The work of Guldin is covered in four separate volumes which he published during his life, they are entitled De Centro Gravitas. Volume one considers centres of gravity with particular reference to the centre of gravity of the Earth. The second volume contains what is now known as Guldin's second rule or Guldin's theorem. Volume three considers cones and cylinders.

Paul Guldin was born Habakuk Guldin in St Gall (now Sankt Gallen), Switzerland. Initially a goldsmith Guldin became a Catholic (his parents were Protestants but of Jewish descent) aged 20 when he joined the Jesuits. On joining the order Guldin changed his name to Paul. In 1609 he was sent to college in Rome where he subsequently taught mathematics. He also taught at Graz in Austria, a position he gave up in 1623 to become professor of mathematics in Vienna. Eventually in 1637 Guldin returned to Graz to teach mathematics. From1627 Guldin kept up a lengthy correspondence with Johannes Kepler, this was initially mostly about religion and only the later letters deal with mathematics and astronomy.

Guldin's theorem is also known as Pappus's theorem and it was originally written down by Pappus of Alexandria sometime in the fourth century. It is believed that this is merely coincidence. Although Guldin had access to translations of the work of Pappus, and he regularly quoted from them, various historians have shown that they were incomplete and lacked Pappus's theorem. Also during his lifetime the theorem was recognised as being that of Guldin, by amongst others Kepler. Guldin ensured that Kepler had a telescope when Kepler was persecuted for religious reasons and Kepler includes a grateful acknowledgement to Guldin in The Dream which was published posthumously by Kepler's son. The letters between Guldin and Kepler are published in Johannes Kepler Gesammelte Werke. Gulidn eventually died in 1643 in Graz, Austria aged 66.