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considered, from a point to a line, from a line to a superfices, and from a superfices to a solid.
A point is a dimensionless figure; or an indivisible part of space.
A line is a point continued, and a figure of one capacity, namely, length.
A superfices is a figure of two dimensions, namely, length and breadth.
A solid is a figure of three dimensions, namely, length, breadth, and thickness.
Of the Advantages of Geometry.* By this science, the architect is enabled to construct his plans, and execute his designs; the general to arrange his
sent 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, superfices, 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 geomery, 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 distance, motions, 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 bearings of kingdoms, provinces, oceans, harbours, and every place upon the globe-It is adapted to artificers in every branch, and from thence, architects derive their measures, justnesses, 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 this subject, we will only repeat 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 lines, and amongst
soldiers; the engineer to mark out ground for encampments; the geographer to give us the dimensions of the world, and all things therein contained, to delineate the extent of seas, and specify the divisions of empires, kingdoms and provinces; by it, also, the astronomer is enabled to make his observations, and to fix the duration of times and seasons, years and cycles. In fine, geometry is the foundation of architecture, and the root of the mathematics.
Music. Music teaches the art of forming concords, so as to compose delightful harmony, by a mathematical and proportional arrangement of acute, grave and mixed sounds. This art, by a series of experiments, is reduced to a demonstrative science, with respect to tones, and the intervals of sound. It inquires into the nature of concords and discords, and enables us to find out the proportion between them by numbers.
Astronomy. Astronomy is that divine art, by which we are taught to read the wisdom, strength and beauty of the Almighty Creator, in those sacred pages the celestial hemisphere. Assisted by astronomy, we can observe the motions, measure the distances, comprehend the magnitudes, and calculate the periods and eclipses, of the heavenly bodies. By it we learn the use of the globes, the system of the world, and the preliminary law of nature.* While we are employed in the study
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 indis. putably 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 planimetry, which the unit is in the arithmetic-for though in measuring rectilinear figures, we are obliged to resolve them into triangles, yet the eraes of these figures are always given in the square. Thence we are led to determine, that the square was the first and original figure in geo. metry, 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.
* 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 seasons and their changes, the life and death of man, as being mcrely accidents in the
of this science, we must perceive unparalleled instances of wisdom and goodness, and, through the whole creation, trace the Glorious Author by his works.
Of the Moral Advantages of Geometry. From this theme we proceed to illustrate the moral advan. tages of Geometry; a subject on which the following observations may not be unacceptable:
Geometry, the first and noblest of sciences, is the basis on which the superstructure of masonry is erected. By geometry, we may curiously trace nature, through her various windings, to her most concealed recesses. By it, we discover the power, the wisdom, and the goodness, of the Grand Artificer of the Universe, and view with delight the proportions which connect this vast machine. By it we discover how the planets move in their different orbits, and demonstrate their various revolutions. By it we account for the return of seasons, and the variety of scenes which each season displays to the discerning eye. Numberless worlds are around us, all framed by the same Divine Artist, which roll through the vast expanse, and are all conducted by the same unerring laws of nature.
A survey of nature, and the observation of her beautiful proportions, first determined man to imitate the divine plan, and study symmetry and order. This gave rise to societies, and birth to every useful art. The architect began to design, and the plans which he laid down, being improved by experience and time, have produced works which are the admiration of every age.
band 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 plan: etary system, the day and night, the seasons in their successions, the animal frame, the vegetation of plants, all afford us subject for astonishment; the greater 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 bis decrees.
It is no wonder, then, that the first institutors of the masonic 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 this science ballowed amongst them, whereby such lights were obtained by man, in the discovery of the great wisdom
of the Creator in the beginning.
The lapse of time, the ruthless hand of ignorance, and the devastations of war, have laid waste and destroyed many valuable monuments of antiquity, on which the utmost exertions of human genius have been employed. Even the temple of Solomon, so spacious and magnificent, and constructed by so many celebrated artists, escaped not the unsparing ravages of barbarous force. Freemasonry, notwithstanding, has still survived. The attentive ear receives the sound from the instructive tongue, and the mysteries of masonry are safely lodged in the repository of faithful breasts. Tools and implements of architecture are selected by the fraternity, to imprint on the memory wise and seri. ous truths; and thus, through a succession of ages, are transmitted unimpaired the excellent tenets of our institution.
Thus end the two sections of the second lecture, which, with the ceremony used at opening and closing the lodge, comprehended the whole of the second degree of masonry. This lecture contains a regular system of science, demonstrated on the clearest principles, and established on the firmest foundation.
At Initiation into the Second Degree. BROTHER—Being now advanced to the second degree of masonry, we congratulate you on your preferment. The internal, and not the external qualifications of a man, are what masonry principally regards. As you increase in knowledge, you will consequently improve in social intercourse.
It is unnecessary to recapitulate the several duties which, as a mason, you are bound to discharge; or to enlarge on the necessity of a strict adherence to them, as your own experience must have convinced you of their value. *(It may be sufficient to observe, that your past behaviour and regular deportment bas merited the additional honor which we have now conferred; and in this new character, it is expected that you will not only conform to the principles of masonry, but steadily persevere in the practice of every commendable virtue.)
The study of the liberal arts, that valuable branch of education, which tends so effectually to polish and adorn the
* The lines in parenthesis may be used, or omitted, at the discretion of the master.
mind, is earnestly recommended to your consideration; especially the noble science of geometry, which is established as the basis of our art. Masonry and geometry were originally synonymous terms, and this science being of a divine and moral nature, is enriched with the most useful knowledge; for, while it proves the wonderful properties of nature, it also demonstrates the more important truths of morality.
(As the solemnity of our ceremonies requires a serious deportment, you are to be particularly attentive to your behaviour in our regular assemblies; to preserve the ancient usages and customs of the fraternity sacred and inviolable; and induce others, by your example, to hold them in due veneration.)
Our laws and regulations you are to support and maintain; and be ever ready to assist in seeing them duly exccuted. You are not to palliate or aggravate the offences of your brethren; but in the decision of every trespass against our rules, you are to judge with candor, to admonish with friendship, and to reprehend with justice.
(In our private assemblies, you may now offer your sentiments and opinions on such subjects as correspond with, and are agreeable to, the tenets of masonry. By the exertion of this privilege, you may improve your rational and intellectual powers; qualify yourself to become an useful member of society; and vie with skilful brethren, in an endeavour to excel in every thing that is good and great.)
Every regular sign, or summons, given and received, you are duly to honor, and punctually to obey, inasmuch as they consist with our professed principles. You are cheerfully to relieve the necessities of your brethren to the utmost of your power and ability, without prejudice to yourself or your private concerns: And on no account are you to injuro a brother, or to see him injured; but you are to apprize him of all approaching dangers, and consider his interest as inseparable from your own.
Such is the nature of your present engagements; and to these duties you are now bound by the most sacred ties.