The 47th Proposition of the 1st Book of Euclid as Part of the Jewel of a Past Master
By: Bro. Thomas Greene, L.L.D.
Extracted from: Ars Quatuor Coronatorum, the Transactions of Quatuor Coronati Lodge No. 2076, UGLE vol. 14, 1901. pp. 27-30
Reproduced with kind permission of Quatuor Coronati Lodge 2076
The Jewel of the Past Master in Scotland consists of the Square, the Compasses, and an Arc of a Circle: In Ireland of the Square and Compasses with the capital ‘G’ in the centre: In England for 85 years, at least, it has been the Square with the 47th Proposition of Euclid pendent within it.
An Irish poet wrote:
Trath is one, and so is light,
Yet how many shades of it.
Freemasonry itself might be looked on as exemplifying unity without monotony;
So let it not be supposed that because they are different there is anything exclusively English, or Irish, or Scotch, about the Past Master’s Jewel in each case;
All are beautiful links in the chainwork of continuation from Operative to Speculative Masonry;
All remind us that the master of an Operative Lodge worked out his plans by that branch of science to which we give the general name of ‘Geometry,’ and which is represented in the Irish Jewel by the Capital ‘G,’ which along with the 47th Proposition were in use both in England and in Ireland probably before 1723;
And if we make a comparison at all, to my mind it should be in favour of the ‘G’ as, primarily at least, standing for Geometry,’ the basis of all Operative Masonic Work, and including that 47th Proposition with which I am about to deal.
The Square is introduced to the Entered Apprentice as one of the three Great Lights of Freemasonry, to the Fellowcraftsman as one of the working tools of his Degree.
It is also one of the Jewels of the Lodge, and the special Jewel of the Master of the Lodge.
It is probably the most important tool of a Mason, whether an Operative or a Speculative one, for it connects and more or less includes the Level and the Plumb Rule, and it is the only tool by which the rough Ashlar can be prepared and tested; and unless the ashlars are perfect the building cannot be built after any wise plan, or with strength, or with beauty.
It is used to form the rude and to prove the perfect mass, and therefore it is of the utmost importance that an implement on which so much depends shall be itself perfectly correct.
It is this last consideration especially which renders the 47th Proposition so appropriate an emblem of the Past Master.
The artificer employs the square to form the rude mass; the Master to prove the work; but whose duty is it to see that this most important tool is itself correct?
The most suitable person would seem to be the Past Master, he, having passed through the stages of using it and testing with it, would be most impressed with the necessity of its being correct.
By what mode can he ensure the correctness of the Square?
How can he ensure that the angle between the two limbs of the Square shall be truly a right or square angle?
There are many ways known to modern science whereby this can be done, but the most ancient, and perhaps the simplest, is by means of the 47th Proposition of the first book of Euclid:
And therefore the Past Master, one of whose chief duties it is to test the working tools, and who is supposed to have arrived at a complete skill in Freemasonry, wears it as part of his distinguishing Jewel:
Indeed the term Past Master is commonly used to describe anyone who is possessed of special knowledge in any particular department whatever.
This Proposition is known certainly for twenty-four centuries, and probably much longer, and by it we can prove that in a triangle, one of the angles of which is a right angle, the square of the side opposite the right angle is equal to both the squares on the sides containing the right angle:
It follows then that if we make any triangle in which the square of one side is equal to both the squares of the two other sides, then the angle opposite that side must be a true right angle,—the angle of a correct square.
In the English Book of Constitutions of 1723 this Proposition appears on the Frontispiece, and it was spoken of then as, ‘That amazing Proposition which is the foundation of all Masonry.’
IMAGE LINKED: wikimedia Attribution 4.0 International (CC BY 4.0)
The diagram shown represents it as used by English Masons nearly 100 years ago; you will see that in order to get a correct square angle it is only necessary to make a triangle the sides of which shall be in the proportion 3-4-5.
In connection with this it is of much interest to know that as the standard and symbol of perfection with Speculative Masons now is the Square, so this right angled triangle, which is almost identical, was with the Egyptians several thousand years ago the standard and symbol of perfection;
And they made it also the basis of all their measurements; they looked on it as the symbol of Universal Nature, the side;
They said 3 was the first perfect odd number, that 4 was the square of 2 the first even number, and 5 was the result of 3 and 2. 
In Freemasonry, the Square is the Symbol of moral perfection: it is the Master’s duty to apply the perfect square of right and truth to the work of the subordinates;
But the far higher and greater responsibility rests on the Past Master of setting out, pointing out, and in himself exemplifying what Right in itself is, and what Truth is, of answering Pilate’s question, ‘What is Truth?’
True Speculative Masonry teaches a man, by the industrious application of the principles of Eternal Truth and Right to the untaught material of humanity, to shape its thoughts and actions so as to erect from it a spiritual building, on sure foundations, with intelligent purpose, and admirable to contemplate.
The Past Master represents one who has erected such a building; but his having done so places him under the responsibility of ensuring that those who are working for the same end shall not fail through want of his affording them, by precept and example, principles which have been put to the test and found to be those of absolute truth and correctness.
It will be said, why then be a Past Master and incur all this responsibility? but it is what one who lives through a Masonic life must come to, and is symbolic of what man is born to, whether he be a Freemason or not.
There is no man but eats more or less of the tree of knowledge of good and evil, and incurs the responsibility attached thereto;
No man can escape being not only the keeper of his brother who is his equal, but also the far greater responsibility of being the keeper of those who are beginners and learners:
And as they are influenced for good or evil, so will they be affected to the third and fourth generation.
But it may be asked how it is that while in Masonry and in human life all the wear and tear and the responsibilities seem to attach to the workers of the different grades, and to the overseers of the work, yet that on the Past Master who has risen through all the grades, and who seems to have earned the calm of smooth waters, free from anxieties, lies the greatest responsibility of all?
The answer, which is a serious one, is this, that while he was a learner his work was carried on in sight and hearing, and he was accountable for it to those above him who were themselves liable to err;
But that now, as a Past Master, both for his own work and the correctness of the rules of night which he supplies to the learners, he is accountable, not to Masons or to men, but to the Great Architect, the Grand Geometrician, the God of the Universe.
‘Squaring the circle’, from Michael Maier’s Atalanta fugiens, emblema XXI, 1618
IMAGE LINKED: wikimedia Attribution 4.0 International (CC BY 4.0)
I may bring before you two instances of the Square being treated in a symbolic way, long before Speculative Masonry existed ; especially as the suggestions were singularly like to ours.
Guillaume de Guileville, a Frenchman, who was born A.D. 1295 and died 1360, wrote a book called ‘Man’s Pilgrimage’ in which, in an imaginative ‘last will’ of Jesus Christ, one clause contains a bequest to mankind of the ‘Pax Triplex,’ ‘Triple Tranquillity,’ symbolized by P.A.X. so disposed on the stem and one limb of a Latin cross, which forms a right angle, as to ind’cate the whole duty of man —his love to God and to his neighbour, in this way,—A. stands for Anima, the soul;
X. Kristos, Christ, finally connected with the soul by love, but directly in the plumbline above it as superior; P. Proximus, a neighbour, properly on the same level, and also firmly connected by love, but not so nearly as to X., Christ, as indicated by the longer stem of the cross. 
The other instance came to light when, at the rebuilding of Baal’s Bridge, near Limerick, a brass square was found, inscribed with the date 1517, and with these words:
I will strive to live with love and care
Upon the level, by the square.
This was the sentiment of a purely Operative Mason, and it is still a fit sentiment for a Speculative one 400 years afterwards.
1. See the exhaustive paper on ‘The Great Symbol,’ by Bro. S. T. Klein, A.Q.C. x., p. 82 et seqq.
2. See W. H. Rylands, ‘Symbolism of the Square,’ A.Q.C. xiii., p. 28.
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