Giulio Carlo, Count Fagnano, Marquis de Toschi (26 September 1682 — 18 May 1766) was an Italian mathematician. He was probably the first to direct attention to the theory of elliptic integrals. Fagnano was born in Senigallia (at the time spelled "Sinigaglia"), and also died there.

Life

Giulio Fagnano was born to Francesco Fagnano and Camilla Bartolini in Senigallia (at the time spelled "Sinigaglia") in 1682. Fagnano had twelve children. One,

Giovanni Fagnano Giovanni Francesco Fagnano dei Toschi (born 31 January 1715 in Senigallia, died 14 May 1797 in Senigallia) was an Italian churchman and mathematician, the son of Giulio Carlo de' Toschi di Fagnano, also a mathematician. Religious career Fagnano was ...

, was also well-known as a mathematician. Another of Fagnano's children became a Benedictine nun. In 1721, Fagnano was made a count by Louis XV; in 1723, he was appointed '' gonfaloniere'' of Senigallia and elected to the Royal Society of London; in 1745 he was made a

marquis A marquess (; french: marquis ), es, marqués, pt, marquês. is a nobleman of high hereditary rank in various European peerages and in those of some of their former colonies. The German language equivalent is Markgraf (margrave). A woman wi ...

of Sant' Onofrio.

Mathematical work

Fagnano made his higher studies at the Collegio Clementino in Rome, and there won great distinction — except in mathematics, to which his aversion was extreme. Only after his college course did he take up the study of mathematics; but then, without help from any teacher, he mastered mathematics from its foundations. Most of his important researches were published in the ''Giornale de' Letterati d'Italia''. Fagnano is best known for investigations on the length and division of arcs of certain curves, especially the lemniscate (cf. Lemniscate elliptic functions); this seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription "Multifariam divisa atque dimensa Deo veritatis gloria" engraved on the title-page of his ''Produzioni Matematiche'', which he published in two volumes (Pesaro, 1750), and dedicated to Pope Benedict XIV. The same figure and words "Deo veritatis gloria" also appear on his tomb. Failing to rectify the

ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

or hyperbola, Fagnano attempted to determine

arc ARC may refer to: Business * Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s * Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services * ...

s whose difference is rectifiable. The word "rectifiable" meant at that time that the length can be found explicitly, which is different from its modern meaning. He also pointed out the remarkable analogy existing between the integrals which represent the arc of a circle and the arc of a lemniscate. He also proved the formula :

\pi = 2i\log

where

i

stands for

\sqrt

. Some mathematicians objected to his methods of analysis founded on the

infinitesimal calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

. The most prominent of these were Viviani, De la Hire and Rolle. Acta Eruditorum - III geometria, 1763 – BEIC 13450778

References

* {{DEFAULTSORT:Fagnano, Giulio Carlo 1682 births 1766 deaths People from Senigallia 18th-century Italian mathematicians 17th-century Italian mathematicians Fellows of the Royal Society