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LECTURE VIII.

ON GEOMETRY.

It is now incumbent upon me to demonstrate to you the great (Tgnification of the letter G, wherewith lodges and the medals of masons are ornamented.

To apply it to the name of God only, is wrong; the symbols, indeed, used in lodges are expressive of the Divinity's being the great ruler of masonry, as architect of the world; and the mighty object of worship and adoration.

But this significant letter also denotes with us geometry; which to artificers, is the science by which all their labours are calculated, formed, and proved; | 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 constrution 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 river 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, 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.

The usefulness of geometry extends to almost every art and science :—by the help of it astronomers turn their observations to advantage; regulate the duration of times, seasons, years, cycles, and epochas; and measure the distsnce, motions, and magnitude of the whole earth, and delineate the extent and bearings of kingdoms, provinces, oceans, harbours, and every place upon the globe.—It is adapted to artificers in every branch; and from thence, a$ we said before, architects derive their measures, businesses, and proportions.

This naturally leads us to conjecture why the square is had by masons, as one of the lights of masonry, and part of the furniture of the lodge. To explain our ideas on that matter, we will only repeat to you the 1 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 f* which the fundamental principles of measuring sur** faces were discovered. They probably began with "those surfaces which terminated by right lines, and "amongst these with the most simple.—It is hard in

deed to determine which of those surfaces, which "are terminated by a small number of right lines, are *f the most simple.—If we were to judge by the numf* ber of sides, the triangle has indisputably the advan"tage:—ryet I am inclined to think, that the square f* was the figure which first engaged the attention of

geometricians.—It was not till some time after this, "thattheybegan to examine equilateral triangles, which "are the most regular of all triangular figures,T^It is "to be presumed that they understood that rectilinear *f figure first, to which they afterwards compared the "areas of other polygons, as they discovered them.-r"It \vas by that means the square became the com'? mon 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 planimetry, which «* the unit is in arithmeticc--- for though in measuring "rectilinear figures, we are obliged to resolve them "into triangles, yet the areas of these figures are aU M ways given in the square."— Tbepee we are led to determine, that the square was the first and original figure in geometry, and as such was introduced to our lodges.

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.

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; save only under Moses, and at the temple at Jerusalem, where with holy bands they executed those works of piety, as the patriarchs erected altars to the honor of the Divinity, for their sacrifices and religious offices ;*—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.

If we should look upon the earth with its produce, the ocean with its tides, the coming and passing

* Genesis iv. 3, 4, viii. ao- xxii. 9. xxviii. 18. xxxiii. 30. xxxi. 7. Exodus ix. J4, xxvii. 1. xxx. 1.—Jolhua xxii. lo, ir.

of day, the starry arch of heaven, the seasons 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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