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Whiteside in "The Mathematical Principles underlying Newton's Principia Mathematica" wrote

.. if we can give credence to an account in The Postboy of 12 April 1731, his tomb in Westminster Abbey in London was once inscribed (on the stone 'parchment' borne proudly by the cherubs who flank his effigy) with an unspecified 'Diagram' and a certain 'converging series'; but these, thanks to the polishers who cleaned the monument twenty years ago, are no longer visible to the naked eye.

Have modern historians with their imaging techniques determined what these inscriptions were and/or were these faithfully restored after Whiteside? If so, what are they? See this blog for an image of the parchments on which there is clearly a geometric figure.

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  • $\begingroup$ Great! So why the discrepancy with Cajori and The Postboy? It's highly improbable that the 'parchment' was originally blank. $\endgroup$ Commented Dec 13, 2022 at 4:58
  • $\begingroup$ @njuffa, so there was some record extant of the original 'paintings'. Nice detective work. (The Westminster Abbey page neglects to describe the paintings--a real oversight.) $\endgroup$ Commented Dec 13, 2022 at 6:18
  • $\begingroup$ Btw, info on Newton's approach to the binomial theorem in "How Isaac Newton Discovered the Binomial Power Series" at quantamagazine.org/… and beginning on p. 168 of The Correspondence of Isaac Newton Vol. II 1676-1687 edited by H. Turnbull (Cambridge Univ. Press, 1960). See footnote 2 on p. 170-1. $\endgroup$ Commented Dec 19, 2022 at 4:14

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Another picture of the scroll, but taken from a different angle, appeared in: Greg Priest, Silvia De Toffoli, Paula Findlen, "Tools of Reason: The Practice of Scientific Diagramming from Antiquity to the Present," Endeavour 42 (2018), 49-59. Examining both pictures I can make out parts of the two-line inscription at the top, which reads $\overline{P + PQ}) ... AQ ... BQ ... CQ$, with undecipherable squiggly marks in the place of the dots.

According to another answer on this site, Newton himself wrote the Generalized Binomial Theorem as follows:

$$\left(P + PQ\right)^{\frac{m}{n}} = P^{\frac{m}{n}} + \frac{m}{n}AQ+\frac{m-n}{2n}BQ + \frac{m-2n}{3n}CQ+\ldots$$

So this appears to be a match. Jean G. Dhombres, "A Tentative Interpretation of the Epistemological Significance of the Encrypted Message Sent by Newton to Leibniz in October 1676", Advances in Historical Studies, Vol. 3, No. 1, 2014, pp. 22-32, notes:

15 Newton did not use parenthesis for the binomial P + PQ, but he drew a line above the whole binomial, ended by a descending vertical line.

As for the diagram taking up the central part of the scroll, it appears to match well with the diagram that appears in Principia, Proposition XI. Problem VI:

If a body revolves in an ellipsis; it is required to find the law of the centripetal force tending to the focus of the ellipsis.

David Brewster, The Life of Sir Isaac Newton, New York: J. & J. Harper 1831, p. 289:

On the sarcophagus is placed the figure of Sir Isaac in a cumbent posture, with his elbow resting on several of his works. Two youth stand before him with a scroll, on which is drawn a remarkable diagram relative to the solar system, and above that is a converging series.

Some seven decades later Cajori could not find any solid evidence of an inscription on the scroll: Florian Cajori, "Was the binomial theorem engraven on Newton's monument?" Bulletin of the American Mathematical Society, Vol. 1, No. 2, 1900, pp. 52-54:

The first step naturally is to question the monument, but we do so in vain. Says Dr. Granville, the present Dean of Westminster, in a letter to the writer: "In front of the half-recumbent figure of Sir Isaac Newton are two winged youths holding a small scroll in which are still, according to Neale, some mathematical figures. ... I fear that the figures on the small marble scroll are quite obliterated. A mathematical friend mounted the monument for me. Time, I fear, and London atmosphere have done their sad work, and the older guide-books, Dart and Neale, while they carefully copy other inscriptions, naturally do not preserve for us mathematical formulæ." A friend of the writer of this article reports, "I looked as close as a chair would permit and saw no sign of engraving on the scroll."

Based on these observations, Cajoli concluded:

Thus it appears pretty conclusively that there is no more foundation for the statement that the Binomial Theorem was inscribed on Newton's tomb or monument than there was authority for the story of the "apple" ...

The reason that modern photographs show a pristine looking diagram and inscription on the scroll is explained authoritatively on the website of Westminster Cathedral (my bolding):

Above the sarcophagus is a reclining figure of Newton, in classical costume, his right elbow resting on several books representing his great works. They are labelled (on the fore-edges) 'Divinity', 'Chronology', 'Opticks' [1704] and 'Philo. Prin. Math' [Philosophiae Naturalis Principia Mathematica, 1686-7)]. With his left hand he points to a scroll with a mathematical design shown on it (the 'converging series'), held by two standing winged boys. The painting on this scroll had been erased or cleaned off in the early 19th century and was re-painted in 1977 from details in Newton's manuscripts

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