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angle of 420 apex architect architecture arcs beautiful centre chapter coincide construction correlations curves described in Plate diagonals of 660 diagram diameter diatoms discloses distance divided division drawn in Plate Egyptian triangle equal equilateral triangle examination example extreme and mean fifth progression five fourth progression geometric Greek gression ground plan harmonic height hexagon horizontal line ideal angle illustrated inscribed intersect laws logarithmic spiral lower line lower pole mathematical mean proportion mean ratio measure Nature Nature's octagon octant outer Parthenon pass tangentally pentagon pentagram line perfect phyllotaxis points polar force portico position primary circle primary square prime circle principles produced progression of 6o0 proportional spaces Pythagorean triangle quadrant chords raking cornice rectangle of 420 regular polyhedron regular progression relation render represents result ruled secant second progression seen shell snow crystal spiral statements third progression tonic triangle of 6o0 unity vectors vertical line vesica piscis vibration width
Page 3 - The heavens themselves, the planets, and this centre, Observe degree, priority, and place, Insisture, course, proportion, season, form, Office, and custom, in all line of order...
Page 190 - Keeping the stretching weight or tension the same, 1 attach pieces of the string to the other forks, and determine in each case the length which swings as a whole. These lengths are in the ratio of 8, 4, 2, 1. 38. Hence the rapidity of vibration is inversely proportional to the length of the string. 39. Here the string, eight feet long, vibrates as a whole when attached to the fork a. I now transfer it to b, still keeping it stretched by the same weight. It vibrates when b vibrates ; but how ? By...
Page 2 - ... that in which each collaborates with the other, all engaged simultaneously upon and engrossed in one great whole, and all alike endowed with a scientific knowledge of the laws of Nature. Then the easel picture, which should be of secondary importance and not the first as we now make it, will take its proper place in our art history.
Page 266 - If from the examination of the general design we pass to the study of the details, every builder will be amazed at the innumerable precautions which have been taken in the construction, and at the manner in which the prudence of the practical mechanic has been united to the boldness of the artist full of resources and imagination.
Page 190 - beats" led Helmholtz to a new theory of harmony. Pythagoras had made the discovery that the simpler the ratio of the two lengths into which a string is divided, the more perfect is the harmony of the sounds produced by these two parts of the string.
Page 266 - This cathedral is very beautiful even in its present unfinished state, but it must be seen that everything is so well prepared in the substructure for the superstructure of the stone spires, that their absence is much to be regretted. As at present existing, there is in the construction and appearance of the towers a superabundant strength which is unjustifiable since they bear no weight...
Page 12 - Nature uses this as one of her most indispensable measuring rods, absolutely reliable, yet never without variety, producing perfect stability of purpose without the slightest risk of monotony.
Page 266 - Everywhere we find indications of a thoroughly understood method, of principles strictly observed, of a perfect knowledge of effect, a purity of style unequalled in modern art, an execution at once delicate and bold, without exaggeration and impressed with all the beauty that serious study and enthusiastic love can confer.