUS EXACTIONEM . IGITUR CUM IN OMNIBUS OPERIS ORDINES 
TRADERENT | MAXIME IN AEDIBUS DEORUM , OPERUM ET LAUDES E T CULPAE AETER­
NAE SOLENT PERMANERE . L . Ill , C . I , 1 , 2 | 3 , 4
Illustration 3
Composition of buildings consists of modular sizes,5 the ratio of which the 
architects should most diligently observe. It arises from proportion which in Greek 
is called analogia. Proportion is (in the) commodulation of all parts8 calculated 
for the members and the whole of the edifice. For no building can have a rational 
composition without modular sizes5 and proportion, as they are in a finely-shaped 
human body. For Nature has composed the human body so th a t... (3.1.1—2.). Fol­
lows a long description of human sizes which have lent their names to units of 
the system of standard sizes, used as building modules.

ITEM SYMMETRIA EST EX IPSIUS OPERIS MEMBRIS CONVENIENS CON­
SENSUS EX PARTIBUSQUE SEPARATIS AD UNIVERSAE FIGURAE SPECIEM RATAE 
PARTIS RESPONSUS . UTI IN HOMINIS CORPORE E CUBITO | PEDE | PALMO , 
DIGITO CETERISQUE PARTICULIS SYMMETROS EST EURYTHMIAE QUALITAS | SIC 
EST IN OPERUM PERFECTIONIBUS . E T PRIMUM IN AEDIBUS SACRIS AUT E 
COLUMNARUM CRASSITUDINIBUS AUT TRIGLYPHO AUT ETIAM EMBATERE j BAL­
LISTA E FORAMINE | QUOD GRAECI PERITRETON VOCITANT | NAVIBUS INTER­
SCALMIO j QUAE DIPECHYAIA DICITUR , ITEM CETERORUM OPERUM E MEMBRIS 
INVENITUR SYMMETRIARUM RATIOCINATIO . L . I , C . Il | A
EX HIS PARS UNA ERIT MODULUS j QUI GRAECE EMBATER DICITUR | 
CUIUS MODULI CONSTITUTIONE RATIOCINATIONIBUS EFFICIUNTUR OMNIS OPERIS DISTRI­
BUTIONES . CRASSITUDO COLUMNARUM ERIT DUORUM MODULORUM ALTITUDO C U M
CAPITULO X I111 . L . IV i C . Ill j 3 , 4
SUPRA EPISTYLIUM CONLOCANDI SUNT TRIGLYPHI CUM SUIS M ETOPIS , 
ALTI UNIUS ET D IM ID IATI MODULI t LATI IN FRONTE UNIUS MODULI | ITA DI­
VISI , UT IN ANGULARIBUS COLUMNIS ET IN MEDIIS CONTRA TETRANTES MEDIOS 
SINT CONLOCATI , ET INTERCOLUMNIIS RELIQUIS B IN I | IN M E D IIS PRONAO ET 
POSTICO TERNI . L . IV C . Ill
Illustration 4
Modular sizes5... in tem ples... can be calculated... from the thickness of co­
lumns, or a triglyph and also from the embater (1.2.4.).
Embater, translated as 'module' by Bury, means a standard size. The verb 
è|ipaTe''d), meaning 'to walk', implies the movement of a human body, analogous 
to the latin passus and gradus. In extension, embater means ony other rhythmically 
repeated unit of sizes.

NO N NULI ANTIQ UI ARCHITECTI 
NEGAVERUNT DORICO GENERE AEDES SA­
CRAS OPORTERE FIE R I | QUOD MENDO­
SAE ET DISCONVENIENTES IN HIS SYMME­
TRIAE CONFICIEBANTUR . ITAQUE NEGAVIT 
ARCESIUS i ITEM PYTHIUS | NON M INU S 
HERMOGENES . NAM IS CUM PARATAM HA­
BUISSET MARMORIS COPIAM IN DORICAE 
AEDIS PERFECTIONEM | COMMUTAVIT EX EA­
DEM COPIA ET EAM IONICAM LIBERO PA­
TRI FECIT . SED TAMEN NON QUOD INVE­
NUSTA EST SPECIES AUT GENUS AUT FOR­
MAE DIGNITAS i SED QUOD INPEDITA EST 
DISTRIBUTIO ET INCOMMODA IN OPERE 
TRIGLYPHORUM ET LACUNARIORUM DISTRI­
BUTIONE . NAMQUE NECESSE EST TRY- 
GLYPHOS CONSTITUI CONTRA MEDIOS TE ­
TRANTES COLUMNARUM | METOPASQUE , 
QUAE INTER TRIGLYPHOS FIENT ( AEQUE 
LONGAS ESSE QUAM ALTAS . CONTRAQUE 
IN ANGULARES COLUMNAS TRIGLYPHI IN EX­
TREMIS PARTIBUS CONSTITUUNTUR ET NON 
CONTRA MEDIOS TETRANTES . ITA METOPA 
QUAE PROXIMAE AD ANGULARES TRIGLYPHOS 
FIUNT i NON EXEUNT QUADRATAE SED OB­
LONGIORES TRIGLYPHI DIMIDIA LATITUDINE . 
AT QUI METOPAS AEQUALES VOLUNT FA­
CERE i INTERCOLUMNIA EXTREMA CONTRA­
HUNT TRIGLYPHI DIMIDIA LATITUDINE . HOC 
AUTEM j SIVE IN METOPARUM LONGITUDI­
NIBUS SIVE INTERCOLUMNIORUM CONTRACTI­
ONIBUS EFFICIETUR , EST MENDOSUM 
QUAPROPTER A NTIQ UI VITARE VISI SUNT 
IN A E D IB U S SACRIS DORICAE SYMMETRIAE 
RATIONEM
NOS AUTEM EXPONIMUS | UTI OR­
DO POSTULAT i QUEMADMODUM A PRAE­
CEPTORIBUS ACCEPIMUS j UTI i SI QUI 
VOLUERIT HIS RATIONIBUS ADTENDENS ITA 
INGREDI i HABEAT PROPORTIONES EXPLI­
CATAS i QUIBUS EMENDATAS ET SINE VI­
TIIS EFFICERE POSSIT AEDIUM SACRA­
RUM DORICO MORE PERFECTIONES . FRONS 
AEDIS DORICAE IN LOCO , QUO COLUMNAE 
CONSTITUUNTUR , DIVIDATUR | SI TETRASTY­
LOS ERIT i IN PARTES XXVII | SI HEXASTY­
LOS i XXXXII . EX HIS PARS UNA ERIT 
MODULUS i QUI GRAECE EMBATER DICITUR | 
CUIUS MODULI CONSTITUTIONE RATIOCINATI­
ONIBUS EFFICIUNTUR OMNIS OPERIS DIS­
TRIBUTIONES . CRASSITUDO COLUMNARUM 
ERIT DUORUM MODULORUM | ALTITUDO CUM 
CAPITULO Xllll . CAPITULI CRASSITUDO U - 
NIUS MODULI i LATITUDO DUORUM ET MO­
DULI SEXTAE PARTIS . CRASSITUDO CAPI­
TULI DIVIDATUR IN PARTES TRES , E QUI­
BUS UNA PLINTHUS CUM CYMATIO FIAT , 
ALTERA ECHINUS CUM ANULIS , TERTIA HY- 
POTRACHELION . CONTRAHATUR COLUMNA ITA ,
Illustration 5 a and b
Vitruvius' prescription for the modular composition of the Doric order.

UTI IN TERTIO LIBRO DE IONICIS EST SCRIPTUM . EPISTYLII ALTITUDO UNIUS MO­
DULI CUM TAENIA ET GUTTIS i TAENIA MODULI SEPTIMA j GUTTARUM LONGITU­
DO SUB TAENIA CONTRA TRIGLYPHOS ALTA CUM REGULA PARTE SEXTA MODULI 
PRAEPENDEAT . ITEM EPISTYLII LATITUDO IMA RESPONDEAT HYPOTRACHELIO SUM­
MAE COLUMNAE . SUPRA EPISTYLIUM CONLOCANDI SUNT TRIGLYPHI CUM SUIS 
METOPIS i ALTI UNIUS (ET) DIMIDIATI MODULI | LA TI IN FRONTE UNIUS MODULI, 
ITA DIVISI i UT IN ANGULARIBUS COLUMNIS ET IN MEOIIS CONTRA TETRANTES ME­
DIOS SINT CONLOCATI , ET INTERCOLUMNIIS RELIQUIS BINI , IN MEDIIS PRONAO 
ET POSTICO TERNI . ITA RELAXATIS MEDIIS INTERVAL!IS SINE INPEDITIONIBUS A- 
DITUS ACCEDENTIBUS ERIT AD DEORUM SIMULACRA . TRIGLYPHORUM LATITUDO DI­
VIDATUR IN PARTES SEX , EX QUIBUS QUINQUE PARTIBUS IN MEDIO , DUAE 
DIMIDIAE DEXTRA AC SINISTRA DESIGNENTUR REGULA . UNA IN MEDIO DEFOR­
METUR FEMUR i QUOD GRAECE MEROS DICITUR j SECUNDUM EAM CANALICULI
AD NORMAE CACUMEN INPRIMANTUR \ EX ORDINE EORUM DEXTRA AC SINIS­
TRA ALTERA FEMINA CONSTITUANTUR i IN EXTREMIS PARTIBUS SEMICANALICULI 
INTERVERTANTUR . TRIGLYPHIS ITA CONLOCATIS' | METOPAE QUAE SUNT INTER 
TRIGLYPHOS | AEQUE ALTAE SINT QUAM LONGAE i ITEM IN EXTREMIS ANGULIS SE­
MIMETOPIA SINT INPRESSA DIMIDIA MODULI LATITUDINE . ITA ENIM ERIT , UT OM­
NIA VITIA ET METOPARUM ET INTERCOLUMNIORUM ET LACUNARIORUM , QUOD AE­
QUALES DIVISIONES FACTAE ERUNT | EMENDENTUR . TRIGLYPHI CAPITULA SEXTA 
PARTE MODULI SUNT FAC IU N DA . SUPRA TRIGLYPHORUM CAPITULA CORONA EST
CONLOCANDA IN PROIECTURA DIMIDIAE ET SEXTAE PARTIS HABENS CYMATIUM DO­
RICUM IN IMO i ALTERUM IN SUMMO . ITEM CUM CYMATIIS CORONA CRASSA EX
DIMIDIA MODULI . DIVIDENDAE AUTEM SUNT IN CORONA IMA AD PERPENDICULUM 
TRIGLYPHORUM ET MEDIAS METOPAS VIARUM DERECTIONES ET GUTTARUM DISTRI­
BUTIONES i ITA UTI GUTTAE SEX IN LONGITUDENEM , TRES IN LATITUDINEM PATEANT .
RELIQUA SPATIA , QUOD LATIORES SINT METOPAE QUAM TRIGLYPHI , PURA RELI­
QUANTUR AUT NUMINA SCALPANTUR , AD IPSUMQUE MENTUM CORONAE INCIDATUR
LINEA QUAE SCOTIA DICITUR . RELIQUA OMNIA , TYMPANA , SIMAE , CORONAE |
QUEMADMODUM SUPRA SCRIPTUM EST IN IONICIS | ITA PERFICIANTUR .
HAEC RATIO IN OPERIBUS DIASTYLI ERIT CONSTITUTA . SI VERO SYSTYLON 
ET MONOTRIGLYPHON OPUS ERIT FACIUNDUM , FRONS AEDIS , SI TETRASTYLO 
ERIT I DIVIDATUR IN PARTES XVIIII S , Si HEXASTYLOS ERIT , OIVIDATUR IN PAR­
TES XXVIIII S . EX HIS PARS UNA ERIT MODULUS , AD QUEM , UTI SUPRA SCRIP­
TUM EST DIVIDANTUR . ITA SUPRA SINGULA EPISTYLIA ET METOPAE ET TRI­
GLYPHI BINI ERUNT CONLOCANDI j IN ANGULARIBUS HOC AMPLIUS , QUANTUM DI­
MIDIATUM EST SPATIUM HEMITRIGLYPHI | ID ACCEDIT . IN MEDIANO CONTRA
FASTIGIUM TRIUM TRIGLYPHORUM ET TRIUM METOPARUM SPATIUM DISTABIT | QUOD 
LATIUS MEDIUM INTERCOLUMNIUM ACCEDENTIBUS AD AEDEM HABEAT LAXAMENTUM 
ET ADVERSUS SIMULACRA DEORUM ASPECTUS DIGNITATEM .
COLUMNAS AUTEM STRIARI XX STRII OPORTET . QUAE SI PLANAE E- 
RUNT i ANGULOS HABEANT XX DESIGNATOS . SIN AUTEM EXCAVABUNTUR , SIC 
EST FORMA FACIENDA | ITA UTI QUAM MAGNUM EST INTERVALLUM STRIAE | 
TAM MAGNIS STRIATURAE PARIBUS LATERIBUS QUADRATUM DESCRIBATUR j IN 
MEDIO AUTEM QUADRATO CIRCINI CENTRUM CONLOCETUR ET AGATUR LINEA RO­
TUNDATIONIS i QUAE QUADRATIONIS ANGULOS TANGAT , ET QUANTUM ERIT CUR­
VATURAE INTER ROTUNDATIONEM ET QUADRATAM DESCRIPTIONEM , TANTUM AD 
FORMAM EXCAVENTUR . ITA DORICA COLUMNA SUI GENERIS STRIATURAE HA­
BEBIT PERFECTIONEM . DE ADIECTIONE EIUS | QUA MEDIA ADAUGETUR | UTI IN 
TERTIO VOLUMINE DE IONICIS EST PERSCRIPTA , ITA ET IN HIS TRANSFERATUR .
QUIONIAM EXTERIOR SPECIES SYMMETRIARUM ET CORINTHIORUM ET DO­
RICORUM ET IONICORUM EST PERSCRIPTA ] NECESSE EST ETIAM INTERIORES 
CELLARUM PRONAIQUE DISTRIBUTIONES EXPLICARE . L . IV , C. Ill

ITEM SYMMETRIA EST EX IPSIUS OPERIS MEMBRIS CONVENIENS CON­
SENSUS EX PARTIBUSQUE SEPARATIS AD UNIVERSAE FIGURAE SPECIEM RATAE 
PARTIS RESPONSUS . UTI IN HOMINIS CORPORE E CUBITO , PEDE , PALMO , 
DIGITO CETERISQUE PARTICULIS SYMMETROS EST EURYTHMIAE QUALITAS , SIC 
EST IN OPERUM PERFECTIONIBUS . ET PRIMUM IN AEDIBUS SACRIS AUT E 
COLUMNARUM CRASSITUDINIBUS AUT TRIGLYPHO AUT ETIAM EMBATERE , BAL­
LISTA E EORAMINE - , QUOD GRAECI PERITRETON VOCITANT , NAVIBUS INTER­
SCALMIO i QUAE DI PECHYAIA DICITUR , ITEM CETERORUM OPERUM E MEMBRIS 
INVENITUR SYMMETRIARUM RATIOCINATIO . L . I , C . II , 4
FRONS AEDIS DORICAE 
D IV ID A TU R SI TETRASTYLOS ERIT
IN LOCO 
IN
QUO COLUMNAE C O N STITU U N TU R
PARTES XXVII i SI HEXASTYLO S , XXXXII 
EX H IS PARS U N A ERIT MODULUS , Q U I GRAECE EMBATER DICITUR , C U IU S 
M ODULI C O N STITUTIO NE R A T IO C IN A T IO N IB U S E F F IC IU N T U R O M N IS O PER IS DISTRI­
BU TIO N ES CRASSITUDO COLUMNARUM ERIT D U O R U M MODULORUM ( ALTITUDO CUM 
CAPITULO X 1111 L . IV , C . Ill , 3
I I

Illustration 6
The modular composition of a Doric temple.
The front of a Doric temple is to be divided along the line where columns are 
set, in 21 parts if it is tetrastyle, in 42 parts if it is hexastyle.M Of these one part 
will be the module, which in Greek is called embater, and when it is constituted its 
multiples affect the distribution of the whole work. The diameter of the column 
will be two modules; the height including capital 14, the height of the capital is 
one module... Above the architrave are to be placed the triglyphs with the metho- 
pes; the triglyphs being a module and a half high and one module wide in fro n t... 
(4. 3. 3—4.).
This and other prescriptions for modular composition of temples suggest that 
Vitruvius had in mind Greek examples, but without knowing the Greek standard 
sizes, used as modules. Therefore he equated the module with the column’ s dia­
meter, and the dimensions of triglyphs and methopes, which were obviously expres­
sible with Greek units of length. The same misjudgement occured in the Renais­
sance, when the modular principle was reintroduced, but without regard to a stan­
dard system of sizes. The universal Roman sizes were supplanted by a host of meas­
ures. In Italy there were piede Vicentino, piede Veneto, canna di Roma, Palermo, 
Genova, Toscana, Sicilia, Sardegna, etc, which introduced the confusion of the 
tower of Babel in the architectural composition of sizes. Therefore the Renaissance 
architecture arbitrarily, and under the influence of Vitruvius, proclaimed as module 
the diameter (or radius) of a column. Since one only module was not enough, the 
diameter was divided in 12, 18, or more, partes.1 3 Consequently the module lost its 
power to coordinate sizes and degenerated into an aesthetic tool.
1 8 Tine Kurent, 'Modularna kompozi­
cija’ (Arhitektura — urbanizam br. 26, 
Beograd 1964); — Tine Kurent, ’ The Ba­
sic Law of Modular Composition’ (The 
Modular Quarterly, winter 1964/65, Lon­
don); — Tine Kurent, Osnovni zakon mo­
dularne kompozicije (Univerza v Ljub­
ljani, Fakulteta za arhitekturo 1967); — 
Tine Kurent, La legge fondamentale del­
la composizione modulare (Politechnico 
di Torino, Facoltà di Architettura, Edi­
zione Quaderni di Studio, Torino 1968); 
— Tine Kurent, Kompozicija modularnih 
mer (Univerza v Ljubljani, Fakulteta za 
arhitekturo 1974).
1 8 T. Kurent, L. Muhič, ’ Merska anali­
za rimskih posod’ (Arheološki vestnik 
XXIII, Ljubljana 1972).
2 0 An attempt to explain the antique 
proportions with the Vitruvian numbers 
without resorting to the Greek and Ro­
man standard sizes is in C. J. Moe, Nu­
meri di Vitruvio (Edizioni del Milione, 
Milano 1945).
2 1 Milica Detoni, Tine Kurent, The 
Modular Reconstruction of Emona (Dis­
sertationes Musei Nationals Labacensis, 
Ljubljana 1963).
2 2 Tine Kurent, 'La composizione mo­
dulare della Porta Palatina a Torino’ 
(Prefabbricare 5, Milano 1969).
2 3 Tine Kurent, 'Stonehenge and the 
Vitruvian Amusium’ (Architectural Asso­
ciation Quarterly, voi. 7 number 3, Lon­
don 1975).

IX
V lil
VII
VI
v
IV
III
I I
o
SPECIES AUTEM AEDIUM SUNT QUINQUE , QUARUM EA SUNT VOCABULA 
PYCNOSTYLOS , ID EST CREBRIS COLUMNIS j SYSTYLOS PAULO REMISSIORIBUS j DIA - 
STYLOS AMPLIUS PATENTIBUS j RARE QUAM OPORTET INTER SE DIDUCTIS ARAEO - 
STYLOS j EUSTYLOS INTERVALLORUM IUSTA DISTRIBUTIONE ERGO PYCNOSTYLOS 
EST i CUIUS INTERCOLUMNIO UNIUS ET DIMIDIATAE COLUMNAE CRASSITUDO INTER­
PONI PO TEST i QUEMADMODUM EST DIVI IULII E T IN CAESARIS FORO VENERIS 
ET S I QUAE ALIAE SIC SUNT COMPOSITAE . ITEM SYSTYLOS EST , IN QUO DUA­
RUM COLUMNARUM CRASSITUDO IN INTERCOLUMNIO POTERIT CONLOCARI , ET SPI­
RARUM PLINTHIDES AEQUE MAGNAE SINT E T SPATIO , QUOD FUERIT INTER DU­
AS PLINTHIDES i QUEMADMODUM EST FORTUNAE EQUESTRIS AD THEATRUM LAPI­
DEUM RELlQUAEQUE , QUAE EISDEM RATIONIBUS SUNT CONPOSITAE . HAEC UTRAQUE 
GENERA VITIOSUM HABENT USUM . MATRES ENIM FAMILIARUM CUM AD SUPPLICA­
TIONEM GRADIBUS ASCENDUNT , NON POSSUNT P ER INTERCOLUMNIA AMPLEXAE A - 
DI RE i NISI ORDINES FECERINT i ITEM VALVARUM ADSPECTUS ABSTRADITUR CO­
LUMNARUM CREBRITATE IPSAQUE SIGNA OBSCURANTUR j ITEM CIRCA AEDEM PROP­
TER ANGUSTIAS INPEDIUNTUR AMBULATIONES . DIASTYLI AUTEM HAEC ERIT CON- 
POSITIO , CUM TRIUM COLUMNARUM CRASSITUDINEM INTERCOLUMNIO INTERPONERE 
POSSUMUS i TAMQUAM EST APOLLONIS E T DIANAE AEDIS . HAEC DISPOSITIO HANC 
HABET DIFFICULTATEM , QUOD EPISTYLIA PROPTER INTERVALLORUM MAGNITUDINEM 
FRANGUNTUR . IN ARAEOSTYLIS AUTEM NEC LAPIDEIC NEC MARMOREIS EPISTY­
LIIS UTI DATUR , SED INPONENDAE DE MATERIA TRABES PERPETUAE . E T IP­
SARUM AEDIUM SPICIES SUNT VARICAE , BARYCEPHALAE , HUMILES , LATAE , OR- 
NANTURQUE SIGNIS FICTILIBUS AUT AEREIS INAURATIS EARUM FASTIGIA TUSCANICO 
MORE , UTI EST AD CIRCUM MAXIMUM CERERIS E T ‘HERCULIS POMPEIANI , ITEM 
CAPITOLI .
REDDENDA NUNC EST EUSTYLI RATIO | QUAE MAXIME PROBABILIS ET 
AD USUM E T AD SPECIEM E T AD FIRMITATEM RATIONES HABET EXPLICATAS . NAM 
QUE FACIENDA SUNT IN INTERVALLIS SPATIA DUARUM COLUMNARUM E T QUARTAE P A R ­
TIS COLUMNAE CRASSITUDINIS , MEDIUMQUE INTERCOLUMNIUM UNUM , QUOD ERIT IN 
FRONTE , ALTERUM , QUOD IN POSTICO , TRIUM COLUMNARUM CRASSITUDINE . SIC 
ENIM HABEBIT E T FIGURATIONIS ASPECTUM VENUSTUM ET ADITUS USUM SINE IN- 
PEDITIONIBUS E T CIRCA CELLAM AMBULATIO AUCTORITATEM . HUIUS AUTEM REI RA­
TIO EXPLICABITUR SIC . FRONS LO CI QUAE IN AEDE CONSTITUTA FUERIT , S I TE-
Illustration 7 a and b
Vitruvius' instruction on how to compose the elevation of temples. The various 
arrangements of columns, i. e. the width and height of the axial intercolumnium 
with regard to the thickness of the column (= module) result in pichnostylos, sy- 
stilos, eustylos, diastylos, and araeostylos.

TRASTYLOS FACIENDA FUERIT , DIVIDATUR IN PARTES XI S PRAETER CREPIDINES 
ET PROIECTURAS SPIRARUM i SI SEX ERIT COLUMNARUM , IN PARTES XVIII \ S I 
OCTOSTYLOS CONSTITUETUR , DIVIDATUR IN XXIV E T SEMISSEM . ITEM EX HIS PAR­
TIBUS SIVE TETRASTYLI SIVE HEXASTYLI SIVE O CTOSTYLI UNA PARS SUMATUR | EAQUE 
ERIT MODULUS . CUIUS MODULI UNIUS ERIT CRASSITUDINIS COLUMNARUM . INTERCO­
LUMNIA SINGULA i PRAETER MEDIA , MODULORUM DUORUM ET MODULI QUARTAE PAR­
TIS j MEDIANA IN FRONTE E T POSTICO SINGULA TERNUM MODULORUM . IPSARUM C O ­
LUMNARUM ALTITUDO MODULORUM HABEBUNT IUSTAM RATIONEM . HUIUS EXEMPLAR 
ROMAE NULLUM HABEMUS | SED IN ASIA TEO HEXASTYLON LIBERI PATRIS .
EAS AUTEM SYMMETRIAS CONSTITUIT HERMOGENES | QUI ETIAM PRIMUS 
EXO STYLON PSEUDODIPTERIVE RATIONEM . EX DIPTERI ENIM AEDIS SYMMETRIAE 
DISTULIT INTERIORES ORDINES COLUMNARUM XXXIV EAQUE RATIONE SUMPTUS OPE­
RASQUE COMPENDII FECIT . IS IN MEDIO AMBULATIONI LAXAMENTUM EGREGIE C IR ­
CA CELLAM FECIT DE ASPECTUQUE NIHIL INMINUIT | SED SINE DESIDERIO SUPER­
VACUORUM CONSERVAVIT AUCTORITATEM TOTIUS OPERIS DISTRIBUTIONE . PTERO M ATO S 
ENIM RATIO ET COLUMNARUM CIRCUM AEDEM DISPOSITIO IDEO EST INVENTA , UT 
ASPECTUS PROPTER ASPERITATEM INTERCOLUMNIORUM HABEAT AUCTORITATEM | PRAE­
TEREA i SI EX IMBRIUM AQUAE VIS OCCUPAVERIT ET INTERCLUSERIT HOMINUM 
MULTITUDINEM , UT HABEAT IN AEDE CIRCAQUE CELLAM CUM LAXAMENTO UBERAM 
MORAM . HAEC AUTEM UT EXPLICANTUR IN PSEUDODIPTERIS AEDIUM DISPOSITIONI­
BUS . QUARE VIDETUR ACUTA MAGNAQUE SOLLERTIA EFFECTUS OPERUM HERMO­
GENIS FECISSE RELIQUISSEQUE FONTES | UNDE POSTERI POSSENT HAURIRE DISCI­
PLINARUM RATIONES .
AEDIBUS ARAEOSTYLIS COLUMNAE SIC SUNT FACIENDAE | UTI CRASSITUDINES 
EARUM SINT PARTIS OCTAVAE AD ALTITUDINES . ITEM IN DIASTYLO OIMETIENDA E S T 
ALTITUDO COLUMNAE IN PARTES O C TO E T DIMIDIUM | ET UNIUS PARTIS COLUMNAE 
CRASSITUDO CONLOCETUR . IN SYSTYIO ALTITUDO DIVIDATUR IN NOVEM ET DIMIDIAM 
PARTEM i ET EX EIS UNA AD CRASSITUDINEM COLUMNAE DETUR . ITEM IN PYCNO- 
STYLO DIVIDENDA EST ALTITUDO IN DECEM | ET EIUS UNA PARS FACIENDA EST 
COLUMNAE CRASSITUDO . EUSTYLI AUTEM AEDIS COLUMNAE | UTI SYSTYLI | IN NO ­
VEM PARTIBUS ALTITUDO DIVIDATUR ET DIMIDIAM PARTEM , E T EIUS UNA PARS CO N­
STITUATUR IN CRASSITUDINE IMI SCAPI . ITA HABEBITUR P R O RATA PARTE INTER­
COLUMNIORUM RATIO . QUEMADMODUM ENIM CRESCUNT SPATIA INTER COLUMNAS , 
PROPORTIONIBUS ADAUGENDAE SUNT CRASSITUDINIS SCAPORUM . NAMQUE S I IN ARAEO- 
STYLO NONA AUT DECIMA PARS CRASSITUDINIS FUERIT | TENUIS ET EXILIS APPA­
REBIT i IDEO QUOD PER LATITUDINEM INTERCOLUMNIORUM AER CONSUMIT E T INMI­
NUIT ASPECTU SCAPORUM CRASSITUDINEM . CONTRA VERO PYCNOSTYLIS SI OCTAVA 
PARS CRASSITUDINIS FUERIT , PROPTER CREBRITATEM ET ANGUSTIAS INTERCOLUMNIORUM 
TUMIDAM ET INVENUSTAM EFFICIET SPECIEM . ITAQUE GENERIS OPERIS OPORTET PER­
SEQUI SYMMETRIAS . ETIAMQUE ANGULARES COLUMNAE CRASSIORES FACIENDAE SUNT E X 
SUO DIAMETRO QUINQUAGESIMA PARTE , QUOD EAE AB AERE CIRCUMCIDUNTUR ET 
GRACILIORES VIDENTUR ESSE ASPICIENTIBUS . ERGO QUOD OCULUS FALLIT | RATIOCI­
NATIONE EST EXEQUENDUM . CONTRACTURAE AUTEM IN SUMMIS COLUMNARUM HY­
POTRACHELIIS ITA FACIENDAE VIDENTUR | UTI t SI COLUMNA SIT AB MINIMO AD PE­
DES QUINOS DENOS , IMA CRASSITUDO DIVIDATUR IN PARTES SEX ET EARUM PARTI­
UM QUINQUE SUMMA CONSTITUATUR . ITEM QUAE ERIT AB QUINDECIM PEDIBUS AD 
PEDES VIGINTI ( SCAPUS IMUS IN PARTES SEX E T SEMISSEM DIVIDATUR , EARUM- 
QUE PARTIUM QUINQUE ET SEMISSE SUPERIOR CRASSITUDO COLUMNAE FIAT . ITEM 
QUAE ERUNT A PEDIBUS VIGINTI AD PEDES TRIGINTA , SCAPUS IMUS DIVIDATUR IN 
PARTES SEPTEM , EARUMQUE SEX SUMMA CONTRACTURA PERFICIATUR . QUAE AUTEM AB 
TRIGINTA PEDIBUS AD QUADRAGINTA A LTA ERIT | IMA DIVIDATUR IN PARTES SEPTEM 
E T DIMIDIAM j EX HIS SEX E T DIMIDIAM IN SUMMO HABEAT CONTRACTURAE RATIO NEM . 
QUAE ERUNT AB QUADRAGINTA PEDIBUS AD QUINQUAGINTA , ITEM DIVIDENDAE SUNT IN 
OCTO PARTES | E T EARUM SEPTEM IN SUMMO SCAPO SUB CAPITULO CONTRAHANTUR . 
ITEM S I QUAE ALTIORES ERUNT , EADEM RATIONE PRO RATA CONSTITUANTUR CONTRAC­
TURAE . HAEC AUTEM PRO PTER ALTITUDINIS INTERVALLUM SCANDENTIS OCULI SPECI­
ES ADICIUNTUR CRASSITUDINIBUS TEMPERATURAE . VENUSTATES ENIM PERSEQUITUR 
VISUS i CUIUS SI NON BLANDIMUR VOLUPTATI PROPORTIONE E T MODULORUM ADIEC- 
TIONIBUS , UTI QUOD FALLITUR TEMPERATIONE ADAUGEATUR | VASTUS E T INVENUS­
TUS CONSPICIENTIBUS REMITTETUR ASPECTUS . D E ADIECTIONE , QUAE ADICITUR IN 
MEDIIS COLUMNIS , QUAE APUD GRAECOS ENTASIS APPELLATUR , IN EXTREMO L I­
BRO ERIT FORMATA RATIO EIUS | QUEMADMOOUM MOLLIS ET CONVENIENS EFFICIA­
TUR i SUBSCRIPTA L. Ill , C. Ill

ITEM SYMMETRIA EST EX IPSIUS OPERIS MEMBRIS CONVENIENS CON­
SENSUS EX PARTIBUSQUE SEPARATIS AO UNIVERSAE FIGURAE SPECIEM RATAE 
PARTIS RESPONSUS . UTI IN HOMINIS CORPORE E CUBITO | PEDE | PALMO i 
DIGITO CETERISQUE PARTICULIS SYMMETROS EST EURYTHMIAE QUALITAS | SIC 
EST IN OPERUM PERFECTIONIBUS . ET PRIMUM IN AEDIBUS SACRIS AUT E 
COLUMNARUM CRASSITUDINIBUS AUT TRIGLYPHO AUT ETIAM EMBATERE | BAL­
LISTA E FORAMINE , QUOD GRAECI PERITRETON VOCITANT | NAVIBUS INTER­
SCALMIO I QUAE DIPECHYAIA DICITUR | ITEM CETERORUM OPERUM E MEMBRIS 
INVENITUR SYMMETRIARUM RATIOCINATIO . L . I , C . II | 4
SEO TAMEN NULLA BALLISTA PERFICITUR NISI AD PROPOSITAM MAGNI­
TUDINEM PONDERIS SAXI i QUOD ID ORGANUM MITTERE DEBET .
L . X i C . XI i I
NAM AUQE BALLISTA DUO PONDO SAXUM MITTERE DEBET | FORAMEN 
ERIT IN EIUS CAPITULO DIGITORUM V j SI PONDO Illi | DIGITORUM SEX |
VI , DIGITORUM VII j DECEM PONDO DIGITORUM VIII j VIGINTI PONDO DIGI­
TORUM X j XL PONDO DIGITORUM XII SK j LX PONDO DIGITORUM XIII ET DI­
GITI OCTAVA PARTE j LXXX PONDO DIGITORUM XV j CXX PONDO I PEDIS 
ET SESQUIDIGITI j C ET LX PEDIS 1 9 j C ET LXXX PES ET DIGITI V j
CC PONDO PEDIS ET DIGITORUM VI j CC ET X PEDIS ET DIGITORUM VI j
CCCLX i PEDIS I S . L . X i C . XI i S
CUM ERGO FORAMINIS MAGNITUDO FUERIT INSTITUTA | DESCRIBATUR 
SCUTULA [ QUAE GRAECE PERITRETOS APPELLATUR | CUIUS LONGITUDO FORA­
MINUM VIII j LATITUDO DUO ET SEXTAE PARTIS L. X , C . XI , 4
Illustration 8
On the modular composition of ballista.
But no ballista is made without regard on the proposed amount of the weight 
of the stone which such a machine is supposed to eject (10.11.1.). When, therefore, 
the size of the hole (= the caliber) is determined (as a module), the scutula, which 
in Greek is called peritretos, is to be drawn (10.11.4.).
Follows the recipe what dimensions are to be taken to build a ballista and the 
detailed description of calibers, i. e. the interdependence of apertures of a foramen 
and of the weight of the projectile.
Obviously, the heavier the projectile, the larger the hole, the larger the module, 
and the larger the ballista itself. Te module is proportionate to the composition.1 8

ITEM SYMMETRIA EST EX IPSIUS OPERIS MEMBRIS CONVENIENS CON­
SENSUS EX PARTIBUSOUE SEPARATIS AD UNIVERSAE FIGURAE SPECIEM RATAE 
PARTIS RESPONSUS . UTI IN HOMINIS CORPORE E CUBITO | PEDE | PALMO | 
DIGITO CETERISQUE PARTICULIS SYMMETROS EST EURYTHMIAE QUALITAS t SIC 
EST IN OPERUM PERFECTIONIBUS . ET PRIMUM IN AEDIBUS SACRIS AUT E 
COLUMNARUM CRASSITUDINIBUS AUT TRIGLYPHO AUT ETIAM EMBATERE | BAL­
LISTA E FORAMINE , QUOD GRAECI PERITRETON VOCITANT , NAVIBUS INTER­
SCALMIO ! QUAE DIPECHYAIA DICITUR | ITEM CETERORUM OPERUM E MEMBRIS 
INVENITUR SYMMETRIARUM RATIOCINATIO L . I | C . II ( 4
A GREEK SHIP FROM THE PERIOD OF THE (MIGRATIONS . THE
ROWERS SIT ALONG BOTH SIDES . THIS SCENE | FROM A GEOMETRICAL VASE | 
SHOWS A MAN APPARENTLY LEADING A WOMAN ON BOARD | AND IT IS AN 
ATTRACTIVE GUESS THAT IT REPRESENTS THE ABDUCTION OF HELEN BY PARIS . 
THE BIRTH OF WESTERN CIVILIZATION - GREECE AND ROME | MICHAEL GRANT
. . . BY THE SPACE BETWEEN THE ROWLOCKS IN A SHIP WHICH IS
CALLED DIPECHYAIA : . . . GRANGER , L. I , C . II | 4 , LONDON MCMLXII
. . . IN A SHIP j FROM THE SPACE BETWEEN THE THOLEPINS ( 6 LCL-
. . . MORGAN I L . I , C. II | 4 , NEW YORK 1960
. . . NAVIBUS i INTERSCALMIO | QUOD 6 LIX JtT| [i. 01 DICITUR j . . . 
POUR LES t NAVI RES : D 1 APRES L1 INTERVALLE DES TOLETS | QUI S 1 AP­
PELLE Ó L a 3 tr|^ [A a . . . CHOISY , L. i i C. III | 3 I PARIS 1909
SIMIGLIANTEMENTE NELLE NAVI DALLO SPACIO | CHE E TRA UN
SCHELMO ALL1 ALTRO | CHE PER ESSER DI MISURA DI DUE CUBITI , SI 
CHIAMA i DIPICHAICHI | . . . BARBARO | VENEZIA 1 584 j L . I | C II
Illustration 9
The size of module for a ship is determined from the space between the row- 
locks, which is called dipechyaia by Greeks.
Embater and dipechyaia are the only modules of Vitruvius defined with a spe­
cific unit of sizes (See ill. 4). The interval of 2 cubits for rowlocks is about 3’ or 
90 cm. The same rhythm is still used as a module for the arrangement of seats in 
theaters, etc.

KAMNITI STEBRIČ­
KI ZA HIPOKAVSTE 
1/2 1 X 1 /2 1 X 2 '
OPEČNI IN KAM­
NITI MOZAIČNI KA­
MENČKI VELIKI : 
1/2 X 1/2 UNCIE i 
1 X 1 UNCIA
UNCIA
SESUNCIA
PALMUS
TRIENS
QUINCUNX
SEMIS
SEPTUNX
BES
DODRANS
DEUNX
PES
PALMIPES
CUBITUS
GRADUS
PASSUS
Illustration 10
The analysis of Roman building components2 1 disclosed that their sizes were 
modular and equal to small multiples of a Roman standard unit of sizes.
Since components were modular, the buildings, as their additive and/or mul­
tiplicative compositions, were modular too. (See illustration 13.)

K l -VA “ RI “ HO MODULARNO PRAVILO JAPONSKIH BIVALIŠČ IZVIRA IZ ZGODNJEGA MOMOYAMA OBDOBJA, IZ 
KONCA 16. STOLETJA. BESEDA KIVARI (PRAVILO O REZANJU LESA) SE JE PRVIČ POJAVILA V TESARSKEM PRIROČNIKU, V 
OBLIKI PETIH PAPIRNIH ZVITKOV, IMENOVANIH SHOMEI (LETA 1608). EDEN TEH ZVITKOV, IMENOVAN BANSHO - SHIKI - 
SHAKU, RAZLAGA SVETO UMETNOST STAVBE
1 . IZVOR- MISTIČNO DARILO BANSHO - SHIKI - SHAKU SHOTOKUJA, PRINCA, VLADARJA (570- 621?)
2 POLOŽAJ: ORIENTACIJA STAVBE IN VRAŽEVEREN ODNOS DO SONCA, LUNE, VETRA IN VODE
3 OBRED: MOLITVE, BOŽJA SLUŽBA IN PRAZNOVANJA OB RAZLIČNIH STOPNJAH GRADNJE 
A . IZVEDBA MERA, PROPORCIJA, KONSTRUKCIJA IN POSTAVITEV STAVBE
H. ENGEL, THE JAPANESE 
HOUSE, RUTLAND, VERMONT, 
TOKYO, JAPAN, 196A
KIVARI MODUL V 
BANSHO-SHIKI- 
SHAKU ROKOPISU 
CELOTNA STAVBA 
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ALI A2 TSUBO. 
ŠIRINA STEBRA JE 
MODULIRANA S 
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OSNI RAZPON JE >5,1, 
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STANDARDIZIRANJE SVETLEGA RAZPONA (KYOTO), OZIROMA OSNEGA (EDO) POMENI ZARADI RAZLIČNO MOČNIH SOH SPREMENLJIV 
OSNI, OZIROMA SVETLI RAZPON .
Illustration 1 1
The traditional Japanese building components are modular since ki-va-ri-ho, 
or the system of cutting wooden components, was introduced in the 16. century A. D.
The Japanese modular system conforms with the traditional Japanese system of 
sizes.1 5
15 — A rheološki vestnik

Illustration 12
The Roman buildings are modular. The still standing Diocletian’s Mausoleum 
in Split is a modular composition. On this plan the rhythm of the module, 1 passus 
long, is shown.

iiiand Xi = siNouisodMOo smnaoH i-------------------------------------------1 i----------------------------------------- « t ---------------------------------1
mano n = snvanionms smnaoH i---------1
snmvd i = 'arciaii smnaoH m i — on-ot-+-oi-+-w-i-oi-+-oi-4-ot-t-oi-i-oiH
2 2 2 °
O J O O
Illustration 13
The Roman buildings are modular. The still standing Porta Palatina2 2 in Turin, Italy, 
is made of Roman brick, called Lydica. The increment of Lydica, or the brick-mo­
dule, is 1 Roman palm in the vertical, and 2 palmi in the horizontal direction. The 
structural module of the elevation is 12 palmi equalling 2 cubiti. The compositional 
module of Porta Palatina, however, is 9 cubiti long.

Illustration 14
The Roman buildings and new towns1 1 . 1 2 are modular. The Diocletian’ s Palace 
in Split, which is more than mere building and less than a town, is a good example 
for both. Its plan and elevations are modular.

PEKING,CAPITAL OF CHINA: TARTAR OR INNER CITY xiv. century a. d.
CHINESE OR OUTER CITY xvi. century a. d.
MODULES L I'/' 680m
M 2LI = 2 Mu = 6Mvju = 6M60 c h a n g = 6 M io o k u n g = ISM'/ju = 18M20chang 
PROPORTION 1:1 p r im a 5 : A q u a d r ia g o n 12 : 5 d o u b l e quadriago n
0
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2000
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4000
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Illustration 15
The modular principle is not restricted only to the Roman architecture. The 
composition of Peking, the capital of China since the XIV century A. D., conforms 
with the traditional Chinese standard sizes, used as modules.
4M2LI

Illustration 16
The modular grid, used as a basis for the Chinese calligraphy, is comparable to 
the modular principle in design of Roman vases1 9 and to the modularity of ike­
bana, the traditional Japanese flower arrangement.1 5

Illustration 17
The composition of Stonehenge, one of the oldest surviving architectural mo­
numents, is modular. Diameters of its circles are in the ratio of 7, 10, 12, 17, 26, 29 
and 34, modules.2 3

Povzetek
Ponovna uvedba modularne koordinacije v današnjo arhitekturo1 je oživila za­
nimanje za Vitruvijevo teorijo o modularni kompoziciji.
Vitruvij razlaga pojma modulus in commodulatio na več mestih svojih desetih 
knjig o arhitekturi. Toda njegov nauk je zaradi neprimernih prevodov, ki so sicer 
jezikovno pravilni, težko razumljiv. Tako na primer vsi prevodi Vitruvij a za besedo 
symmetria uporabljajo termine symmetry v angleščini, symetrie v francoščini, 
Symmetrie v nemščini, simmetria v italijanščini, simetrija pri nas. Toda ta pojem 
je Vitruviju pomenil nekaj čisto drugega kot nam. Besede s časom pač spreminjajo 
svoj pomen. Cetus Faventinus5 nam sporoča, da so »Grki... modularne mere ime­
novali ... jujjjietpiav.« Druga napaka, ki se vleče skozi vse prevode Vitruvija, je ge­
nerični genitiv ratae partis, ki ga prevajajo v ednini, kot v originalu, čeprav Vitruvij 
ima v mislih vsak »izračunani del« ali »modul«, torej vse »module« in ne le ene­
ga.4 . 6 . 8 Če vemo za obe mesti, kjer dobesedno prevajanje pokvari smisel, lahko za 
arhitekta najpomembnejši Vitruvijev precept beremo takole:
»Kompozicija zgradb je odvisna od modularnih mer, katerih razmerja se morajo 
arhitekti nad vse vestno držati. Ta pa izhaja iz proporcije, ki jo Grki imenujejo 
analogia. Proporcija pa je izbor merskih enot za vsak gradbeni člen in za celoto 
zgradbe ter njihova medsebojna vsklajenost (commodulatio), pri čemer pride do 
izraza razmerje modularnih mer. Kajti brez modularnih mer in brez proporcije no­
bena zgradba ne more imeti racionalne kompozicije, to se pravi, če nima natančnih 
razmerij kot med udi lepo oblikovanega človeka.« (Vitr. 3. 1. 1.)
Nerazumevanje tega Vitruvijevega pravila, ki mu botruje slabo prevajanje, je 
glavni razlog, da je moderna arhitektura zašla v mersko zmedo, ki ni kaj dosti 
manjša od tiste, ko so gradili babilonski stolp.