DISCOVERY 



19 



the churches of Treves, Speyer, and Freiberg have 

 their plans based on either one or two hexagons. It 

 is especially interesting to find, by examination of the 

 plans in Sir E. A. Wallis Budge's handbook of the 

 Nile, that the temples of Kamak, Medinet Habu, and 

 Denderah reveal the same method of planning.^ 



The revival of classic architecture gave birth to a 

 multitude of arbitrant' rules derived from the study 

 of the finest buildings of Greece and Rome in the hope 

 of emulating their beauty of proportion. Some of 

 these rules, even when divorced from classic design, 

 remained in use until the Victorian age. Thus it was 

 held that beauty of design in any rectangle, such as a 

 window opening or panel, was ensured when the width 

 and length equalled respectively the side and the 

 diagonal of a square, that is to say, were as i to 1-414. 

 For simplicity the approximation 7 to 10 was used by 

 the craftsman. The same rule was also applied to the 

 designing of elliptical brick arches over doorways and 

 will be found recommended for this purpose in 1S40 

 in the Surveyor and Engineer, a technical journal of 

 the time. 



The construction of a right angle by means of a 

 triangle whose sides were in the ratio of 3.4.5 was a 

 process familiar to the " rope stretcher " or surveyor 

 of Egypt, China, and India in the earliest ages, and the 

 influence exercised by this figure on the design of 

 buildings in later times was dealt with at some length 

 in the previous article in Discovery.- Some further 

 examples of its use are now offered, but to show in 

 detail the various methods in which it was applied 

 would necessitate more space for illustrative plans 

 than can well be spared here. The references, then, 

 are intended chiefly as indicating where confirmation 

 of the statements of its use may be found. If the 

 plans of York Minster be examined, it will be seen 

 that three diamonds — each formed from four 3.4.5 

 triangles with their four right angles in juxtaposition, 

 in the manner formerly described — will fill the width 

 and length of the nave from the west end to the altar, 

 and another half-diamond will complete the length 

 to the east end of the building. In Beverley Minster 

 and, possibh', in Newark Church, the same figure 



• In the previous article in Discovery, the Manchester Free 

 Trade Hall was referred to as having been designed from the 

 proportions of the Vesica Piscis, which is the figure formed by 

 placing two equilateral triangles base to base. By calculation 

 it can be shown that in such a figure the relation of width to 

 length is i to 1-732. An example of the use of this propor- 

 tion in Indian architecture so long ago as 257 B.C. will be found 

 in Mr. E. B. Havell's Handbook of Indian Art (John Murray, 

 1920). On p. 24, in the description of Lomas Rishi Cave, near 

 Gaya, it is stated that the interior hall measures 33 ft. long 

 and ig ft. wide. These dimensions are in the ratio of i to 

 1-736, a negligible difference. 



» Vol. II, No. 19, July 192 1. 



determines the principal proportions. In the church 

 at Bradford-on-Avon, built by St. Aldhehn in the 

 eighth century, the dimensions of the chancel, accord- 

 ing to Sir W. Besant's London, are 10 ft. by 13 ft. 2 in. 

 On the supposition that the 3 by 4 rectangle had been 

 the originating figure, it will be seen that a width of 



10 ft. should theoretically require a length of 10 + — . 



or 13 ft. 4 in., being within 2 in. of the recorded length. 

 A building which is permeated throughout by this 

 root-figure is Magdalen College, Oxford. In the 

 British Architect of September 15, 1907, measured 

 elevations will be found, and investigation will show 

 that the pitch of the roofs is based on the use of the 

 3.4.5 triangle, while the whole fa9ade of the eleva- 

 tion may be divided into rectangles measuring 3 by 4, 

 each rectangle being composed of two 3.4.5 triangles 

 placed " head to tail." 



The interior angles of the 3.4.5 triangles are respectively 

 90^. 53^ 8', and 36° 52'. The architect, when preparing 



6< 



5' ^'A 



Fig. I,— setting out the hes.^pla. 



his drawings, included among his instruments a set- 

 square made to this shape, and when he wished to 

 design a gable, either at the end of a roof or as an 

 ornamental feature, he made use of such one of the 

 three angles as suited his purpose. Examples of aU 

 three uses are plentiful ; as an example of the use of 

 the intermediate angle, reference may be made to the 

 measured drawings of a richly decorated sepulchre at 

 All Saints' Church, Hawton, illustrated in the British 

 Architect of February ig, 191 1. French and Italian 

 architecture of two or three centuries ago exhibit many 

 instances of the same controlling methods. 



The most romantic of all discoveries in this con- 

 nection, and one which lifts the theory into the domain 

 of popular interest, is that which clearly establishes 

 its relation to the Pyramids of Egypt. It is generally 

 supposed that if anything can give weight to the 

 validity of a new idea, whether it relate to the pre- 

 cession of the equinoxes, the squaring of the circle, 

 the chronology of history, the weights and measures 

 of England, or the coinage of America, no argument 

 can surpass the calhng in of the Pyramids as witnesses 

 to its truth. Their confinnatory evidence is irresistible 



