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LECTURE VIII
On Geometry
It is now incumbent upon me to demonstrate to you the great signification of the letter G, wherewith lodges and the medals of Masons are ornamented.
To apply it to the name of God only, is depriving it of part of its Masonic import; although I have already shewn that the symbols used in lodges are expressive of the Divinity's being the great object of Masonry, as Architect of the world.
This significant letter denotes Geometry, which, to artificers, is the science by which all their labors are calculated and formed; and, to Masons, contains the determination, definition, and proof of the order, beauty, and wonderful wisdom of the power of God in his creation.
Geometry is said originally to have signified nothing more than the art of measuring the earth, or any distances or dimensions within it; but, at present, it denotes the science of magnitude in general, comprehending the doctrine and relations of whatsoever is susceptible of augmentation or diminution. So to geometry may be referred the construction not only of lines, superficies, and solids, but also of time, velocity, numbers, weight, and many other matters.
This is a science which is said to have its rise, or, at least, its present rules, from the Egyptians, who by nature were under a necessity of using it, to remedy the confusion which generally happened in their lands by the overflowing of the Nile, which carried away yearly all boundaries, and effaced all limits of their, possessions. Thus this science, which consisted only in its first steps of the means of measuring lands, that every person might have his property restored to him, was called Geometry, or the art of measuring land; and it is probable that the draughts and schemes the Egyptians were annually compelled to make, helped them to discover many excellent properties of those figures, and which speculation continually occasioned to be improved.
From Egypt geometry passed into Greece, where it continued to receive new improvements in the hands of Thales, Pythagoras, Archimedes, Euclid, and others. The elements of geometry, which were written by Euclid,1 testify to us the great perfection to which this science was brought by the ancients, though much inferior to modern geometry; the bounds of which, by the invention of fluxions, and the discovery of an infinite order of curves, are greatly enlarged.
1 An old MS. on Masonry says, "Euclid was the pupil of Abraham, and in his time the river Nile overflowed so far that many of the dwellings of the people of Egypt were destroyed. Euclid instructed them in the art of making mighty walls and ditches, to stop the progress of the water; and by geometry, measured out the land, and divided it into partitions, so that each man might ascertain his own property." The MS. is incorrect in making Euclid cotemporary with Abraham; but it truly adds that he gave to Masonry the name of Geometry. -EDITOR.
The usefulness of geometry extends to almost every art and science; by the help of it, astronomers turn their observations to advantage, regulate the 4uration of time, seasons, years, cycles, and epoch as, and measure the distance, 'notions, and magnitude of the heavenly bodies. It is by this science that geographers determine the figure and magnitude of the whole earth, and delineate the extent and bearing of kingdoms, provinces, oceans, harbors, and every place upon the globe. It is adapted to artificers in every branch; and from thence, as I said before, architects derive their measures, justnesses, and proportions.
This naturally leads me to conjecture why the square is had by Masons as one of the lights of Masonry, and part of the furniture of the lodge.1 To explain my ideas on that matter, I will only repeat to you the words of a celebrated author, treating of the rise and progress of sciences. He says : -- "We find nothing in ancient authors to direct us to the exact order in which the fundamental principles of measuring surfaces were discovered. They probably began with those surfaces which terminated by right angles, and amongst these with the most simple. It is hard, indeed, to determine which of those surfaces, which are terminated by a small number of right lines, are the most simple. If we were to judge by the number of sides, the triangle has indisputably the advantage; yet I am inclined to think that the square was the' figure which first engaged the attention of geometricians. It was not till some time after this that they began to examine equilateral triangles, which are the most regular of all triangular figures. It is to be presumed that they understood that rectilinear figure first, to which they afterwards compared the areas of other polygons, as they discovered them. It was by that means the square became the common measure of all surfaces; for, of all ages, and amongst all nations of which we have any knowledge, the square has always been that in planimetery which the unit is in arithmetic; for though in measuring rectilinear figures we are obliged to resolve them into triangles, yet the areas of these figures are always given in the square." Thence I am led to determine that the square was the first and original figure in geometry, and as such was introduced to our lodges.2 The square was the figure under which the Israelites formed their encampments in the wilderness, and under which they fortified or defended the holy tabernacle, sanctified with the immediate presence of the Divinity.3
1 Appendix, I.
1 The square was the first geometrical figure which was brought into practical use by operative masons. In the construction of cities and private dwellings, camps and fastnesses, right angles were generally used; as in the ark of Noah, the camp of the Israelites, the cities of Babylon and Nineveh, with the temples of Egypt and India, or the established form of a Mason's lodge. The square is a symbol of perfection and happiness, arising out of morality and justice; and, with this meaning in view, it has been assigned to the Worshipful Master. Plutarch informs us, that "the incense offered at the evening sacrifice in Egypt is composed of no less than sixteen different ingredients; because their number forms the square of a square, and is the only number which, having all its sides equal, wakes its perimeter equal to its area; and also on account of the rich aromatic nature of those ingredients. -EDITOR.
3 The square is formed by uniting the hypothenuse, or side subtending the right angle of two right angled isoceles triangles. Of trilateral and quadrilateral figures, none are admissible into symbolical geometry but those whose respective lines and angles bear the relation of equality, or such integral proportions as may he adequately expressed by some of the numerical terms of the tetraetys. -EDITOR.
As we before declared it to be our opinion that this society was never formed for, or of, a set of working architects or masons, but as a religious, social, and charitable establishment, and that the members thereof never were embodied or exhibited to the world as builders,1 save only under Moses, and at the temple at Jerusalem, where, with holy hands, they executed those works of piety, as the patriarchs erected altars to the honor of the Divinity, for their sacrifices and religious offices;2 so we are persuaded that the adoption of geometry by Masons, or any emblem of that science, implies no more than a reverence for such device of the mind of man as should demonstrate the wisdom of the Almighty in his works, whereby the powers of Abrax are defined, and the system of the starry revolutions in the heavens determined.
1 See the notes to lecture xiii.
2 Genesis, iv. 3, 4; viii. 20; xxii. 9: xxviii. 18; xxxi. 7; xxxiii. 20. Exodus xx. 24; xxvii. 1; xxx 1. Joshua, xxii. 10, 11.
If we should look upon the earth with its produce, the ocean with its tides, the coming and passing of day, the starry arch of heaven, the sea-sons and their changes, the life and death of man, as being merely accidents in the hand of nature, we must shut up all the powers of judgment, and yield ourselves to the darkest folly and ignorance. The august scene of the planetary system, the day and night, the seasons in their successions, the animal frame, the vegetation of plants, all afford us subject for astonishment; the greatest too mighty, but for the hand of a Deity, whose works they are - the least too miraculous, but for the wisdom of their God.
Then how much ought we to esteem that science through whose powers it is given to man to discover the order of the heavenly bodies, their revolutions, and their stations, thereby resolving the operations of the Deity to an unerring system, proving the mightiness of his works, and the wisdom of his decrees?
It is no wonder, then,' that the first institutors of this society, who had their eye on the revelation of the Deity, from the earliest ages of the world unto the days of its perfection under the ministry of the Son of God, that they should hold that science hallowed amongst them, whereby such lights were obtained by man, in the discovery of the great wisdom of the Creator in the beginning.
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