SECT. II. EARLY USE OF GEOMETRY AND OF A MEASURE. The idea is now generally sanctioned, that the medieval architects had some settled system of proportioning their designs either by simple geometric forms or by combinations of them. It will be our endeavour to indicate the sources whence the facts on this subject can be drawn, and to notice such of the details as our space will permit. The knowledge of geometry previous to, and in, the 12th century has been commented upon in par. 309, et seq. The Album of Wilars de Honecort, an architect living in the middle of the 13th century, exhibits the use of geometry in various ways. This manuscript was published in facsimile by M. Lassus in 1858, and an English translation was edited by Professor Willis in 1859. The sketches also show a certain mastership of figure drawing, besides many designs of portions of buildings. Some original drawings still exist of Reims Cathedral, known to be before 1270, thus of the same period as those of Wilars, and two of them have been published in the Annales Archéologiques, vol. v. page 92. The drawings were traced with a masterly line; they only showed how the design was to be arranged; and by means of axial lines only, the whole was set out as regularly as could be done for the most classical building. Scarcely any of the later original drawings still existing in many continental cities show the use of geometric figures (see fig. 1073.). Yet, on the 14th of February, 1321, during the erection of the cathedral at Siena, five persons who had been appointed for the purpose reported that “the new work ought not to be proceeded with any further, because if completed as it had been begun, it would not have that measure in length, breadth, and height, which the rules for a church require." The old structure, it also appears, "was so justly proportioned, and its members so well agreed with each other in breadth, length, and height, that if in any part an addition were made to it under the pretence of bringing it to the right measure of a church, the whole would be destroyed." Della Valle, Lettere Sanesi, ii. p. 60; noticed in Hawkins, Gothic Architecture, 1813, p. 183. This statement would seem to prove that some system had existed. In par. 620, we have already mentioned the disputes on the great question of proportioning the cathedral at Milan, 1387-1392, by the foreign system of squares, or by the native theory of triangles. The first notice in England of this unique instance of a dispute appears to have been taken by J. W. Papworth, who presented in 1854 to the Institute of British Architects some extracts from the Records of the Board of Works for Milan Cathedral, published by Giulini, Memorie di Milano, 4to. Milan 1776, part 2, pp. 448-60 of the Continuazione. These notes further condensed show, that on the 1st of May, 1392, fourteen of the artists employed upon the works made affidavit of their opinion on ten points submitted to them, on the part of the German Enrico di Gamondia, who was one of the number. On the third point, thirteen declared that the said church, not including the intended cupola, should be raised non al quadrato ma fino al triangolo, that is to say, on the triangular proportion. The same opinion is given on the fifth point as to the versed sine of the vaulting. Enrico, who on all the points held a contrary opinion to the thirteen, was thereupon dismissed. Another meeting of similar character, held 26th of March, 1401, of thirteen artists employed on the building, and two amateurs, was not so nearly unanimous upon the question of the alterations proposed by the Frenchman Giovanni Mignotto, and upon that occasion Guidolo della Croce (one of those employed) declared that the alterations were correct, and that Mignotto was a verus operarius geometra, because his ratios were like those of the dismissed maestro Enrico. The dismissal of this Jean Mignot, 13th of October, 1401, was accompanied by a charge for the expense of pulling down the work that he had erected during two years. Although the chronicle makes the curious mistake that the magister Enricus and the magister Annex (i.e. Johann von Fernach, 1391-92), also a German, had advocated the triangular system, it rightly adds that the triangular system prevailed over that of the square; and the lines may be supposed to have been truly given by Cesare Cesariano. The conclusion we have arrived at in the matter is that the plan was designed on the principle of the square (exhibited in fig. 1231.), while the elevation was designed on that of the triangle (shown in fig. 1232.). Cesare Cesariano, the first transiator of Vitruvius, Como, 1521, terms the geometric principle of design," Germanic symmetry,” and “rule of the German architects.” Rivius who translated this work (Nur. 1548), names the order resulting from the triangle as "the highest and most distinguished principle of the stonemasons.' One principle rested on the arrangement of the square, or of the octagon which proceeds from it, in the same way as that of the equilateral triangle was based upon the hexagon or dodecagon which resulted from it. On this law of the square is founded the work by M. Roriczer, On the Ordi→ nation of Pinnacles, 1486, which was printed by Heideloff, in Die Bauhütte des Mittelalters in Deutschland, Nuremberg, 1844; and also by Reichensperger, who translated it int modern German, Trier, 1845. It was noticed in the Journal of the Archeological Institute of Great Britain, 1847; and translated in a concise manner by J. W. Papworth for the Architectural Publication Society, Detached Essay, 1848, with woodcuts. An appendix follows On the Construction of a Canopy, which was also given in Heideloff's publication. The square, or octagon system, maintained itself among the German stonemasons until the commencement of the 19th century. Heideloff relates that the chef-d'œuvre of Kieskalt, the last city architect of Nuremberg (1806), was founded on the rules used in Roriczer, and those in the book of instructions written 1506 by Laurenz Locher, architect of the Count Palatine, on the art of the stonemason, nach des Choresmaass und Gerichtigkeit, according to the measure and ordination of the choir." "The system depending on the equilateral triangle for its variety of form," states E. Cresy, Stone Church, 1840, " continued in use till the beginning of the 15th century in France, when it underwent a great and important change by the introduction of the isosceles triangle and its compound the pentagon. A pupil of Berneval, the designer of the Church of St. Ouen at Rouen, proved that these figures could furnish novelties in design. We can well imagine how displeasing this innovation must have been to the whole fraternity of masons; their mystery was invaded." Pommeraye, in his History of the Abbey of St. Ouen, mentions that the master was so incensed at the clergy preferring the rose window of the northern transept (fig. 1293.) executed by his pupil, where this innovation was first introduced, to that of the south (fig. 1288.), of his own execution, upon the ancient triangular system, that in a fit of jealousy he killed his rival, and was himself condemned to be hanged. (See page 1036.) In the year 1525, Albert Duerer published in German his Geometrical Elements, showing therein clustered columns, and a few other details of Gothic architecture, In 1532 a Latin edition was published at Paris, entitled Albertus Durerus, Institutionum Geometricarum; and in 1606 a second edition was printed at Arnheim. It is this author who first brings to our notice the use of a figure called the vesica piscis, which is explained in Sect. III. In 1589 Spenser published his Faëry Queene, and in it allusion is made to the proportion of a building in words which deserve attention (b. 2, canto 9, v. 21). In 1593 Sir Thomas Tresham erected the curious lodge at Rushton Hall, Northamptonshire, entirely constructed on the equilateral triangle; it contains one room of an hexagonal form; the upper windows are mostly triangular openings (Builder, iii. 538. 550.). Stieglitz, in Altdeutscher Baukunst, 4to. Leipzig, 1820, records the possession of a manuscript Treatise on Architecture, giving the rules and instructions according to which the ancient werkmeisters and steinmetzen worked. Judging from the character of the handwriting, it must belong to the middle of the 17th century, and this is also indicated by the drawings which exhibit the Italian style of that epoch. But the rules for the construction of churches belong to a more remote period, and the author of the manuscript states that these rules were never described, but were transferred in a traditional way to, and kept by, the artists, who called them, like the ancients, Measure of the Choir and Justice. It seems to be the only written directions for a building which has come down to us. The drawings in it, which are only shaded, are finely executed by a steady and practised hand, They show the formation of the several cornices, mouldings, jambs for doors and windows, plinths, and arches, and also the formation and the arches of the vaulting. The building is proved to have strict rules and an established module, according to which all the members are regulated by the ensemble of the structure, and the whole is again regulated by the members. The choir is considered as the key, and after its breadth is regulated, the thickness of the enclosure-wall, and also all the dimensions for the cornices and other members are obtained. Thence the saying, "Measure of the Choir and Justice." At first, from a given circle an octagon is to be constructed, and according to it, the ground-plan and the pentagonal projection of the choir are to be devised. Should the choir contain 20 feet in the clear, its wall would be 2 feet thick; and if 30 feet wide, then 3 feet. The pillars of the choir are commonly 25 feet thick at their base, exclusive of the ground table (schrägesims), and the depth is double of the thickness. The width of the windows is regulated by the space between the columns, which is divided into 5 parts: 3 are given to the window in the clear, together with the mullions. If the choir be very extensive, and therefore the lights of the windows be too wide, in such case intermediate mullions are introduced; but small windows have only one main or two subsidiary mullions. The nave and aisles are regulated after the manner of the choir, being made equal to it in width, yet in such a manner that the pillars, although equal in thickness to the wall of the choir, do not run in the same line of the opening, but project with three sides of their octagonal form. The breadth of the choir being divided into 3 equal parts, 2 are to be given to each aisle, including the wall of the choir. The same dimension of two such parts is applied to the pillars from one centre to the other, which shows at the same time the space for the buttresses on the enclosure-wall. As, in consequence of the aisles, the nave portion requires a wider vaulting than the choir, the enclosure-wall of the nave ought to be constructed one-third thicker than that of the choir. The buttresses are the same in thickness and breadth as for the choir. The windows are kept of the same width throughout the whole structure. The transept projects as far as the breadth of the aisles, and its wall has the same thickness as the wall of the choir. The length of the church is for the most part regulated according to the requirements of the population. The towers, erected on both sides of the façade, are devised from the width of the inner shafts and external pillars, which width formed into a square gives the external enclosureline of the towers. If only a single tower be constructed, it ought to be regulated after the choir, and agree with the same. The thickness of the tower-wall is regulated by the height of the tower itself. Thus for every 100 feet of height, 5 feet in thickness is required for the wall. Then, to this thickness one half more is to be given for the foundation. But if the ground be firm and good, this thickness need only be kept as far as the base, and thence gradually reduced. The formation of the groining is not so clearly developed by the editor, and we therefore omit it. A choir The outline and elevation of the choir are also calculated from its width. which is 20 feet broad, ought to be one and a half or twice as high. The latter height was called the real height. An ordinary choir requires only four tables or strings. The ground table (schrägesims) rises from the floor or ground to a height equal to the thickness of the counterforts. The string course (kaffsims) above is placed as high as the distance between the pillars. The supporting string (tragesims) ought not to rise higher than the capital of the pillars in the interior of the choir. The top, or roof-cornice (dachsims) ought to be placed at least half a foot higher than the vaulting. The pillar-cornice is measured by taking the thickness of the pillars twice down from the top cornice. A choir of greater height requires more cornices and decorations. The height of the nave portion is fixed by taking twice the width of the choir, and this is measured from the ground-table to above the top-cornice. The ground floor of the tower ought to be as high as the whole tower is broad, and the upper floors to be regulated accordingly. We have only to add that the form given to the towers by the author of the MS. shows the Italian style of his epoch, whilst the church itself is constructed in German fashion, that is, with high pointedarched windows and buttresses, which are drawn without any mouldings. SECT. III. THE VESICA PISCIS. If on the diameter of a circle (fig. 1225.), with an axis perpendicular to it, an equilateral triangle be described, whose vertical height shall be equal to the semi-diameter of such circle, and from the angles of the triangle on the diameter, with a radius equal to one side of the triangle, arcs of circles be described cutting each other superiorly and inferiorly, the figure described is that which is called the vesicu piscis, or fish's bladder. Fig. 1225. The Greek word ixeùs, signifying a fish, seems to have been in early ages a mystical word, under which Christ was denominated, “ Eò quod in hujus mortalitatis abysso, velut in aquarum profunditate, sine peccato esse potuerit, quemadmodum nihil salsedinis a marinis aquis pisci affricatur; that is, Because in the unfathomed deep of this mortal life he could exist without sin, even as a fish in the depths of the sea is not affected by its saltness. The term, too, at a very early period, furnished an anagram, whose parts were expanded into the expression, Ἰησοῦς Χριστὸς Θεοῦ Υἱὸς Σωτήρ. The initials of these words were, in their turn, expanded into a long acrostic (to which reference may be had, sub voce Acrostichia, and also under the term Ichthys, in Hoffmann's incomparable Lexicon) on the Day of Judgment, said to have been delivered, divino afflatu, by the Erythrean sybil, but much more resembling the hard-spun verses of a learned and laborious man than the extemporaneous effusions of a mad woman. This acrostic is recognised by Eusebius, and by St. Augustine, Civ. Dei., &c. There is nothing, declared Mr. Gwilt, to afford any proof of the connection of this monogram with the form and plan of the churches erected during the mediæval period of the art. Apology, perhaps, would be due for any digression upon it, had it not been for an opinion in favour of its use expressed by the late Professor C. R. Cockerell, whose talents and learning deservedly ranked high in the eyes of the public, in his essay on the Architectural Works of William of Wykeham, read 1845, before the Archæological Institute of Great Britain and Ireland. Ramée, in his Histoire, has also gone more at length into this subject. Professor Cockerell likewise noticed that the writers of the 16th century, Cesariano 1521, Caporali 1536, and De Lorme 1576, recommend this figure, chiefly as that geometrical rule by which "two lines may be drawn on the ground at right angles with each other in any scale, according to the conception of Euclid's mind." From an early time the triangle seems to have been associated with as much mystery and veneration as the number 3. Without here touching on symbolism, in its use, whether equilateral or isosceles-we cannot but perceive, both in one and the other, a tendency to the production of the pointed arch. The geometrical law for describing it is, as every one knows, founded on the intersection of two circles of the same radius (fig. 1226.) The Pythagoreans called the equilateral triangle, Tritogeneia. It was, according to Plutarch, the symbol of justice. The subdivision of the arcs bounding an equilateral triangle by other ares of equal radius, gives other modifications of the pointed arch, and by their intersections are obtained the skel ton lines of ornamented windows of Fig. 1226. an early period, which, at a later date, branched out into the most luxuriant forms. Mrs Jameson, in Sacred and Legendary Art, 3rd edition, 1857, vol. i. p 93, gives a drawing from an ancient Greek picture, wherein the upper part of the representation of the Infant Christ is placed in a figure formed of four equilateral triangles (which produce the dodecagon). The head of the infant may be supposed to occupy in the diagram the site of a chancel, the body in the place of a nave, and the hands, being held forth, assume the place of the transepts. SECT. IV. MODERN INVESTIGATIONS. Among the investigators early in the present century was C. L. Stieglitz, who published his Altdeutschen Baukunst, 1820, as already mentioned. Therein he states that, "with regard to the ground-plans of churches, it seems that two sorts have been employed. With the first, the nave of the church was in breadth equal to that of each of the aisles. With the second, if, for instance, such a breadth be taken as an unit, the breadth of the nave would be the diagonal line of the square, and the breadth of each aisle an unit. The length of the interior of the churches of these two sorts, measured from the entrance to the choir, contains usually nine units The church of St. Stephen, at Vienna, is an illustration of the first system; and the Münster at Strassburg of the second. The cathedral at Cologne is a variety of the first plan. In this instance the nave is the breadth of its aisle, but each aisle is divided into two by a row of columns in the middle. The fore-part of the church has usually three diagonals of the square for its breadth, wherefrom the unit, should it be unknown, can easily be deduced. According to this principle, if the whole inner breadth of the church be considered as the root of a square, the diagonal of the same will be equal to the whole breadth of the front on the outside. In the first sort of plan, the nave of the church is raised either to an equal height with the aisles or a little higher. In the second, however, the nave is constructed far higher. Owing to the first disposition, both the nave and the aisles are brought under a single roof, as in St. Stephen's at Vienna. In those of the second sort, the nave and the choir (which was equal in breadth to the nave) had each, as well as the aisles, a separate roof. The wall of the nave and of the choir, on account of its small thickness, comparatively with its height, required some support at the sides, and this was provided for by arched counterforts or flying buttresses from the enclosure-wall of the aisles. The cathedral at Cologne shows a similar disposition, although the nave is equal in breadth to one of the aisles, wherefore the aisles are divided into two rows by pillars, for the purpose of giving to this portion of the vault (when it will be finished), on account of its smaller arching, a less height than the one intended for the vault of the nave and of the choir. The ground plan of this cathedral is a Latin cross. The aisles surround the choir, which rises high above them, and therefore the enclosure-wall of the choir is connected with the pillars of the outer wall by means of arched buttresses. According to Boecker's observations, the number 7, consecrated by religion and philosophy, is applied all over the parts of this edifice, not only in the measures of length, in the proportions of height, in the pillars of the nave, as well as in those of the choir, but also in the decorations and details." The inner height of the choir is stated to be 161 feet; the height to the gable, corresponding to the entire width of the west front, is 231 feet; the (proposed) height of the towers is equal to the entire length of the building, 522 feet; the height of the side aisles $70 feet, and so forth. In a similar manner, at the entrances on either side, are pedestals for seven statues; in each of the entrances as many spaces for statues; there are 14 corner tabernacles on the southern tower; and with attention, the same combination may be traced in all the details. Twenty years appear to have elapsed, and then Hoffstadt published the Gothisches ABC Buch, Frankfort, 1840, which enters fully into the formation of details by a geometric system. In England, the subject was not thoroughly taken up until 1840, when R. W. Billings published his Attempt to Define the Geometric Proportions, &c. He therein considers that Clerestory during the Norman period, no intricate figures were used for regulating the proportions of the various parts of buildings. He exhibits the early simplicity of propor tion, in the elevation of a compartment of the Norman nave of Gloucester 1 square. Cathedral, as in the annexed fig. 1227. Something of the same sort of equality may be perceived at Winchester Cathedral, as shown in fig. 1266., where the width K I. gives the heights I. M and M N; the diagonal of this square gives the height LO; and O P is a square in height; but we are at a loss to regulate the upper part, unless the triangle be used, when PQ will give the upper point at R, the centre of the head of the semicircular window. Triforium square. Arch square. Column 14 square. In the projection of the plans of the nave and choir of Carlisle Cathedral (fig. 1228.), the architect, says Mr. Billings, was guided by the repetition of a circle whose diameter in the first or Norman part was the extreme width of the building; and in the second part, erccted 200 years subsequently, it was the width between the internal walls. The distribution and even the substance of the columns was regulated by some recognisable subdivision of the circle; and a circle, or are of a circle regulated by the width of each compartment thus formed, was the basis upon which the heights of the different portions of the interior were framed. The woodcut must suffice to show this principle as regards the Fig. 1227. plan. The precise divisions will not probably answer in any other build. ing, but must be modified. The east wall, it will be perceived, is included within the boundary lines; this is also the case at the Temple Church, London. From the result of calculations, the scale for the choir was made 8 parts of the radius of the principal circle, orth of the diameter; this sixteenth part is equal to 4 feet 6 inches (or a yard and a half), In the nave, the piers and the dimensions of the building may be calculated therefrom. are exactly 5 feet 8 inches, or th of the diameter, and it was this exact division, states Mr. Billings, which induced the application of the scale of twelve parts to the diagram of that end of the building. 8.311.105.0 17.1. In every portion of the elevation of a compartment of the choir (fig. 1229), there is evidence of its geometric formation. The student must have recourse to the publication itself for the further detailed development of the system in connection with this figure, but it is necessary to state that from the dimensions of the arch Mr. Billings divided the width between the centres of the piers into 6 parts for a scale; this gives all the remaining proportions. The same scale of 6 parts of the width was applied by Mr. Billings to a bay of the presbytery of the choir at Worcester, and finding it satisfactory, though totally at variance in its proportions, with the exception of the principal arch, it was considered as confirmatory of the theory. These two examples are of nearly the saine period in the style. In 1846 Mr. Billings published his Architectural Antiquities of the County of Durham, and in collecting the measurements of its churches he was led to compare their proportions. The result is given by him in two tables, proving a groundwork of squares, and this he states "would at once account for the non-existence of ancient working drawings, for the designer would only have to communicate a rough diagram of his plan, bounded by series of equal squares, and give the dimensions of one, to be properly understood by a practical man. Most singularly, the measure is in each case one square yard (as above noticed). No less than six of the chancels are 15 feet; three others are 18 feet; and three of 21 feet. At Houghton, the widths of the chancel, of the transept, and the distance between the columns of the nave, are all 15 feet." 20 soft. big 1229. BAY IN CHOIR; CARLISLE, |
