Johann Vallerius – did he teach Leibniz' theories?
Johann Vallerius succeeded his father Harald as professor of mathematics in 1712. He had already had the opportunity to teach at the University as an adjunct. There are a number of dissertations written by Johann that treat the infinitely small. However, he did not leave behind any works dealing with differential calculus or the theory of fluxions. On the other hand, the catalog of what lectures were to be held states that Johann Vallerius would be lecturing privately (that is, in his home) about ”Geometria Analysin Finitorum&infinitorum, Calculum differentialem, Rectificationem Curvarum.”
This indicates that Johann was prepared to teach parts of Leibniz' differential calculus. However, we do not know whether the lectures were ever really carried out, nor how much Johann really knew about the new calculus.
Johann Vallerius never had a chance to develop his knowledge of mathematics. He died of tuberculosis in 1718 at the age of 41.
This dissertation deals with the contact angle (also called the horn angle) that is the ”angle” between a circle and a tangent to the circle. Euclid states in Elements, book 3, theorem 16, that the contact angle is smaller than any rectilinear angle. We can therefore say that the contact angle is the only ”visible” infinitesimal.