Giulio Carlo de' Toschi di Fagnano

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’s work is considered the foreunner of the theory of Elliptic functions.Template:Sfn

Life

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

In 1705 he married Francesca Conciatti, by whom he had twelve children. One, Giovanni Fagnano, 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; He was also a member to the German Academy of Sciences at Berlin and was proposed for the French Academy of Sciences in 1766 but died before he could be elected.

Mathematical work

File:Fagnano - Produzioni matematiche, 1750 - 1506824.jpg

Produzioni matematiche, 1750

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 or hyperbola, Fagnano attempted to determine arcs 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

$\pi =2i\log \frac{1-i}{1+i}$

where $i$ stands for $\sqrt{-1}$.

Fagnano's works on elliptical functions gained him international reputation. In 1751, Maupertuis submitted his work to the German Academy of Sciences at Berlin for consideration of Fagnano as a foreign member. Leonhard Euler was assigned the task of evaluating the quality of Fagnano's works. He was so impressed by Fagnano's discoveries in the theory of the lemniscate that he immediately commenced his own research in the same direction. Euler developed and generalised Fagnano's methods and results, in particular giving the famous addition formula for elliptic integrals. Fagnano corresponded with the leading mathematicians of the day, most notably Luigi Guido Grandi, Jacopo Riccati, Thomas Leseur, and François Jacquier; his work was highly praised by Bernard Le Bovier de Fontenelle, the permanent secretary of the French Academy of Sciences.Template:Sfn Joseph-Louis Lagrange dedicated his first scientific publication to him.

Works

File:Acta Eruditorum - III geometria, 1763 – BEIC 13450778.jpg

Illustratiom from Illustratio theorematis actis lipsiensibus... published in Acta Eruditorum, 1762

References

An original entry was based on the book A Short Account of the History of Mathematics (4th edition, 1908) by W. W. Rouse Ball.

Further reading

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External links

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