The Pythagorean Theorem

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Euclid’s 47th proposition

Query 1267.—(XXVII, 11, 26, 38, 58).—The Forty-seventh Proposition of Euclid.—The late M.W. Bro. S. Clifton Bingham, P.G.M. in New Zealand, in 1938 investigated the history of the Past Master's Jewel with special reference to the 47th Proposition of Euclid. His conclusions are set out in a paper entitled The Jewel of a Past Master, published in the Transactions of the Masters and Past Masters' Lodge No. 130 (Christchurch, New Zealand), volume viii, at pages 146-152, and may be summarised as follows:

1. This particular theorem (the 47th proposition) has been associated with the name of Pythagoras by many, but it does not necessarily follow that he is the author.

2. This theorem is the 47th in the first book of Euclid’s Elements and that following (48th), being the converse, should also be taken into consideration. (The 48th is that actually used in practice by builders to prove the square by the 3, 4, and 5 method.)

3. Euclid’s period was two centuries later than Pythagoras. The statements referring to Euclid as the founder or inventor of Geometry are repeated in the hundred variations of our MSS. Charges now known.

4. When Dr. Anderson "digested these Old Charges" he thought fit to insert on the frontispiece of his book in 1723 (and also in the revised edition in 1738) a representation of the 47th proposition.

5. Unfortunately Dr. Anderson placed the Greek word "Eureka " underneath the diagram, thus perpetuating an error which our rituals still continue.

6. The story that Pythagoras used this word os signifying "I have found it" (its ordinary Greek meaning), and sacrificed a hecatomb, is an error of Plutarch's.

7. In the early days of speculative masonry little notice was taken of the Past Masters until the advent of the Antients. The status of Past Masters was then improved and the presentation of jewels to them gradually became more frequent.

8. The usual form of P.M. jewels in the eighteenth century was a pair of compasses opened on the segment of a circle with a sun between the legs of the compasses. Under the "Ancients" a Square across the legs of the compasses was added very similar to the Scottish P.M. Jewel to-day.

9. There was no regulation pattern pre-union, and Lodges went to whichever jeweller they pleased.

10. The last statement (that Lodges went to whatever jeweller they pleased) possibly provides the key to the answer.

11. An outstanding Freemason who was also a jeweller in the latter half of the eighteenth century was Thomas Harper. Bro. Bingham had an engraving of a jewel in the collection of Wor. Bro. A. F. Calvert, which jewel was of Harper's make, bearing the hall-mark of 1798/9. This is exactly our present form of P.M. jewel with the exception that the quadrant containing the 47th proposition is suspended from the short arm of the Square, thus making a "gallows" jewel. This is inscribed "Bro. Peter Gilkes" very celebrated Freemason of the period 1786-1833.

12. An engraved portrait of Gilkes, the work of his friend and Brother, John Harris, of Tracing Board fame, presented and dedicated to the Globe Lodge in 1830, shows him wearing a "gallows" form of P.M. jewel.

13. Thomas Harper, whose occupation was that of silversmith, was one of the most influential members of the "Antients" Grand Lodge.

14. Notwithstanding his membership of the "Ancients" he joined the Globe (a "Modern" Lodge) in 1787, was Master in 1793 and Grand Steward in 1796. Durlng this period he would have been intimately connected with Bro. Gilkes, who as an exceedingly active worker in this and many other Lodges.

15. The theory Bro. Bingham endeavoured to develop is that Thomas Harper designed the form of our present P.M. Jewel firstly in one that he made for presentation to his friend and close masonlc associate, Peter Gilkes; but Wor. Bro. Dr. Hammond, in his book on Masonic Jewels, describes and illustrates a similar jewel, now in the museum of the Grand Lodge of England, and states that it is of date 1783 (also made by Thomas Harper).

16. It would appear therefore that the theory cannot be sustained; nevertheless it seems apparent that the design was Harper's, and that he must be credited with it.

17. Bro. Bingham considered there is sufficient evidence to credit Bro. Thomas Harper as inventor of our present Past-Masters's Jewel, and this Jewel was adopted as the official form in the Book of Constitutions issued in 1815, that is after the Union. No reference thereto appears in the minutes of the Grand Lodge of that period, so far as he was aware.

18. In his paper Bro. Bingham did not suggest that Harper associated any particular detailed symbolism with the 47th proposition of Euclid, but quoted from one of the Catechetical Lectures (an unorthadox version of pre-union date), and from American Monitors (usually based on Preston's work), and also cited a quotation given by Bro. Rev. Covey-Crump in his paper on The Pythagorean Proposition, in which he quoted extensively from a somewhat scarce masonic work entitled Wisdom, Strength and Beauty.

19. Though he did not say so in so many words, Bro. Bingham appeared to think that when Harper invented the P.M. Jewel in the form of the 47th Proposition the idea "caught on" and everyone accepted it. Possibly explanations were invented for it later.

Miscellanea Latomorum or Masonic Notes and Queries. A Serial intended to facilitate Intercommunications between Masonic Students on matters of interest in connection with Freemasonry. May, 1943. Margate : Printed for Private Circulation by W. J. Parret, Ltd., 25, Cecil Square. New Series Vol. XXVII, No. 8. Editor : Colonel F. M./ Rickard, 27, Great Queen St., W.C.2, London, England. p. 123-125.

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