to let no dangers shake, no pains dissolve the inviolable fidelity he owes to the trusts reposed in him.

FORTY-SEVENTH PROBLEM. The forty-seventh problem of Euclid's first book, which has been adopted as an emblem in the Master's degree, is thus enunciated. "In any right angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle." This interesting problem, on account of its great utility in making calculations, and drawing plans for buildings, is sometimes called the "carpenter's theorem."

on.

For the demonstration of this problem, the world is indebted to Pythagoras, who, it is said, was so elated after making the discovery, that he made an offering of a hecatomb, or a sacrifice of a hundred oxen to the gods.* The devotion to learning which this religious act indicated, in the mind of the ancient philosopher, has induced Masons to adopt the problem as a memento, instructing them to be lovers of the arts and sciences.

The triangle, whose base is 4 parts, whose perpendicular is 3, and whose hypothenuse is 5, and which would exactly serve for a demonstration of this problem,† was, according to Plutarch, a symbol frequently employed by the Egyptian priests, and hence it is called by M. Jomard, the Egyptian triangle. It was, with the Egyptians, the symbol of universal nature, the base representing Osiris, or the male principle, the perpendicular, Isis, or the female principle, and the hypothenuse, Horus, their son, or

The well-known aversion of Pythagoras to the shedding of blood has led to the supposition that the sacrifice consisted of small oxen, made of wax, and not of living animals.

For the square of the base is 4 x 4, or 16, the square of the perpendicular is 3 × 3, or 9, and the square of the hypothenuse is 5 × 5, or 25; but 25 is the sum of 9 and 16, and therefore the square of the longest side is equal to the sum of the squares of the other two, which is the forty-seventh problem of Euclid.

In his "Exposition du Système Métrique des Anciens Egyptiens."

the produce of the two principles. They added that 3 was the first perfect odd number, that 4 was the square of 2, the first even number, and that 5 was the result of 3 and 2.

But the Egyptians made a still more important use of this triangle. It was the standard of all their measures of extent, and was applied by them to the building of the pyramids. The researches of M. Jomard, on the Egyptian system of measures, published in the magnificent work of the French savans on - Egypt, has placed us completely in possession of the uses made by the Egyptians of this forty-seventh problem of Euclid, and of the triangle which formed the diagram by which it was demonstrated.

If we inscribe within a circle a triangle, whose perpendicular shall be 300 parts, whose base shall be 400 parts, and whose hypothenuse shall be 500 parts, which of course bear the same proportion to each other as 3, 4 and 5; then, if we let a perpendicular fall from the angle of the perpendicular and base to the hypothenuse, and extend it through the hypothenuse to the circumference of the circle, this chord or line will be equal to 480 parts, and the two segments of the hypothenuse, on each side of it, will be found equal, respectively, to 180 and 320. From the point where this chord intersects the hypothenuse, let another line fall perpendicularly to the shortest side of the triangle, and this line will be equal to 144 parts, while the shorter segment, formed by its junction with the perpendicular side of the triangle, will be equal to 108 parts. Hence, we may derive the following measures from the diagram: 500, 480, 400, 320, 180, 144, and 108, and all these without the slightest fraction. Supposing, then, the 500 to be cubits, we have the measure of the base of the great pyramid of Memphis. In the 400 cubits of the base of the triangle, we have the exact length of the Egyptian stadium. The 320 give us the exact number of Egyptian cubits contained in the Hebrew and Babylonian stadium. The stadium of Ptolemy is represented by the 480 cubits, or length of the line falling from the right angle to the circumference of the circle, through the hypothenuse. The number 180, which

expresses the smaller segment of the hypothenuse, being doubled, will give 360 cubits, which will be the stadium of Cleomedes. By doubling the 144, the result will be 288 cubits, or the length of the stadium of Archimedes, and by doubling the 108, we produce 216 cubits, or the precise value of the lesser Egyptian stadium. In this manner, we obtain from this triangle all the measures of length that were in use among the Egyptians; and since this triangle, whose sides are equal to 3, 4, and 5, was the very one that most naturally would be used in demonstrating the forty-seventh problem of Euclid; and since by these three sides the Egyptians symbolized Osiris, Isis, and Horus, or the two producers and the product, the very principle, expressed in symbolic language, which constitutes the terms of the problem as enunciated by Pythagoras, that the sum of the squares of the two sides will produce the square of the third, we have no reason to doubt that the forty-seventh problem was perfectly known to the Egyptian priests, and by them communicated to Pythagoras.

FREE BORN. The constitutions of our order require that every candidate shall be free born. And this is necessary, for, as admission into the fraternity involves a solemn contract, no one can bind himself to its performance who is not the master of his own actions; nor can the man of servile condition or slavish mind be expected to perform his masonic duties with that "freedom, fervency, and zeal," which the laws of our institution require. Neither, according to the authority of Dr. Oliver,* ❝can any one, although he have been initiated, continue to act as a Mason, or practise the rites of the order, if he be temporarily deprived of his liberty or freedom of will." On this subject, the Grand Lodge of England, on the occasion of certain Masons having been made in the King's Bench prison, passed a special resolution in November, 1783, declaring "That it is inconsistent with the principles of masonry for any Freemason's lodge to be

Historical Landmarks, i. 110.

held, for the purpose of making, passing, or raising Masons, in any prison or place of confinement."*

The same usage existed in the spurious Freemasonry of the ancient mysteries, where slaves could not be initiated, the requisites for initiation being that a man must be a free-born denizen of the country, as well as of irreproachable morals.

FREEMASON. The word "free," in connection with "Mason," originally signified that the person so called was free of the company or guild of incorporated Masons. For those operative Masons who were not thus made free of the guild, were not permitted to work with those who were. A similar regulation still exists in many parts of Europe, although it is not known to this country. The term appears to have been first thus used in the tenth century, when the travelling Freemasons were incorporated by the Roman Pontiff. See Travelling Freemasons.

FREEMASONRY. "A beautiful system of morality, veiled in allegory, and illustrated by symbols." To this sublime definition of our order, borrowed from the lectures of our English brethren, and prefixed by Dr. Oliver, as a motto to one of his most interesting works, I shall take the liberty of adding an exposition of its principles from the pen of De Witt Clinton, as pure a patriot as ever served his country, and as bright a Mason as ever honoured the fraternity.

"Although," says he, "the origin of our fraternity is covered with darkness, and its history is, to a great extent, obscure, yet we can confidently say, that it is the most ancient society in the world-and we are equally certain that its principles are based on pure morality-that its ethics are the ethics of Christianityits doctrines, the doctrines of patriotism and brotherly love-and its sentiments, the sentiments of exalted benevolence. Upon these points, there can be no doubt. All that is good, and kind,

Minutes of the Grand Lodge, quoted by Oliver, ut supra.

and charitable, it encourages; all that is vicious, and cruel, and oppressive, it reprobates."*

FRENCH RITE. Rite Français ou moderne. The French or Modern rite is one of the three principal rites of Freemasonry. It consists of seven degrees, three symbolic and four higher, viz. 1. Apprentice; 2. Fellow Craft; 3. Master; 4. Elect; 5. Scotch Master; 6. Knight of the East; 7. Rose Croix. This rite is practised in France, in Brazil, and in Louisiana. It was founded in 1786, by the Grand Orient of France, who, unwilling to destroy entirely the high degrees which were then practised by the different rites, and yet anxious to reduce them to a smaller number, and to greater simplicity, extracted these degrees out of the rite of Perfection, making some few slight modifications. Most of the authors who have treated of this rite have given to its symbolism an entirely astronomical meaning, Among these writers, we may refer to Ragon, in his "Cours Philosophique," as probably the most scientific.

FUNERAL RITES. None but Master Masons can be interred with the funeral honours of masonry, and even then the performance of the service is subjected to certain unalterable restrictions. No Mason can be buried with the formalities of the order, except by his own request, preferred, while living, to the Master of the lodge of which he was a member, strangers and the higher officers of the order excepted. No public procession can take place, nor can two or more lodges assemble for this purpose, until a dispensation has been granted by the Grand Master. The ceremonies practised on the interment of a brother are to be found in all the Monitors. It is unnecessary, therefore, to specify them here.

1852.

Address at the installation of Grand Master Van Renssellaer, New York,