BOOKS ON ARCHITECTURE
|| Goldmann, Nicolaus
Vitruvii voluta ionica..., in M. Vitruvii... De architectura libri decem...
||Amsterdam, L. Elzevier, 1649
||Besançon, Bibliothèque municipale, 66878
Nicolas’ Goldmann’s opuscule on the Ionic volute appears in the Vitruvian encyclopedia published by Jean de Laet in 1649. Goldmann was attracted by the uncommon symmetry of the volute in the Ionic capital, and made a description of it that was as precise as it was faithful to Vitruvius’ text, noting with assurance that “ Ex omnibus capitulis columnarum, a Vitruvio descriptis, cum Scamozzio affirmamus, solum Ionicum nobis arridere ” (we assert with Scamozzi that among all the capitals of the columns described by Vitruvius only the Ionic one smiles on us) (p. 267). In order to understand Goldmann’s method, it is necessary to follow the initial diagram (p. 266) where he sometimes designates the points with letters, according to the modern custom, sometimes with Arabic numerals, (often repeated), and sometimes with Roman numerals. He divides the cathetus (the vertical line perpendicular to the abacus which goes through the center of the volute) into 9 ½ parts, thus obtaining the diameter of the eye (IK in the diagram). Next, he divides this diameter into four equal parts and on the part between points 1 and 4 on the detail of the enlarged eye he constructs the square marked 1, 2, 3, 4. One will notice that the side 1, 4 of the square is equal to radius IE of the eye, and that segment 2, 3 is tangent to the eye at point F. Then he divides segment 1, 4 into six equal parts and starting with these division points he draws several lines parallel to radius EF, which divide into three equal parts the segments drawn from the center of eye E towards corners 2 and 3 of the square. He adds the points 1, 2, 3 and up to 12, as indicated in the detail of the eye; these points designate the twelve centers of the quadrants making up the volute. Once the volute is drawn this way, he transfers onto the drawing the starting points of the quadrants, numbering also them from 1 to 12. It remains to determine the listel which surrounds the volute, with a similar scroll. In the eye he takes a ninth part of half of the side of square IE, marks point 13 under point 1 and point 16 under point 4. He divides segments E, 16 and E, 13 into three equal parts; starting from these he draws lines on the diagonals, obtaining the twelve other points necessary for drawing the listel, numbered from 13 to 24.
This volute, very similar to the one in the Theatre of Marcellus in Rome, is drawn with an approximately geometric line and is very pleasant to look at. In addition, it follows Vitruvius’ text in many ways. For example, the centers of two successive arcs and their point of contact are aligned. Goldmann’s construction is an alternative to the one, simpler and probably better known for that reason, by the painter Giuseppe Salviati (Regola di far perfettamente col compasso la voluta...,Venice, F. Marcolini, 1552, pp. 11-15); but it is substantially different from the Archimedian interpretation of the Vitruvian volute made by Giovan Battista Bertani in 1558.
If we compare Goldmann’s volute with Salviati’s (1552) which was followed almost without changes by Andrea Palladio in the Vitruve by Daniele Barbaro (moreover to whom it is dedicated), by Palladio himself in his own treatise (1570) and by Philibert De l’Orme (1567), the overall principles, inspired by Vitruvius’ text, turn out to be the same: construction in quadrants and only three revolutions. In his Regola, Salviati, drawing his inspiration from proposition five of Euclid’s book IV, reduces the radius of each quadrant of the first revolution by half of the diameter of the eye, by a third for the second revolution and by a sixth for the last one. Salviati specifies that this method is consistent with an interpretation of the Vitruvian passage (III, 5, 6), “Tunc ab summo sub abaco”, which he translates as: “allora dal sommo sotto l’abaco per ogni azione di tetranti comincia a minuire il dimidiato spatio dell’occhio insino che ritorna nel medesimo tetrante”, deducing the reduction of half of the space of the eye for each quadrant.
Independently of Salviati, Goldmann respects the same principle, but through a more complex calculation. He gives up the method of the twelve centers placed in the middle of the four quadrants of the eye, and transfers them on only two quadrants, leaving two centers outside the eye. In order to remain faithful to the passage in which Vitruvius wrote, “in singulis tetrantorum (sive quadrantum) actionibus, dimidiatum oculi spatium minuatur, donicum in eundem tetrantem, qui est sub abaco (et in 5 incipit), veniat” (p. 267), he looks for this new position of the centers in order to arrive at an exact geometry by the union of all the quadrants, with the precise intention of finding the end of each revolution of the spiral on the cathetus line itself, as only Serlio had tried to do in 1537, in a volute which was not very Vitruvian. For his part Goldmann obtains a volute similar to the one in the Theatre of Marcellus, opening the way to the English architect William Newton’s stimulating research in his edition of Vitruvius published in 1771.
Goldmann’s interpretation of Vitruvius’ passages determining the symmetrical rationality of the Ionic volute showed particular originality (“his symmetriis conformabuntur”, III, 5, 5), already adroitly brought to light by the antique author. Thus Goldmann draws on this passage: “Recedendum autem est ab extremo Abaco (B) in interiorem partem, frontibus Volutarum, parte duodevigesima; (BC) et eius dimidia (BA) ” (ibid.); next, he divides the abacus into 18 equal parts; at 1/18 starting at the edge of the abacus, that is length BC, he places the cathetus CD, and he makes a second setback BA equal to half of an eighteenth part starting at the same edge, drawing a second perpendicular line A 3. And when Vitruvius writes (III, 5, 6) “tunc ab linea (ID) quae secundum Abaci extremam partem (I) demissa erit, in interiorem partem alia (XVII, G) recedat, unius et dimidiatae partis (C, XVII) latitudine” (p. 267), Goldmann eliminates the conjunction “and” between “unius” and “dimidiate”, reading “unius dimidiate partis”. On the top of the abacus, where Vitruvius reduces the lines in question to one and a half parts, he makes sure that point XVII is a half part away from C; he lowers the perpendicular XVII G, which with line A 3 determines the width of the eye. In doing this, he does not take into account Vitruvius’ text literally, which, a few lines further, explains that the width of the eye must be one of the eight parts (III, 5, 6; Goldmann, ibid.: “signeturque ducaturque ex eo centro rotunda circinatio, tam magna in Diametro, quam una pars ex octo partibus est; ea erit oculi magnitudine, et in ea Catheto (hoc est Normae) respondens Diametros (FG) agatur”). In conclusion, it is not possible to say that Goldmann provides a totally faithful restitution of the Vitruvian volute, even if he follows the text of the De architectura quite closely.
Maria Losito (Rome) – 2012
J. Goudeau, Nicolaus Goldmann (1611-1665) en de wiskundige architectuurwetenschap, PhD thesis, Groningen, 2005.
M. Losito, "La ricostruzione della voluta ionica vitruviana nei trattati del Rinascimento", Mélanges de l’École Française de Rome. Italie et Méditerranée, 105-1, 1993, pp. 133-175.
M. Losito, Il capitello ionico nel Rinascimento italiano toscano, romano e veneto (1423-1570). Dissertazione di Perfezionamento in Storia dell'Arte e dell'Archeologia Classica, Pisa, Scuola Normale Superiore, 1993.
M. Losito, "La ricostruzione della voluta del capitello ionico vitruviano nel Rinascimento italiano (1450-1570)", P. Gros (ed.), Vitruvio de Architectura, translated by A. Corso and E. Romano, Turin, Einaudi, 1997, pp. 1409-1428.
M. Losito, "Symétrie » de la nature dans le dessin de la volute ionique vitruvienne-archimédienne", R. Gargiani (ed.), La Colonne. Nouvelle histoire de la construction, Lausanne, Presses polytechniques et universitaires romandes, 2008, pp. 164-171.
M. Losito, notes U A 619 v°, U A 1192 r° and v°, U A 4151 r° and v°, U A 4152 r°, U A 4153 r°, U A 4154 r°, U A 1553 r° and v°, C. L. Frommel & G. Schelbert (ed.), The Architectural Drawings of Antonio da Sangallo the Younger and his Circle, Cambridge (Mass.), MIT Press, vol. III (forthcoming).
M. Newton, The Architecture of M. Vitruvius Pollio, Translated from the original Latin by W. Newton, London, I & J. Taylor, R. Faulder, P. Elmsly & T. Sewell for J. Newton, 1771, 1.