Giovanni Ceva

1647?-1734

Italian Mathematician

As an engineer, Giovanni Ceva concerned himself with applied mathematics; but his other career, as a geometer, took him deep into the realm of pure math. He became the era's foremost authority on geometric problems, working particularly with transversals, and is also credited with Ceva's theorem, on a triangle's center of gravity. Other writings addressed areas of mathematical application ranging from mechanics to economics.

The son of a wealthy and influential family—his younger brother Tomasso (1648-1737), was destined to become a famous mathematician as well—Ceva studied at Pisa. Some of his most significant writing appeared during the late 1670s and early 1680s, when he was in his early to mid-thirties. Perhaps his most notable work was De lineis rectis (Concerning Straight Lines), published in 1678. This work contained Ceva's theorem, on the geometry of triangles, which in turn related to an area of interest throughout much of Ceva's career: center of gravity. His theorem found the center of gravity for an equilateral triangle at the place where lines drawn from the vertices to opposite sides intersected.

Ceva followed De lineis with Opuscula mathematica (A Short Mathematical Work) in 1682. Here he again returned to centers of gravity, this time expanding his studies to other shapes. The book also contained an infamous error on Ceva's part, his statement that the periods of oscillation pendulums are on the same ratio as their lengths.

It is easy to understand how he could have mistakenly deduced such a correlation, and in any case Ceva corrected his mistake in a later book, Geometrica motus (The Geometry of Motion, 1692). The latter concerned the geometry of motion, and contained elements that foreshadowed the infinitesimal calculus soon to be developed independently by Gottfried Wilhelm von Leibniz (1646-1716) and Sir Isaac Newton (1642-1727).

Ceva married in the 1670s and fathered a daughter in 1679. When he was a little more than 40 years old, in 1686, he went to work for the Duke of Mantua, a region where he would spend much of his career. In addition to holding a professorship at the local university, Ceva served the duke in a variety of official capacities. He continued his mathematical studies, however, and in 1711 published a study of economics, De re numeraria (Concerning Money Matters), in which he applied his knowledge.

Indeed, applied mathematics was at the center of Ceva's later career. As a hydraulic engineer in Mantua, he was responsible for a number of projects, but—in an act that suggests he may have been an early conservationist—he successfully opposed a scheme to divert the River Reno into the Po. As time went on, Ceva found that professional and family pressures kept him away from his mathematical studies, however. He died on February 3, 1737, and was buried at St. Teresa de Carmelitani Scalzi, a church in Mantua.

JUDSON KNIGHT