Giulio Carlo de' Toschi di Fagnano

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Giulio Carlo, Count Fagnano, and Marquis de Toschi, (December 6, 1682 Sinigaglia - September 26, 1766) was an Italian mathematician. He was probably the first to direct attention to the theory of elliptic functions.

[edit] Work

He is best known for investigations on the length and division of arcs of certain curves, especially the lemniscate; 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 should be rectifiable. He also pointed out the remarkable analogy existing between the integrals which represent the arc of a circle and the arc of a lemniscate. Finally he proved the formula

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

where i stands for $\sqrt -1$ .

His works were collected and published in two volumes at Pesaro in 1750.

Some mathematicians objected to his methods of analysis founded on the infinitesimal calculus. The most prominent of these were Viviani, De la Hire, and Rolle.

[edit] Life

He made his higher studies at the Collegio Clementino in Rome and there won great distinction, except in the one subject which has made him famous. His aversion to mathematics was extreme, and it was only after his college course that he took up its study. Then, without the help of any teacher, he mastered it from its foundations. Most of his important researches were published in the current numbers of the Giornale de' Letterati d'Italia.

Practical piety characterized his life; his attachment to his religion was warm and sincere, and of his twelve children one became archdeacon of the cathedral of Sinigaglia and another a Benedictine nun.

As a writer he is praised by his contemporaries for his mildness in controversy, as well as for his clearness and accuracy of thought and diction.