In 1704 he held the departmental chair at Collège Mazarin and also became professor of mathematics at the Collège Royal.
He was elected to the Berlin Academy in 1713 and to the Royal Society in 1718.
Many of his works were published in Paris in 1725, three years after his death.
His lectures at Mazarin were published in Elements de mathematique in 1731.
Varignon was a friend of Newton, Leibniz, and the Bernoulli family.
Varignon's principal contributions were to graphic statics and mechanics.
Except for l'HĂ´pital, Varignon was the earliest and strongest French advocate of infinitesimal calculus, and exposed the errors in Michel Rolle's critique thereof.
He recognized the importance of a test for the convergence of series, but analytical difficulties prevented his success.