1. Aedium compositio constat ex symmetria, cuius rationem diligentissime architecti tenere debent. Ea autem paritur a proportione, quae graece analogia dicitur. Proportio est ratae partis membrorum in omni opere totiusque commodulatio, ex qua ratio efficitur symmetriam. Namque non potest aedis ulla sine symmetria atque proportione rationem habere compositionis, nisi uti ad homines bene figurati membrorum habuerit exactam rationem.
1. The planning of temples depends upon symmetry: and the method of this architects must diligently apprehend. It arises from proportion (which in Greek is called analogia). Proportion consists in taking a fixed module, in each case, both for the parts of a building and for the whole, by which the method of symmetry and proportion is put into practice. For without symmetry and proportion no temple can have a regular plan; that is, it must have an exact proportion worked out after the fashion of the members of a finely-shaped human body.
2. Corpus enim hominis ita natura composuit, uti os capitis a mento ad frontem summam et radices imas capilli esset decimae partis, 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 ad summum verticem quartae. Ipsius autem oris altitudinis tertia est pars ab imo mento ad imas nares, nasum ab imis naribus ad finem medium superciliorum tantundem, ab ea fine ad imas radices capilli frons efficitur item tertiae partis. Pes vero altitudinis corporis sextae, cubitum quartae, pectus item quartae. Reliqua quoque membra suas habent commensus proportiones, quibus etiam antiqui pictores et statuarii nobiles usi magnas et infinitas laudes sunt adsecuti.
2. For Nature has so planned the human body that the face from the chin to the top of the forehead and the roots of the hair is a tenth part; also the palm of the hand from the wrist to the top of the middle finger is as much; the head from the chin to the crown, an eighth part; from the top to the breast with the bottom of the neck to the roots of the hair, a sixth part; from the middle of the breast to the crown, a fourth part; a third part of the height of the face is from the bottom of the chin to the bottom of the nostrils; the nose from the bottom of the nostrils to the line between the brows, as much; from that line to the roots of the hair, the forehead is given as the third part. The foot is a sixth of the height of the body; the cubit a quarter, the breast also a quarter. The other limbs also have their own proportionate measurements. And by using these, ancient painters and famous sculptors have attained great and unbounded distinction.
3. Similiter vero sacrarum aedium membra ad universam totius magnitudinis summam ex partibus singulis convenientissimum debent habere commensus responsum. Item corporis centrum medium naturaliter est umbilicus. Namque si homo conlocatus fuerit supinus manibus et pedibus pansis circinique conlocatum centrum in umbilico eius, circumagendo rotundationem utrarumque manuum et 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.
3. In like fashion the members of temples ought to have dimensions of their several parts answering suitably to the general sum of their whole magnitude. Now the navel is natually the exact centra of the body. For if man lies on his back with hands and feet outspread, and the centre of a circle is placed on his navel, his figure and toes will be touched by the circumference. Also a square will be found described within the figure, in the same way as a round figure is produced. For if we measure from the sole of the foot to the top of the head, and apply the measure to the outstretched hands, the breadth will be found equal to the height, just like sites which are squared by rule.
4. Ergo si ita natura conposuit corpus hominis, uti proportionibus membra ad summam figurationem eius respondeant, cum causa constituisse videntur antiqui, ut etiam in operum perfectionibus singulorum membrorum ad universam figurae speciem habeant commensus exactionem. Igitur cum in omnibus operibus ordines traderent, maxime in aedibus deorum, operum et laudes et culpae aeternae solent permanere.
4. Therefore if Nature has planned the human body so that the memberscorrespond in their proportions to its complete configuration, the ancients seem to have had reason in determining that in the execution of their works they should observe an exact adjustment of the several members to the general pattern of the plan. Therefore, since in all their works they handed down orders, they did so especially in building temples, the excellences and the faults of which usually endure for ages.
5. Nec minus mensurarum rationes, quae in omnibus operibus videntur necessariae esse, ex corporis membris collegerunt, uti digitum, palmum, pedem, cubitum, et eas distribuerunt in perfectum numerum, quem Graeci teleon dicunt. Perfectum autem antiqui instituerunt numerum qui decem dicitur; namque ex manibus digitorum numerum; ab palmo pes est inventus. Si autem in utrisque palmis ex articulis ab natura decem sunt perfecti, etiam Platoni placuit esse eum numerum ea re perfectum, quod ex singularibus rebus, quae monades apud Graecos dicuntur, perficitur decusis. Qui simul autem undecim aut duodecim sunt facti, quod superaverint, non possunt esse perfecti, donec ad alterum decusis perveniant; singulares enim res particulae sunt eius numeri.
5. Moreover, they collected from the members of the human body the proportionate dimensions which appear necessary in all building operations; the finger or inch, the palm, the foot, the cubit. and these they grouped into the perfect number which the Greeks call teleon. Now the ancients determined as perfect the number which is called ten. For from the hands they took the number of the inches; from the palm, the foot was discovered. Now while in the two palms with their fingers, ten inches are naturally complete, Plato considered that number perfect, for the reason that from the individual things which are called monades among the Greeks, the decad is perfect. But as soon as they are made eleven or twelve, because they are in excess, they cannot be perfect until they reach the second decad. For individual things are minor parts of that number.
6. Mathematici vero contra disputantes ea re perfectum dixerunt esse numerum qui sex dicitur, quod is numerus habet partitiones eorum rationibus sex numero convenientes sic: sextantem unum, trientes duo, semissem tria, besem quem dimoeron dicunt quattuor, quintarium quem pentemoeron dicunt quinque, perfectum sex. Cum ad supplicationem crescat, supra sex adiecto asse ephectum; cum facta sunt octo, quod est tertia adiecta, tertiarium alterum, qui epitritos dicitur; dimidia adiecta cum facta sunt novem, sesquialterum, qui hemiolus appellatur; duabus partibus additis et decusis facto bes alterum, quem epidimoerum vocitant; in undecim numero quod adiecti sunt quinque, quintarium, quem epipempton dicunt; duodecim autem, quod ex duobus numeris simplicibus est effectus, diplasiona.
6. But mathematicians, disputing on the other side, have said that the number called six is perfect for the reason that this number has divisions which agree by their proportions with the number six. Thus a sixth is one; a third is two; a half is three; two-thirds, which they call dimoeros, four; five-sixths, which they call pentemoeros, five; the perfect number, six. When it grows to the double, a twelfth added above six makes ephectos; when eight is reached, because a third is added, there is a second third, which is called epitritos; when half is added and there are nine, there is half as much again, and it is called hemiolios; when two parts are added and a decad is made, we have the second two-thirds, which they call epidimoeros; in the number eleven, because five are added, we have five-sixths, which they call epipemptos; twelve, because it is produced from two simple numbers, they call diplasios.
7. Non minus etiam, quod pes hominis altitudinis sextam habet partem, (ita etiam, ex eo quod perficitur pedum numero, corporis sexies altitudinis terminavit) eum perfectum constituerunt, cubitumque animadverterunt ex sex palmis constare digitisque XXIIII. Ex eo etiam videntur civitates Graecorum fecisse, quemadmodum cubitus est sex palmorum, in drachma qua nummo utentur, aereos signatos uti asses ex aequo sex, quos obolos appellant, quadrantesque obolorum, quae alii dichalcha, nonnulli trichalcha dicunt pro digitis viginti quattuor in drachma constituisse.
7. Not less also because the foot has the sixth part of a man's height, and also because six times, that is the number six, in that it is completed by the number of feet, determined the heiht of the body, they fixed that number as perfect, observing that the cubit consists of six palms and twenty-four fingers. Hence also the cities of the Greeks seem to have made in a like fashion (just as the cubit is of six palms) six parts of the drachma, the coin which they use, stamped bronze coins like asses, which they call obols; and to have fixed twenty-four quarter obols, called by some dichalcha, by others trichalcha to correspond to the fingers.
8. Nostri autem primo fecerunt antiquum numerum et in denario denos aeris constituerunt, et ea re conpositio nominis ad hodiernum diem denarium retinet. Etiamque quarta pars quod efficiebatur ex duobus assibus et tertio semisse, sestertium vocitaverunt. Postea quam animadverterunt utrosque numeros esse perfectos, et sex et decem, utrosque in unum coiecerunt et fecerunt perfectissmum decusis sexis. Huius autem rei auctorem invenerunt pedem. E cubito enim cum dempti sunt palmi duo, relinquitur pes quattuor palmorum, palmus autem habet quattuor digitos. Ita efficitur, ut habeat pes sedecim digitos et totidem asses aeracius denarius.
8. We, however, at first followed the ancient number, and in the denarius fixed ten bronze coins; whence to this day the derived name keeps the number ten (denarius). And also because the fourth part was made up of two asses and a half, they called it sestertius. But afterwards they perceived that both numbers were perfect, both the six and the ten; and they threw both together, and made the most perfect number sixteen. Now of this they found the origin in the foot. For when two palms are taken from the cubit, there is left a foot of four palms, and the palm has four fingers. So it comes that the foot has sixteen fingers, and the bronze denarius as many asses.
9. Ergo si convenit ex articulis hominis numerum inventum esse et ex membris separatis ad universam corporis speciem ratae partis commensus fieri responsum, relinquitur, ut suscipiamus eos, qui etiam aedes deorum immortalium constituentes ita membra operum ordinaverunt, ut proportionibus et symmetriis separatae atque universae convenientesque efficerentur eorum distributiones.
9. Therefore, if it is agreed that number is found from the articulation of the body, and that there is a correspondence of the fixed ratio of the separate members to the general form of the body, it remains that we take up those writers who in planning the temples of the immortal gods so ordained the parts of the work that, by the help of proportion and symmetry, their several and general distribution is rendered congruous.
This is a very important chapter for the understanding of the principles of Vitruvius, because his architecture and the rules of proportion that govern this architecture are based on the modulus, the module as leading measure in all buildings.
In the first sentence Vitruvius explains once again his idea about symmetria which has already been exposed in book I, 2,4: Symmetry also is the appropriate harmony arising out of the details of the work itself; the correspondence of each given detail among the separate details to the form of the design as a whole. As in the human body, from cubit, foot, palm, inch and other small parts comes to the symmetric quality of eurhythmy. In this quote eurhythmy is translated as proportion. Vitruvius, at the start of his books III and IV, which are about temple architecture, goes back to one of his principal statements about the components of good architecture. These rules of proportion and symmetry are in his opinion, and in ancient opinion in general, based on the proportions of the human body. These proportions were elaborated by ancient sculptors. The system is explained in sentences 2 to 4.
It is important to know whether Vitruvius wants to describe a real metric system or just a general layout.
In sentences 5 to 8 great attention is payed to the ancient mathematical systems based on the perfect numbers 10 and 6. The number 10 is derived from the number of fingers on the hand, while the number 6 is derived from the height of the human body which was equal to 6 feet.
The metric system, as described by vitruvius, is a compilation of the different mathematical theories of antiquity, used in a digital system which operates by dividing each foregoing number in two. So the foot, as basic measure derived from the height of the body, is divided in 2, this, on his turn is divided in two, which gives the palm, the palm again is divided in 2 which on his turn is divided in 2, which gives the inch. In other words, 1 foot = 4 palms; 1 palm = 4 inches; or 1 foot = 16 inches. The number 16, which in sentence 8 is finally proposed as the most perfect number, is the combination of the two mathematical systems.
From the rest of the text it is clear that the relation foot - palm - inch is the leading principle. The cubit is mentioned in sentences 5 and 7 but is not used as a basic measure. The cubit is derived from the uncial system which operates by dividing in 12 and is composed of 4 times the perfect number 6. Indeed: the cubit equals 1 1/2 foot or 6 palms or 24 inches. The prevalence of the foot is easily understandable when we have in mind that 1 cubit = 6 palms while the height of the human body = 6 feet. Since the human body as a whole is the starting point of all the proportionate dimensions which appear necessary in all building operations, it is unthinkable that the cubit, as only a part of the human body, could be taken as leading measure.
Les dix livres d'architecture de Vitruve, Corrigés et traduits en 1684 par C. Perrault, Paris, 1684.
Vitruvius, De Architectura libri X, ed. F. Granger, London, 1962.
Ton Peters, Vitruvius, Handboek bouwkunde, Amsterdam, 1999.
H. Knell, Vitruvs Architekturtheorie, Versuch einer Interpretation, Darmstadt, 1985.
J.J.Coulton, Modules and Measurements in Ancient Design and Modern Scholarship, in Munus non Ingratum, ed. H.Geertman&J.J.De Jong, Leiden, 1989, pp.85-89.
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