Who did invent the "Lemniscata"?--
A pair of years back a small polemic had risen on the use of the term "lemniscata" attributed to the 8 curve, that shows the mean time.
I state beforehand that in Anglo-Saxon background the curve is called Analemma,(in Italy that is only the name of the geometric figure of Ptolemy); in French is called Méridienne du temps moyen, and the _expression_ is more understandable.
These few notes would want to rake up the matter, adding any news, that perhaps anybody already knows. Since nothing under the sun is new, I don't claim to give the latest news.
Let we tell what is the Lemniscata, the true one: and here we find before two or three topic definitions:
Lemniscus: it was a ribbon that enveloped around the triumphal Roman garlands.
Then we must go back in the time, to Eudossus of Cnido (400-347 AC) to find the study of a curve (that then was called hippopeda, "horse-foot") with a form like to which we refer: it was dealt with find the line of intersection between a cylinder and a sphere, when the cylinder is tangent by interior to the spherical surface.
A nearer curve to our was studied by Bernoulli (Which? Jakob (1654-1705) or Johann (1667-1748)? brothers, both "great" mathematicians, they quarrelled on the priority of the invention of any new solution. Their works were published only in the 1742): the new curve is the locus of the points of a plane for which the product of the distances from two fixed points is equal to the square of the half-distance between the two points.
Simple, or not?
Therefore the name comes from the likeness of the 8-curve to the shoe-lace, or, once, to the blue ribbon of the children of the elementary Schools in Italy.
Go back to the subject: who invented the 8- curve?-
Here we need refer to the history of the astronomy, with the "nautical" implications, the spur of his development in the 17th and in the 18th centuries:
I don't dwell to say what is well-known on the search of the method to find the Longitude: from the beginning of what we could call the modern Astronomy (after Tycho Brahe) existed a strong rivalry between Paris and London: the two observatories went to competition in searches and publish tables, charts, ephemerides, etc...
The development of the watchmaking , essential to give a scientific order to the searches, and the parallel one of the optics, could begin to allow too a critical acquaintance of the astronomic data, so much that already from the half of the 17th century searches of geodetic character were been initiated, (unthinkable without a strong technical support).
The irregularity of the apparent motion of the sun and of the length of the day was a known datum until from remote times (Hipparcus, Ptolemy), but the exact determination of the values of such anomalies goes up again necessarily at the end of 1600, e.g. with the work of the Observatory of Paris and of his manager, Gian Domenico Cassini (1625-1712). (The same of the dial in San Petronio of Bologna)
It's on the base of these tables of the ephemerides that was possible to invent the curve of the mean hours, from a fellow of the Real Academy of the Sciences of Paris.
I bring up what M. Déparcieux writes [page 94] in his "Traité de Gnomonique " published in 1741 (Paris): M. Grand-Jean de Fouchy, de l'Académie Royale des Sciences, est le premier que je sçache avoir parlé de cette Méridienne, qui n'est pas bien commune; je n'en connois encore que trois; la premiere est celle que M. de Fouchy traça chez Monseigneur le Comte de Clermont; & deux que j'ai tracé l'année derniere, l'une chez M. le Marquis de Bonnelle, et l'autre chez M. le Marquis d'Hoüel.
Considering that the approval of the real Censors and of the Académie des Sciences goes back at 1738, we deduce therefore that the first line of the mean hours was drawn in Paris about in 1735, or so. (and the first book with this line was the Gnomonique of Dépacieux)
The circumstance was confirmed by Dom Bédos de Celles, which however could have simply read it on the treatise of Déparcieux. But the account should not be false, because in the 1774 (the date of the second edition of the text-book of Bédos, with the approval of the Académie) the perpetual secretary of the Académie, signatory of the certifications, was quite Grand-Jean de Fouchy.
Bédos has words of praise for the text-book of his predecessor: in the preface of his "Gnomonique pratique" he writes:-
L'on peut dire que M. Deparcieux est le pere & le restaurateur de la Gnomonique. C'est lui qui le premier a enseigné à faire les Cadrans avec la plus grande justesse, par le choix des bonnes méthodes, etc..--
That's all, folks.
