**Tommaso Ceva** was the brother of Giovanni Ceva. Their father, Carlo Francesco Ceva (1610-1690), was a man who undertook many different activities such as buying and selling houses and land. He also worked for the duke of Milan in an official capacity, collecting excise duty. This meant that he was a wealthy man, able to provide a high quality lifestyle for his family. He married Paola Columbo, the daughter of Cristoforo Columbo and Elisabetta Caballina, on 20 September 1639. They had several children: Laura Maria Francesca Elisabetta Ceva (born 1640), Clara Giustina Bonaventura Ceva (born 1642), Iginio Nicolò Ceva (born 1644), Francesco Ceva (born 1645), Giovanni Benedetto Ceva (who also has a biography in this archive, born 1647), Tomasso Ceva (the subject of this biography, born 1648), Teresa Francesca Ceva (born 1650), and Cristoforo Vittore Ceva (born 1652). Laura, Iginio, Francesco, Tomasso, Teresa and Cristoforo all had ecclesiastical careers, with Francesco, Tomasso, Teresa and Cristoforo becoming Jesuits, joining the Society of Jesus.** **Tomasso Ceva's cousin, also named Carlo Francesco Ceva, was the Bishop of Tortona.

After studying in Milan at the Academy Braidense, on 24 March 1663, while not yet fifteen years of age, he entered the Society of Jesus. After completing his religious education in Genoa and Nice, in 1675 he returned to Milan, where in 1682 he made his solemn vows. His education was entirely within the Jesuit Order and he obtained a degree in theology.

Tommaso Ceva became professor of mathematics and rhetoric at the Jesuit College of Brera in Milan and taught rhetoric, moral theology and mathematics there for more than forty years. During most of this time the city was under Spanish rule and Ceva made sure of their support by writing pieces to celebrate civic events and dedicating works to Guzman, the Spanish governor of Milan. Ceva published *De natura gravium* in 1669, a work which dealt with physics, particularly gravity, but this work is not mathematical but rather he took a philosophical, even thelogical, approach [1]:-

Ceva wrote the treatise in two months of steady work; in his "Conclusion," he asks his readers for emendations.

At this stage he seems to accept at least some of Isaac Newton's ideas although later he rejected them, almost certainly because of the attitude of the Church. His most famous student at this College of Brera in Milan was Giovanni Saccheri who began his studies there in 1690. Many would suggest that Ceva's success in persuading Saccheri to undertake research in mathematics was his greatest contribution to the subject.

His mathematical work, almost entirely concentrated in the five years between 1695 and the end of the century, is summed up in *Opuscula Mathematica* (1699) which examines arithmetic, geometric-harmonic means, the cyloid, division of angles, higher order conic sections and curves, and gravity. He also designed an instrument to divide a right angle into a given number of equal parts. Although his 1669 work appears to be accepting at least some of the new revolutionary ideas of the "new physics", in a book *Philosophia novo-antiqua* of 1704 he most certainly rejects the ideas of Copernicus and Descartes. During his career, Ceva corresponded with several other mathematicians including Vicenzo Viviani, Guido Grandi and, of course, his brother Giovanni Ceva who was living in Mantua [1]:-

Higher-order curves are ... the primary subject of an extensive correspondence between Ceva and Guido Grandi. Ceva proposed the problem; Grandi reported that such curves had well-defined properties. Grandi replied to Ceva's questions not only in letters, but also in a work on the logarithmic curve published in1701with an appended letter by Ceva.

Ceva was a close friend of the mathematician Pietro Paolo Caravaggio (1617-1688). Caravaggio, who was born in Milan, was professor of mathematics at a college in Milan where he taught both mathematics and Greek literature. Like Ceva, he published both mathematics (his most famous work is *In Geometria Male Retaurata* (1650)) and poetry. Ceva also formed a close friendship with Caravaggio's son, also named Pietro Paolo Caravaggio (1658-1723), who was an assistant to his father at the Milan College, becoming professor of mathematics there in 1688 following his father's death.

However, in many ways Tommaso Ceva was more of a Jesuit humanist than a mathematician, spending more time producing Latin prose than he did mathematics. He was a noted poet, his Latin poem *Jesus Puer*, dedicated to the Holy Roman emperor Joseph I, being translated into many languages including German and Italian. It return, Joseph named Ceva 'Caesarian Theologian'. Milan had been under Spanish rule since the first half of the 16^{th} century but this weakened in 1701 with the outbreak of the War of the Spanish Succession. In 1706 Prince Eugene of Savoy entered Milan. He became its first Austrian governor and the city was, from that time, under Austrian rule. Ceva immediately recognised the new rulers and transferred his allegiance to them.

We have mentioned some of Ceva's friends above, but there is another friend who we should mention since she played an important role in Ceva's career. This is Clelia Grillo (1684-1777), the daughter of Marcantonio, the Marquess of Clarafuentes and the Patrizio of Genoa. She married Giovanni Benedetto Borromeo, the Count of Arona and Marquess of Angera, on 7 July 1707 - she is better known under her married name Clelia Borromeo. Cathy Kessel writes [4]:-

She read Latin, Italian, Spanish, French, English, German, and Arabic, and was so learned that a medal with the inscription "Gloria Genuensium"("Glory of the Genoese")was struck in her honour. She corresponded with people in many European countries, and her home was frequented by cultivated citizens of Milan and illustrious travellers.

Clelia Borromeo was a competent mathematician and is described by Mozans (in *Woman in Science*):-

In addition to a special talent for languages, she possessed so great a capacity for mathematics and mechanics that no problem in these sciences seemed beyond her comprehension.

Clelia Borromeo founded the Academy for Natural Science in Milan (the Accademia dei Vigilanti) and both Tommaso Ceva and his student Giovanni Saccheri were members of this Academy. Ceva gained much from his frequent visits to the Academy and it was through his friendship with Clelia Borromeo that he made contact with both Vicenzo Viviani and Guido Grandi, corresponding with them on mathematical matters.

In addition to this scientific academy, Tommaso Ceva was also a fellow of the literary Academy of Arcadia from 1718. This academy was founded in Rome in 1690 to promote a more natural, simple poetic style. In particular the academy promoted poetry written in the classical Greek or Roman style, so Ceva's poetic style fitted extremely well and his poetry was rated very highly by the Academy.

**Article by:** *J J O'Connor* and *E F Robertson*

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