In 1583 Thomas Fincke produced a mathematical text book entitled Geometria Rotunda, which brought the world the terms tangent and secant. This work also includes several trigonometric equations relating to these functions.

Thomas Fincke was born in Flensburg in what was then part of Denmark (Flensburg is now a part of Germany). His university studies covered such places as Strasbourg, Jena, Wittenberg, Heidelberg, Leipzig, Basel, Padua, and Pisa. After all of this study he qualified as a medical doctor, a role which he took from 1587 to 1591 in Flensburg. Fincke left this position to become professor of mathematics at Copenhagen (after a personal invitation by the chancellor, Niels Kaas), which he relinquished in 1602 to become professor of rhetoric. This chair lasted for only one year as in 1603 he became professor of medicine at Copenhagen. On five occasions between 1598 and 1633 Fincke served as rector of the university. As well as his mathematical text book Geometria Rotunda, Fincke also produced several works on astronomy and astrology. He died in Copenhagen at the age of 95. For the last 16 years of his life he was still professor of medicine, though he appointed a deputy to carry out the majority of his duties.

The generally accepted form of spelling of his name is Thomas Fincke, though some texts may refer to the archaic Danish spelling of Finke or indeed Finck.