Mueller Science - Viturvius: De architectura

Figure 22:

Marcus Vitruvius Pollio: De architectura libri 10

Text and English translation by William P. Thayer

http://penelope.uchicago.edu/Thayer/L/Roman/Texts/Vitruvius/

All passages wit the words „modul-„

Of the 55 latin passages only 21 are translated in English by „module“; once „modulatio“ is translated by „modulation“

Inserted in the Latin text are the words used in the first Italian translation:

Viturvius: De Architectura. Trad. Cesare Cesariano. Como 1521

Inserted in the English translation are the words used in the first French translation:

Vitruve: Architecture, ou Art de bien bastir. Trad. Jan Martin. Paris: Iacques Gazeau 1547, erneut Paris: Marnef & Cavellat 1572; Cologny: Iean de Tournes 1618; Reprint Ridgewood, N. J.: Gregg 1964

(For model as small-scale device Vitruvius uses „exemplar“

see: Vitruv über Modelle (exemplaria, exempla)

content

Liber 1 Caput 1

Caput 2

Liber 3 Caput 1

Caput 3

Caput 5

Liber 4 praefatio

Caput 1

Caput 3

Caput 7

Caput 9

Liber 5 Caput 4

Caput 5

Caput 9

Liber 6 Caput 3

Liber 7 praefatio

Liber 10 Caput 8

Caput 11

On water pipes

Liber 8 Caput 6

Liber 1, Caput 1

Italian: Capo primo

French: Chap. III

15. igitur in hac re Pytheos errasse videtur quod non animadvertit ex duabus rebus singulas artes esse compositas, ex opere et eius ratiocinatione. ex his autem unum proprium est eorum qui singulis rebus sunt exercitati, id est operis effectus, alterum commune cum omnibus doctis, id est ratiocinatio, uti medicis et musicis est de venarum rhythmo et ad pedem motu, at si vulnus mederi aut aegrum eripere de periculo oportuerit, non accedet musicus, sed id opus proprium erit medici. item in organo non medicus sed musicus modulabitur (modulara acio), ut aures suam cantionibus recipiant iucunditatem.

15. Wherefore Pythius seems to have been in error, forgetting that art consists in practice and theory. Theory is common to, and may be known by all, but the result of practice occurs to the artist in his own art only. The physician and musician are each obliged to have some regard to the beating of the pulses, and the motion of the feet, but who would apply to the latter to heal a wound or cure a malady? so, without the aid of the former, the musician affects the ears of his audience by modulations (par la doulceur, 5) upon his instrument.

Liber 1, Caput 2

Italian: Capo secundo

French: Chap. IIII

2. Ordinatio est modica membrorum operis commoditas separatim universaeque proportionis ad symmetriam comparatio. haec componitur ex quantitate, quae graece „ποσοτης“ dicitur. quantitas autem est modulorum (de li moduli) ex ipsius operis <membris> sumptio e singulisque membrorum partibus universi operis conveniens effectus. Dispositio autem est rerum apta conlocatio elegansque e compositionibus effectus operis cum qualitate. species dispositioniis, quae graece dicuntur „ιδεαι“, sunt hae, ichnographia orthographia scaenographia. ichnographia est circini regulaeque modice contines usus, e qua capiuntur formarum in solis arearum descriptiones. orthographia autem est erecta frontis imago modiceque picta rationibus operis futuri figura. item scaenographia est frontis et laterum abscedentium adumbratio ad circinique centrum omnium linearum responsus. hae nascuntur ex cogitatione et inventione. cogitatio est cura, studii plena et industriae vigilantiaeque, effectus propositi cum voluptate. inventio autem est quaestionum obscurarum explicatio ratioque novae rei vigore mobili reperta. hae sunt terminationes dispositionum.

2. Fitness is the adjustment of size of the several parts to their several uses, and required due regard to the general proportions of the fabric (un gect ou modelle, 5+): it arises out of dimension (quantitas), which the Greeks call „ποσότης“. Dimension regulated the general scale of the work, so that the parts may all tell and be effective. Arrangement is the disposition in their just and proper places of all the parts of the building, and the pleasing effect of the same; keeping in view its appropriate character. It is divisible into three heads, which, considered together, constitute design: these, by the Greeks, are named „ἰδέαι“: they are called ichnography, orthography, and scenography. The first is the representation on a plane of the ground-plan of the work, drawn by rule and compasses. The second is the elevation of the front, slightly shadowed, and shewing the forms of the intended building. The last exhibits the front and a receding side properly shadowed, the lines being drawn to their proper vanishing points. These three are the result of thought and invention. Thought is an effort of the mind, ever incited by the pleasure attendant on success in compassing an object. Invention is the effect of this effort; which throws a new light on things the most recondite, and produces them to answer the intended purpose. These are the ends of arrangement.

Liber 3, Caput 1

1. Aedium compositio constat ex symmetria, cuius rationem diligentissime architecti tenere debent. ea autem paritur a proportione, quae graece „αναλογια“ dicitur. proportio est ratae partis membrorum in omni opere totiusque commodulatio (commodulatione), ex qua ratio efficitur symmetriarum. namque non potest aedis ulla sine symmetria atque proportione rationem habere compositionis, nisi uti ad hominis bene figurati <speciem> membrorum habuerit exactam rationem.

1. The design of Temples depends on symmetry, the rules of which Architects should be most careful to observe. Symmetry arises from proportion, which the Greeks call „ἀναλογία“. Proportion is a due adjustment (un certain rapport & convenance, 27+) of the size of the different parts to each other and to the whole; on this proper adjustment symmetry depends. Hence no building can be said to be well designed which wants symmetry and proportion. In truth they are as necessary to the beauty of a building as to that of a well formed human figure,

Liber 3, Caput 3

Italian: Capo secundo

French: Chap. II

7. huius autem rei ratio explicabitur sic. frons loci quae in aede constituta fuerit, si tetrastylos facienda fuerit, dividatur in partes XI S praeter crepidines et proiecturas spirarum, si sex erit columnarum, in partes XVIII. si octastylos constituetur, dividatur in XXIV et semissem. item ex his partibus sive tetrastyli sive hexastyli sive octastyli una pars sumatur eaque erit modulus (sera il modulo). cuius moduli (dil quale modulo) unius erit crassitudo columnarum. intercolumnia singula, praeter media, modulorum duorum et moduli quartae partis (sera de dui moduli & de una quarta parte del modulo). mediana in fronte et postico singula ternum modulorum (de tri moduli). ipsarum columnarum altitudo modulorum VIIII (de octo moduli) et dimidiae moduli partis (de la meza parte de uno modulo). ita ex ea divisione intercolumnia altitudinesque columnarum habebunt iustam rationem.

7. The rule for designing it is as follows. The extent of the front being given, it is, if ‚tetrastylos’, to be divided into eleven parts and a half, not including the projections of the base and plinth at each end: if ‚hexastylos’, into eighteen parts: if ‚octastylos’, into twenty-four parts and a half. One of either of these parts, according to the case, whether ‚tetrastylos’, ‚hexastylos’, or ‚octastylos’, will be a measure (Modele, 33) equal to the diameter of one of the columns. Each intercolumniation, except the middle one, front and rear, will be equal to two of these measures and one quarter, and the middle intercolumniation three (trois Modeles tous entiers, 33). The heights of the columns will be eight parts and a half. Thus the intercolumniations and the heights of the columns will have proper proportions (mesures convenables, 33+).

13. haec autem propter altitudinis intervallum, scandente oculi specie, adiciuntur crassitudinis temperaturae. venustatem enim persequitur visus, cuius si non blandimur voluptati proportione et modulorum adiectionibus (con le adiectione de li modulli), uti quod fallit temperatione adaugeatur, vastus et invenustus conspicientibus remittetur aspectus. de adiectione quae adicitur in mediis columnis, quae apud Graecos „εντασις“ appellatur, in extremo libro erit forma et ratio eius quemadmodum mollis et conveniens efficiatur subscripta.

13. always remembering, that as the upper parts of columns are more distant from the eye, they deceive it when viewed from below, and that we must, therefore, actually add what they apparently lose. The eye is constantly seeking after beauty; and if we do not endeavour to gratify it by proper proportions and an increase of size (par additions convenables, 34+), where necessary, and thus remedy the defect of vision, a work will always be clumsy and disagreeable. Of the swelling which is made in the middle of columns, which the Greeks call „ἔντασις“, so that it may be pleasing and appropriate, I shall speak at the end of the book.

Liber 3, Caput 5

Italian: Capo tertio

French: Chap. III

8. de volutarum descriptionibus, uti ad circinum sint recte involutae quemadmodum describantur, in extremo libro forma et ratio earum erit subscripta. Capitulis perfectis, deinde <pro ratione> columnarum non ad libellam sed ad aequalem modulum conlocatis (ma a lo equale modulo collocati) , quae adiectio in stylobatis facta fuerit, in superioribus membris respondeat, epistyliorum ratio sic est habenda uti si columnae fuerint a minima 12 pedum ad quindecim pedes, epistylii sit altitudo dimidiae crassitudinis imae columnae, item si ab XV pedibus ad XX, columnae altitudo dimetiatur in partes tredecim et unius partis altitudo epistylii fiat, item si a XX ad XXV pedes, dividatur altitudo in partes XII et semissem et eius una pars epistylii in altitudine fiat, item si ab XXV pedibus ad XXX, dividatur in partes XII et eius una pars altitudo fiat. item <si altior>, rata parte ad eundem modum ex altitudine columnarum expediendae sunt altitudines epistyliorum.

8. The method of describing volutes, in order that they may be properly turned and proportioned, will be given at the end of the book. The capitals being completed, and set on tops of the shafts, not level throughout the range of columns (non a la reigle ou au nyueau, 38+), but so arranged with a gauge as to follow the inclination which the small steps on the ‚stylobata’ produce, which must be added to them on the central part of the top of the ‚abacus’, that the regularity of the ‚epistylia’ may be preserved: we may now consider the proportion of these ‚epistylia’, or architraves. When the columns are

t at least twelve and not more than fifteen feet high, the architrave must be half a diameter in height. When they are

t from fifteen to twenty feet in height, the height of the column is to be divided into thirteen parts, and one of them taken for the height of the architrave. So

t from twenty to twenty-five feet, let the height be divided into twelve parts and a half, and one part be taken for the height of the architrave. Thus, in proportion to the height of the column, is the architrave to be proportioned;

9. quo altius enim scandit oculi species, non facile persecat aeris crebritatem. dilapsa itaque altitudinis spatio et viribus exsucta incertam modulorum renuntiat sensibus quantitatem (la incerta quantitate de li moduli). quare semper adiciendum est rationis supplementum in symmetriarum membris, ut cum fuerint aut altioribus locis opera aut etiam ipsa colossicotera, habeant magnitudinum rationem. epistylii latitudo in imo quod supra capitulum erit quanta crassitudo summae columnae sub capitulo erit tanta fiat, summum quantum imus scapus

9. always remembering, that the higher the eye has to reach, the greater is the difficulty it has in piercing the density of the air, its power being diminished as the height increases; of which the result is, a confusion of the image (une incertaine proportion de modules, 38+). Hence, to preserve a sensible proportion of parts, if in high situations, or of colossal dimensions, we must modify them accordingly, so that they may appear of the size intended. The under side of the architrave is to be as wide as the upper diameter of the column, at the part under the capital; its upper part equal in width to the lower diameter of the column.

Liber 4, praefatio

2. ex tribus generibus, quae subtilissimas haberent proportionibus modulorum quantitates (quantitate con le proportione de li moduli), ionici generis moribus docui. nunc hoc volumine de dorici corinthiique constitutis rationibus dicam eorumque discrimina et proprietates explicabo.

2. confining myself, however, to the use of the Ionic order, which, of the three, from the great delicacy of its proportions (proportions, 43+), requires the most attention in its use. I shall now, in this book, point out the difference and properties of the Doric and Corinthian Orders.

Liber 4, Caput 1

8. posteri vero elegantia subtilitateque iudiciorum progressi et gracilioribus modulis delectati (de piu gracili moduli delectati) septem crassitudinis diametros in altitudinem columnae doricae, ionicae novem constituerunt. id autem <genus>, quod Iones fecerunt primo, Ionicum est nominatum. Tertium vero, quod Corinthium dicitur, virginalis habet gracilitatis imitationem, quod virgines propter aetatis habet teneritatem gracilioribus membris figuratae effectus recipiunt in ornatu venustiores.

8. The successors of these people, improving in taste, and preferring a more slender proportion (se delectans des formes delicates, 48+), assigned seven diameters to the height of the Doric column, and eight and a half to the Ionic. That species, of which the Ionians were the inventors, has received the appellation of Ionic. The third species, which is called Corinthian, resembles in its character, the graceful elegant appearance of a virgin, in whom, from her tender age, the limbs are of a more delicate form, and whose ornaments should be unobtrusive.

Liber 4, Caput 3

3. Nos autem exponimus, uti ordo postulat, quemadmodum a praeceptoribus accepimus, uti si qui voluerit his rationibus attendens ita ingredi, habeat proportiones explicatas, quibus emendatas et sine vitiis efficere possit aedium sacrarum dorico more perfectiones. frons aedis doricae in loco quo columnarum constituuntur dividatur, si tetrastylos erit, in partes 12, si hexastylos, XXXXII. ex his pars una erit modulus (sera il modulo), qui graece „εμβατης“ dicitur, cuius moduli (del modulo) constitutione ratiocinationibus efficiuntur omnis operis distributiones.

3. I will, however, proceed to explain the method of using it, as instructed therein by my masters; so that if any one desire it, he will here find the proportions detailed, and so amended, that he may, without a defect, be able to design a sacred building of the Doric order. The front of a Doric temple, when columns are to be used, must if ‚tetrastylos’, be divided into twenty-seven parts; if ‚hexastylos’, into forty-two parts; one of which parts is called a module (servira de mesure ou module, 53+), by the Greeks „ἐμβάτης“: from the module (sur icelluy module, 53+) so found the distribution of all the parts is regulated.

4. Crassitudo columnarum erit duorum modulorum (dui moduli), altitudo cum capitulo XIIII. capituli crassitudo unius moduli (de uno modulo), latitudo duorum et moduli (modulo) sextae partis. crassitudo capituli dividatur in partes tres, e quibus una plinthus cum cymatio fiat, altera echinus cum anulis, tertia hypotrachelion. contrahatur columna ita uti in tertio libro de ionicis est scriptum. epistylii altitudo unius moduli (de uno modulo) cum taenia et guttis, taenia moduli (modulo) septima, guttarum longitudo sub taenia contra triglyphos alta cum regula parte sexta moduli (modulo) praependeat. item epistylii latitudo ima respondeat hypotrachelio summae columnae. supra epistylium conlocandi sunt triglyphi cum suis metopis, alti unius et dimidati moduli (modulo), lati in fronte unius moduli (modulo), ita divisi ut in angularibus columnis et inmediis contra tetrantes medios sint conlocati, et in intercolumniis reliquis bini, in mediis pronao et postico terni. ita relaxatis mediis intervallis, sine inpeditionibus aditus accedentibus erit ad deorum simulacra.

4. The thickness of the columns is to be equal to two modules (deux d’iceulx modules, 53+), their height equal to fourteen. The height of the capital one module (un module, 53+), its breadth one module and a sixth. Let the height of the capital be divided into three parts; then one of those parts is to be assigned for the ‚abacus’ and its ‚cymatium’, another for the ‚echinus’, with its fillets; the third for the ‚hypotrachelium’. The diminution of the column is to be as directed for the Ionic order in the third book. The architrave or ‚epistylium’, with its ‚tænia’ and ‚guttæ’, is to be one module (un module de mesure, 56+) in height; the ‚tænia’ is the seventh part of a module; the length of the ‚guttæ’ under the ‚tænia’ plumb with the triglyphs, and including the fillet, the sixth part of a module (de ceste mesure, 56+). The width of the soffit of the architrave is to correspond with the thickness of the column at the ‚hypotrachelium’. Over the architrave triglyphs are placed, with ‚metopæ’ one module and a half high (qu’un Module & demy, 56+), and one module wide on the face. They are to be distributed so, that as well over the columns at the angles, as over the intermediate columns, they may stand above the two central quarters of the columns. Two are to be placed in each intercolumniation, except in the central one of the ‚pronaos’ and ‚posticum’, in which three are to be set; because, by making the middle intercolumniations wider, a freer passage will be given to those who approach the statues of the gods.

5. triglyphorum latitudo dividatur in partes sex, ex quibus quinque partes in medio, duae dimidiae dextra ac sinistra designentur regular. una in medio deformetur femur, quod graece „μερος“ dicitur. secundum eam canaliculi ad normae cacumen inprimantur. ex ordine eorum dextra ac sinistra altera femina constituantur. in extremis partibus semicanaliculi intervertantur. triglyphis ita conlocatis, metopae quae sunt inter triglyphos aeque altae sint quam longae, item in extremis angulis semimetopia sint inpressa dimidia moduli (modulo) latitudine. ita enim erit ut omnia vitia et metoparum et intercolumniorum et lacunariorum, quod aequales divisiones factae erunt, emendentur.

5. The width of a triglyph is divided into six parts, of which five are left in the middle, and of the two halves of the remaining part, one is placed on the right and the other on the left extremity. In the centre a flat surface is left, called the ‚femur’ (thigh), by the Greeks „μηρὸς“, on each side of which channels are cut, whose faces form a right angle; and on the right and left of these are other ‚femora’; and, lastly, at the angles are the two half channels. The triglyphs being thus arranged, the ‚metopæ’, which are the spaces between the triglyphs, are to be as long as they are high. On the extreme angles are semi-‚metopæ’ half a module wide. In this way all the defects in the ‚metopæ’, intercolumniations, and ‚lacunaria’, will be remedied.

6. triglyphi capitula sexta parte moduli (modulo) sunt faciunda. supra triglyphorum capitula corona est conlocanda in proiectura dimidiae et sextae partis habens cymatium doricum in imo, alterum in summo. ita cum cymatiis corona crassa ex dimida moduli (modulo). dividendae autem sunt in corona ima ad perpendiculum triglyphorum et medias metopas viarum directiones et guttarum distributiones, ita uti guttae sex in longitudinem, tres in latitudinem pateant. reliqua spatia, quod latiores sunt metopae quam triglyphi, pura relinquantur aut fulmina scalpantur, ad ipsumque mentum coronae incidatur linea quae scotia dicitur. reliqua omnia, tympana et simae coronae, quemadmodum supra scriptum est in ionicis, ita perficiantur.

6. The capitals of the triglyphs are to be made the sixth part of a module (la sixième partie d’un module, 57+). Over the capitals of the triglyphs the ‚corona’ is to be laid, whose projection is one half and a sixth part of a module (d’icelluy module, 57+), with a Doric cymatium over it, and another above it, so that, with the ‚cymatia’, the ‚corona’ is one half of a module (module, 57+) high. In the soffit of the ‚corona’, perpendicularly over the triglyphs and centres of the ‚metopæ’, are arranged ‚guttæ’ and sinkings. The former, so as to have six ‚guttæ’ appearing in front, and three on the return: the remaining spaces, which occur from the increased width of the ‚metopæ’ beyond that of the triglyphs, are left plain or sculptured with representations of thunderbolts, and near the edge of the ‚corona’ a channel is cut, called a ‚scotia’. The remaining parts, the ‚tympana’, ‚simæ’, and ‚coronæ’, are to be executed similar to those described for Ionic buildings.

7. Haec ratio in operibus diastylis erit constitua. si vero systylon et monotriglyphon opus erit faciundum, frons aedis, si tetrastylos erit, dividatur in partes XVIIII S, si hexastylos erit, dividatur in partes XXVIIII S. ex his pars una erit modulus (modulo), ad quem uti supra scriptum est dividatur.

7. The above is the method used in diastyle works. If the work be systyle, with a monotriglyph: the front of the building, when ‚tetrastylos’, is to be divided into twenty-three parts; when ‚hexastylos’, into thirty-five: of these, one part is taken for a module (l’une d’icelles sera la mesure, 58+); according to which, as above directed, the work is to be set out.

Liber 4, Caput 7

3. spirae earum altae dimidia parte crassitudinis fiant. habeant spirae earum plinthum ad circinum altam suae crassitudinis dimida parte, torum insuper cum apophysi crassum quantum plinthus. capituli altitudo dimidia crassitudinis. abaci latitudo quanta ima crassitudo columnae. capitulique crassitudo dividatur in partes tres, e quibus una plintho, quae est abaco, detur, altera echino, tertia hypotrachelio cum apophysi.

supra columnas trabes compactiles inponantur altitudinis modulis (con quisti moduli) is qui a magnitudine operis postulabuntur, eaeque trabes eam habeant crassitudinem, quanta summae columnae erit hypotrachelium, et ita sint compactae subscudibus et securiculis ut compatura duorum digitorum habeant laxationem. cum enim inter se se tangunt et non spiramentum et perflatum venti recipiunt, concalefaciuntur et celeriter putrescunt.

3. Their bases are to be half a diameter in height. The plinths, which are to be circular, are half the height of the base, with a ‚torus’ and fillet on them as high as the plinth. The height of the capital is to be half a diameter. The width of the ‚abacus’ is equal to the lower diameter of the column. The height of the capital must be divided into three parts, of which one is assigned to the plinth or ‚abacus’, another to the ‚echinus’, the third to the ‚hypotrachelium’, with its ‚apophyge’.

Over the columns coupled beams are laid of such height (dont l’espoisseur soit tele, 64+) as the magnitude of the work may require. Their width must be equal to that of the ‚hypotrachelium’ at the top of the column, and they are to be so coupled together with dovetailed dowels as to leave a space of two inches between them. For if they are laid touching each other, and the air does not play round them, they heat and soon rot.

Liber 4, Caput 9

Latin Library:

1. ... Ita idoneae his institutionibus explicabuntur in meditationibus arearum deformationes.

William P. Thayer:

1. ... ita idoneae his institutionibus explicabuntur in meditationibus ararum deformationes.

P. G. W. Glare (Hrsg.):Oxford Latin Dictionary. 1982 has:

1. ... idoneae his institutionibus explicabuntur in modulationibus ararum deformationes.

Liber 5, Caput 4

2. vox enim mutationibus cum flectitur alias fit acuta alias gravis, duobusque modis movetur, e quibus unus effectus habet in finitionibus consistit neque in loco ullo, efficitque terminationes non apparentes, intervalla autem media apparentia, uti sermone cum dicamus sol lux flox vox. nunc enim nec unde incipit nec ubi desinit intellegitur, sed quod ex acuta facta est gravis et ex gravi acuta, apparet auribus. per distantiam autem e contrario. namque cum flectitur inmutatione vox statuit se in alicuius sonitus finitione, deinde in alterius, et id ultro citro crebre faciendo constans apparet sensibus, uti in cantionibus cum flectentes vocem varietatem facimus modulationis (la varietate de la modulatione). itaque intervallis ea cum versatur, et unde initium fecit et ubi desiit apparet in sonorum patentibus finitionibus, mediana autem latentia intervallis obscurantur.

2. The inflexion of the voice is two-fold; first, when it is monotonous, second, when it proceeds by intervals. The first is not limited by cadences at the close, nor in any other place; no perceptible difference of tone being discoverable between its beginning and ending, the time between each sound is however distinctly marked, as in speaking, when we pronounce the words, ‚sol’, ‚lux’, ‚flos’, ‚nox’. Herein the ear does not perceive any difference of tone between the beginning and ending, by the voice rising higher or descending lower; neither, that from a high pitch it becomes lower, nor the contrary. But when the voice moves by intervals, it is differently inflected, being sometimes at a high pitch, and sometimes at a low one, and resting at different times on different tones; by doing which with quickness and facility, it appears unfixed. Thus in singing, the variety of inflexion produces an air (les hommes font plusieurs accords differents, 71+). In short, by the use of different intervals, the tones are so marked and determined, that we perceive the pitch at which it begins, and that at which it finished, though the intermediate tones are not heard.

3. Genera vero sunt modulationum (de la modulatione) tria, primum quod Graeci nominant „αρμονιαν“, secundum „χρωμα“, tertium „διατονον“. est autem harmoniae modulatio (modulatione) ab arte concepta, et ea re cantio eius maxime gravem et egregiam habet auctoritatem. chroma subtili sollertia ac crebritate modulorum (de li moduli) suaviorem habet delectationem. diatoni vero quod naturalis est, facilior est intervallorum distantia. in his tribus generibus dissimiles sunt tetracordorum dispositiones, quod harmonia tetrachorum et tonos et diheses habet binas. dihesis autem est toni pars quarta, ita in hemitonio duae diheses sunt conlocatae. chromati duo hemitonia in ordine sunt composita, tertium trihemitonium est intervallium. diatono toni duo sunt continuati, tertium hemitonium finit tetrachordi magnitudinem. ita in tribus generibus tetrachorda ex duobus tonis et hemitonio sunt peraequata, sed ipsa cum separatim uniuscuiusque generis finibus considerantur, dissimilem habent intervallorum designationem

3. There are three sorts of modulation (trois especes de resonance, 71+), the enharmonic („ἁρμονία“), the chromatic („χρῶμα“), and the diatonic („διάτονος“), so-called by the Greeks. The enharmonic (Ceste doulceur d’Harmonie, 71+) is so constructed by art, as to be full of majesty and pathos. The chromatic by the skilful contrivance and closeness of its intervals has more sweetness. The diatonic, whose intervals are more simple, is most natural. The disposition of the tetrachords, in these genera, are dissimilar. The enharmonic tetrachord consists of two ‚dieses’, and two whole tones; a ‚diesis’ being the fourth part of a tone, and two of them consequently equal to a semitone. In the chromatic tetrachord, there are two consecutive semitones, and the third interval contains three semitones. The diatonic tetrachord has two consecutive tones, and an interval of a semitone. Thus in each genus, the whole tetrachord is equal to two whole tones and a semitone. But the intervals in each genus, differ when considered separately.

5. Sonitus, qui graece „φθογγοι“ dicuntur, in unoquoque genere sunt X et VIII, e quibus VIII sunt in tribus generibus perpetui et stantes, reliqui X cum non uniter modulantur (si modulano) sunt vagantes. stantes autem sunt qui inter mobiles interpositi, continent tetrachordi coniunctionem et e generum discriminibus suis finibus sunt permanentes, appellantur autem sic, proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon. mobiles autem sunt qui in tetracordo inter inmotos dispositi in generibus ex locis loca mutant, vocabula autem habent haec, parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, <paranete synhemmenon,> trite diezeugmenon, paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.

5. Each genus consists of eighteen sounds, which the Greeks call „φθόγγοι“ (‚phthongi’). Of these, eight sounds in each of the genera, vary neither in sound nor situation. The remaining ten in each are not common to the other two genera. Those which do not vary, contain between them the variable sounds, and are the limits of the tetrachords in all the genera. Their names are as follow: ‚proslambanomenos’, ‚hypatè hypatôn’, ‚hypatè mesôn’, ‚mesè’, ‚netè synèmmenôn’, ‚paramesè’, ‚netè diezeugmenôn’, ‚netè hyperbolæôn’. The variable, which lie between those that are not variable, change their places according to the genus. Their names are ‚parhypatè hypatôn’, ‚lichanos hypatôn’, ‚parhypatè mesôn’, ‚lichanos mesôn’, ‚tritè synèmmenôn’, ‚paranetè synèmmenôn’, ‚tritè diezeugmenôn’, ‚paranetè diezeugmenôn’, ‚tritè hyperbolæôn’, ‚paranetè hyperbolæôn’.

6. ei autem qua moventur, recipiunt virtutes alias, intervalla enim et distantias habent crescentes. itaque parhypate, quae in harmonia distat ab hypate <dimidium> hemitonium, in chroma transmutata habet hemitonium. quae lichanos in harmonia dicitur, ab hypate distat hemitonium, in chroma translata progreditur duo hemitonia, in diatono distat ab hypate tria hemitonia. ita X sonitus propter translationes in generibus efficiunt triplicem modulationum (modulatione) varietatem.

6. Those sounds which shift their places, change also their nature, and are at different intervals, as, for instance, the interval between ‚hypatè’ and ‚parhypatè’, which in the enharmonic genus is only a ‚diesis’ or quarter tone, in the chromatic genus a semitone. So the ‚lichanos’ is only a semitone distant from the ‚hypatè’ in the enharmonic genus; whereas in the chromatic it is two semitones distant, and in the diatonic three semitones. Thus, the ten sounds, by their situation in the different genera, make three different sorts of melody (trois diversites de consonance, 72).

7. tetrachorda autem sunt quinque, primum gravissimum, quod graece dicitur „υπατον“, secundum medianum, quod appellatur „μεσον“, tertium coniunctum, quod „συνημμενον“ dicitur, quartum disiunctum, quod „διεζευγμενον“ nominatur, quintum, quod est acutissimum, graece „υπερβολαιον“ dicitur. concentus quos natura hominis modulari potest (la natura del homo po conmodulare), graece quae „συμφονιαι“ dicuntur, sunt sex, diatessaron, diapente, diapason, <diapason> et diatessaron, <diapason> et diapente, et disdiapason.

7. There are five tetrachords. The Greeks call the lowest „ὕπατον“ (‚hypaton’); the second, which is in the middle, „μέσον“ (‚meson’). The third, which is joined to the two preceding, is called „συνημμένον“ (‚synèmmenon’). The fourth, which is disjoined, called „διεζευγμένον“ (‚diezeugmenon’). The fifth, which is the highest, the Greeks call „ὑπερβόλαιον“ (‚hyperbolæon’). The natural consonances (les sortes de consonances dont la nature de l’homme peult rendre melodie, 72), which the Greeks call „συμφωνίαι“ (‚symphoniæ’), are six in number; ‚diatessarôn’ (fourth), ‚diapente’ (fifth), ‚diapasôn’ (octave), ‚diapasôn’ with ‚diatessarôn’ (eleventh), ‚diapasôn’ with ‚diapente’ (twelfth), and ‚disdiapasôn’ (fifteenth).

Liber 5, Caput 5

6. haec autem si qui voluerit ad perfectum facile perducere, animadvertat in extremo libro diagramma musica ratione designatum, quod Aristoxenus magno vigore et industria generatim divisis modulationibus constitum (modulatione constituito) reliquit. De quo si qui ratiocinationibus his attenderit, ab natura vocis ad audientium delectationes facilius valuerit theatrorum efficere perfectiones.

6. He who is desirous of more fully understanding these matters, must refer to the musical diagram at the end of the book, which is that left to us by Aristoxenes, who with much intelligence and labour, formed a general scale of the tones (apres avoir ... divisé les modulations en propre genres & especes, 74). Hence, he who carefully attends to these rules, to the nature of the voice, and to the taste of the audience, will easily learn the method of designing theatres with the greatest perfection.

Liber 5, Caput 9

2. quae videntur ita oportere conlocari uti duplices sint habeantque exteriores columnas doricas cum epistyliis et ornamentis ex ratione modulationis (de la modulatione) perfectas. latitudines autem earum ita oportere fieri videntur uti quanta altitudine columnae fuerint exteriores, tantam latitudinem habeant ab inferiore parte columnarum extremarum ad medias et a medianis ad parietes qui circumcludunt porticus ambulationes. medianae autem columnae quinta parte altiores sint quam exteriores, sed aut ionico aut corinthio genere deformentur.

2. which ought to be constructed double, with their exterior columns of the Doric order, whose architraves, and cornices are to be wrought after the Doric method (a la symmetrie de cest ordre, 80). Their width is to be thus proportioned: the height of the exterior columns is equal to the distance from the lower part of the shaft of the exterior columns to that of those in the middle, and from them to the walls which surround the walks of the portico is an equal distance. The middle range of columns is one fifth part higher than the exterior range; and is of the Ionic or Corinthian order.

3. columnarum autem proportiones et symmetriae non erunt isdem rationibus quibus in aedibus sacris scripsi. aliam enim in deorum templis debent habere gravitatem, aliam in porticibus et ceteris operibus subtilitatem. itaque si dorici generis erunt columnae, dimetiantur earum altitudines cum capitulis in partes XV. ex eis partibus una constituatur et fiat modulus (sia facto il modulo), ad cuius moduli (modulo) rationem omnis operis erit explicatio. et in imo columnae crassitudo fiat duorum modulorum (de dui moduli), intercolumnium quinque et moduli (modulo) dimidia parte, altitudo columnae praeter capitulum XIIII modulorum (de.xiiii.moduli), capituli altitudo moduli (modulo) unius, latitudo modulorum duorum (de dui moduli) et moduli (modulo) sextae partis. ceteri operis modulationes (le altre modulatione) uti in aedibus sacris in libro IIII scriptum est ita perficiantur.

3. The proportions and symmetry of these columns are not to be guided by the rules delivered for those of sacred buildings. For the style used in the temples of the gods should be dignified; whereas, in porticos and similar works, it may be of a lighter character. If, therefore, the columns be of the Doric order, their height, including the capitals, is to be divided into fifteen parts, of which one is taken as a module (le module, 80+). By this all the work is set out, making the thickness of the lower part of the column equal to two modules (deux de ces mesures, 80+). The intercolumniation is of five modules and a half. The height of a column, exclusive of the capital, fourteen modules; the height of the capital one module (un de ces modules, 80+), the width of it two modules and a sixth. The proportions of the rest of the work are to be the same as those described for sacred buildings in the fourth book.

Liber 6, Caput 3

Italian: Capo quarto

French: Chap. IIII

7. Peristylia autem in transverso tertia parte longiora sint quam introrsus, columnae terram altae quam porticus latae fuerint. peristylorum intercolumnia ne minus trium, ne plus quattuor columnarum crassitudine inter se distent. sin autem dorico more in peristylo columnae erunt faciundae, uti in quarto libro de doricis scripsi ita moduli sumantur (li moduli siano sumpti) et ad eos modulos (ad epsi moduli) triglyphorumque rationes disponantur.

7. The cloister (‚peristylium’) is transversely one third part longer than across. The columns are to be as high as the width of the portico; and the intercolumniations of the ‚peristylia’ are not to be less than three nor more than four diameters of the columns. But if the columns of a ‚peristylium’ are of the Doric order, modules (modules, 93) are taken, and the triglyphs arranged thereby (selon ces modules, 93), as described in the fourth book.

Liber 7, praefatio

17. eam autem postea cum Demetrius Phalereus Athenis rerum potiretur, Philo ante templum in fronte columnis constitutis prostylon fecit. ita aucto vestibulo laxamentum initiantibus operique summam adiecit auctoritatem. in asty vero Olympio amplo modulorum (moduli) comparatu corinthiis symmetriis et proportionibus, uti supra scriptum est, arcitectandum Cossutius suscepisse memoratur, cuius commentarium nullum est inventum. nec tamen a Cossutio solum de his rebus scripta sunt desideranda sed etiam a C. Mucio, qui magna scientia confisus aedis Honoris et Virtutis Marianae cellae columnarumque et epistyliorum symmetrias legitimis artis institutis perfecit. id vero si marmoreum fuisset, ut haberet quemadmodum ab arte subtilitatem sic ab magnificentia et inpensis auctoritatem, in primis et summis operibus nominaretur.

17. This structure, when Demetrius Phalereus governed Athens, was turned by Philus into a prostyle temple, with columns in front, and by thus enlarging the vestibule, he not only provided accommodation for the noviciates, but gave great dignity to its appearance. Lastly, in Athens it is said that Cossutius was the architect of the temple of Jupiter Olympius, which was of large dimensions, and of the Corinthian order and proportions (de modules ou mesures fort amples, & de symmetries Corinthiennes, 101+), as above mentioned. From the pen of this man no treatise is extant; nor is it from him alone that such would have been less desirable, than from Caius Mutius, who with great science, and according to the just rules of art, completed the cell, columns, and entablature of the temples of Honour and Virtue, near the trophy of Marius, a work, which, had it been of marble, and thereby endowed with the splendour and richness which the material must have added, would have been reckoned among the first and most excellent temples.

Liber 10, Caput 8

Italian: Capo XIII

French: Chap. XIII

6. itaque cum pinnae manibus tactae propellunt et reducunt continenter regulas alternis obturando foramina alternis aperiundo, e musicis artibus multiplicibus modulorum varietatibus (varietate de moduli) sonantes excitant voces. Quantum potui niti ut obscura res per scripturam dilucide pronuntiaretur contendi, sed haec non est facilis ratio neque omnibus expedita ad intellegendum praeter eos qui in his generibus habent exercitationem. quodsi qui parum intellexerit ex scriptis, cum ipsam rem cognoscet profecto inveniet curiose et subtiliter omnia ordinata.

6. By the quick motion of the levers still compressing the air, it finds its way through the apertures of the stops, and fills the channels with wind. Hence, when the keys are touched by hand, they propel and repel the rules, alternately stopping and opening the holes, and producing a varied melody (engedrant plusieurs diversites d’harmonie, 145) founded upon the rules of music. I have done my utmost to give a clear explanation of a complex machine. This has been no easy task, nor, perhaps, shall I be understood, except by those who are experienced in matters of this nature. Such, however, as comprehend but a little of what I have written, would, if they saw the instrument, be compelled to acknowledge the skill exhibited in its contrivance.

Liber 10, Caput 11

Italian: Capo XVI

French: Chap. XVI

2. nam quae fiunt in capitibus foramina, per quorum spatia contenduntur capillo maxime muliebri vel nervo <torti> funes, magnitudine ponderis lapidis quem debet ea ballista mittere et ratione gravitatis proportione sumuntur, quemadmodum catapultis de longittudinibus sagittarum. itaque ut etiam qui geometriam non noverunt habeant expeditum, ne in periculo bellico cogitationibus detineantur, quae ipse faciundo certa cognovi quaeque ex parte accepi a praeceptoribus finita exponam, et quibus rebus Graecorum pensiones ad modulos habeant rationem (a le mensure conformitate), ad eam ut etiam nostris ponderibus respondeant tradam explicata.

2. For instance, holes are made in the capitals, and through them are brought the cords, made either of woman's hair, or of gut, which are proportioned to the weight of the stone that the ‚balista’ is to throw, as in the ‚catapultæ’ the proportions are derived from the length of the arrow. But that those who are not masters of geometry and arithmetic, may be prepared against delay on the occasions of war, I shall here state the results of my own experience as well as what I have learnt from masters, and shall explain them, by reducing the Greek measures (mesures, 149+).to their correspondent terms in our own.

On water pipes

Liber 8, Caput 6

Italian: Capo VII

French: Chap. VII

1. Ductus autem aquae fiunt generibus tribus rivis per canales structiles, aut fistulis plumbeis, seu tubulis fictilibus quorum hae sunt rationes (con li rivi p li structili canali: aut con le fistule di plumbo: o vero con li tubuli fictilii). si canalibus ut structura fiat quam solidissima solumque rivi libramenta habeat fastigata ne minus in centenos pedes sicilico, eaeque structurae conformicentur ut minime sol aquam tangat. cumque venerit ad moenia, efficiatur castellum et castello coniunctum ad recipiendam aquam triplex inmissarium, conlocenturque in castello tres fistulae (tre fistule) aequaliter divisae intra receptacula coniuncta, uti cum abundaverit ab extremis, in medium receptaculum redundet.

1. Water is conducted in three ways, either in streams by means of channels built to convey it, in leaden pipes or in earthen tubes ( Fosses ou trenchees, ... Canaulx de pierre bien cymentes, ... goulets de Plomb ou tuyaux de terre cuytte, 118), according to the following rules. If in channels, the structure must be as solid as possible, and the bed of the channel must have a fall of not less than half a foot to a length of one hundred. These channels are arched over at top, that the sun may strike on the water as little as possible. When they are brought home to the walls of the city a reservoir (castellum) is built, with a triple cistern attached to it to receive the water. In the reservoir are three pipes (tuyaux, 118+) of equal sizes, and so connected that when the water overflows at the extremities, it is discharged into the middle one,

2. item e medio ponentur fistulae (le fistule) in omnes lacus et salientes, ex altero in balineas ut vectigal quotannis populo praestent, exque ustio in domos privatas ne desit in publico. non enim poterunt avertere, cum habuerint a capitibus proprias ductiones. haec autem quare divisa constituerim, eae sunt causae et uti qui privatim ducent in domos vectigalibus tueantur per publicanos aquarum ductus.

2. in which are placed pipes (goulets, 118+) for the supply of the fountains, in the second those for the supply of the baths, thus affording a yearly revenue to the people; in the third, those for the supply of private houses. This is to be so managed that the water for public use may never be deficient, for that cannot be diverted if the mains from the heads are rightly constructed. I have made this division in order that the rent which is collected from private individuals who are supplied with water, may be applied by collectors to the maintenance of the aqueduct.

4. Sin autem fistulis plumbeis (le fistule plumbeae) ducetur, primum castellum ad caput struatur, deinde ad copiam aquae lumen fistularum constituatur, eaeque fistulae e castello conlocentur ad castellum quod erit in moenibus fistulae ne minus longae pedum denum fundantur. quae si centenariae erunt, pondus habeant in singulas pondo MCC, si octogenariae pondo DCCCCLX, si quinquagenariae pondo DC, quadragenariae pondo CCCCLXXX, tricenariae pondo CCCLX, vicenariae pondo CCXL, quinum denum pondo CLXXX, denum pondo CXX, octonum pondo C, quinariae pondo LX.

e latitudine autem lamnarum, quot digitos habuerint, antequam in rotundationem flectantur, magnitudinum ita nomina concipiunt fistulae (le fistule). namque quae lamna fuerit digitorum quinquaginta, cum fistula perficietur ex ea lamna, vocabitur quinquagenaria similiterque reliquae.

4. If the water is to be brought in leaden pipes (par des Goulets de Plomb, 119), a reservoir is first made near the spring, from whence to the reservoir in the city, pipes are laid proportioned to the quantity of water. The pipes must be made in lengths of not less than ten feet: hence if they be

• one hundred digits wide (centenariæ), each length will weigh • twelve hundred pounds; if

• eighty digits (octogenariæ), • nine hundred and sixty pounds; if

• fifty digits (quinquagenariæ), • six hundred pounds; if

• forty digits (quadragenariæ), • four hundred and eighty pounds; if

• thirty digits (tricenariæ), • three hundred and sixty pounds; if

• twenty digits (vicenariæ), • two hundred and forty pounds; if

• fifteen digits (quinumdenum), • one hundred and eighty pounds; if

• ten digits (denum), • one hundred and twenty pounds; if

< octonum pondo C, >

• five digits (quinariæ), • sixty pounds.

It is to be observed that the pipes (ces lames de Plomb, 119) take the names of their sizes from the quantity of digits in width of the sheets, before they are bent round: thus, if the sheet be fifty digits wide, before bending into a pipe, it is called a fifty-digit pipe; and so of the rest.