A Philosophical and Mathematical Dictionary (London, 1815), Vol. 1, p. 226.
[920]. Following the example of Archimedes who wished his tomb decorated with his most beautiful discovery in geometry and ordered it inscribed with a cylinder circumscribed by a sphere, James Bernoulli requested that his tomb be inscribed with his logarithmic spiral together with the words, “Eadem mutata resurgo,” a happy allusion to the hope of the Christians, which is in a way symbolized by the properties of that curve.—Fontenelle.
Eloge de M. Bernoulli; Oeuvres de Fontenelle, t. 5 (1758), p. 112.
[921]. This formula [for computing Bernoulli’s numbers] was first given by James Bernoulli. He gave no general demonstration; but was quite aware of the importance of his theorem, for he boasts that by means of it he calculated intra semi-quadrantem horae! the sum of the 10th powers of the first thousand integers, and found it to be
91,409,924,241,424,243,424,241,924,242,500.
—Chrystal, G.
Algebra, Part 2 (Edinburgh, 1879), p. 209.
[922]. In the year 1692, James Bernoulli, discussing the logarithmic spiral [or equiangular spiral, ρ = αθ] ... shows that it reproduces itself in its evolute, its involute, and its caustics of both reflection and refraction, and then adds: "But since this marvellous spiral, by such a singular and wonderful peculiarity, pleases me so much that I can scarce be satisfied with thinking about it, I have thought that it might not be inelegantly used for a symbolic representation of various matters. For since it always produces a spiral similar to itself, indeed precisely the same spiral, however it may be involved or evolved, or reflected or refracted, it may be taken as an emblem of a progeny always in all things like the parent, simillima filia matri. Or, if it is not forbidden to compare a theorem of eternal truth to the mysteries of our faith, it may be taken as an emblem of the eternal generation of the Son, who as an image of the Father, emanating from him, as light from light, remains ὁμοούσιος with him, howsoever overshadowed. Or, if you prefer, since our spira mirabilis remains, amid all changes, most persistently itself, and exactly the same as ever, it may be used as a symbol, either of fortitude and constancy in adversity, or, of the human body, which after all its changes, even after death, will be restored to its exact and perfect self, so that, indeed, if the fashion of Archimedes were allowed in these days, I should gladly have my tombstone bear this spiral, with the motto, “Though changed, I arise again exactly the same, Eadem numero mutata resurgo.”—Hill, Thomas.
The Uses of Mathesis; Bibliotheca Sacra, Vol. 32, pp. 515-516.
[923]. Babbage was one of the founders of the Cambridge Analytical Society whose purpose he stated was to advocate "the principles of pure d-ism as opposed to the dot-age of the university.”—Ball, W. W. R.