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Updated: June 11, 2025
There are two chief types, the longitudinal and the radial; but since these may exist either in plan or in elevation, four possibilities result: the longitudinal-horizontal, as in an aisle; the longitudinal-vertical, as in a tower; the radial-horizontal, illustrated by every equilateral plan triangle, square, regular polygon, and above all, the most perfect form of this type, the circle; and finally, the radial-vertical, of which domed spaces, like the Pantheon or St.
Hereafter you may be I fancy that I know you well enough to prophesy that you will be able to recognise in the equilateral triangle inscribed within the circle, and touching it only with its angles, the three supra-sensual principles of existence, which are contained in Deity as it manifests itself in the physical universe, coinciding with its utmost limits, and yet, like it, dependent on that unseen central One which none dare name.
Ivan he had already placed on the nearer side, and Alexis at the bottom so that they were thus set at the three angles of a triangle, nearly equilateral. On assigning to each of them his station, the Indian further instructed them to creep forward among the bushes which still separated them from the water and to do so without making any noise, till they should hear a "whoop" from himself.
It is a singular fact that the large towns of Holland have remarkably regular forms, although they were built on unstable land and with great difficulty. Amsterdam is a semicircle, the Hague is a square, Rotterdam an equilateral triangle.
He placed this triangle on the bank at A B C, sighting the line A B for the little Hemlock D, and put three pegs in the ground exactly under the three pegs where the triangle was; moved the triangle to E F G and placed it so that F G should line with A C and E G with D. Now A G D also must be an equilateral triangle; therefore, according to arithmetic, the line D H must be seven-eighths of A G. A G was easily measured 70 feet.
Six of these united form eight solid angles, each of which is made by the combination of three plane right angles; the figure of the body thus composed is a cube, having six plane quadrangular equilateral bases. There was yet a fifth combination which God used in the delineation of the universe.
The following quotation is typical of the leading essay writers on this subject: "The Equilateral Triangle enters largely into, if it does not entirely control, all mediæval proportions, particularly in the ground plans. With slight deviation, most, if not all, the ground plans of the French Cathedrals are measurable in this manner, and their choirs may be so measured almost without exception.
In this vehicle were pent up, first, the stately figure of Mr. Oldbuck himself; secondly, the scarce less portly person of the Reverend Mr. Blattergowl, minister of Trotcosey, the parish in which Monkbarns and Knockwinnock were both situated. The reverend gentleman was equipped in a buzz wig, upon the top of which was an equilateral cocked hat.
But, after the period of the renaissance, a better spirit and a purer taste began to pervade the artists of the church, and thenceforth the Supreme Being was represented only by his name the tetragrammaton inscribed within an equilateral triangle, and placed within a circle of rays.
The most I can do is to name the architects of the most famous of the palaces and draw the reader's attention to the frequency with which the lovely Ducal gallery pattern recurs, like a theme in a fugue, until one comes to think the symbol of the city not the winged lion but a row of Gothic curved and pointed arches surmounted by circles containing equilateral crosses.
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