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   An Illustration of Geometry from the Margarita Philosophica
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An Illustration of Geometry from the Margarita Philosophica

This is an illustration of geometry from the 'mathematical appendix' to the 1512 version of a book called the Margarita Philosophica. It shows a simple mathematical instrument called a 'Jacob's staff' being used to measure the height of a building, based on the principle of similar triangles.

The Margarita Philosophica first came out in 1503. Roughly translated, the title Margarita Philosophica means 'pearl of knowledge'. The Margarita Philosophica was the most important and longest encyclopaedia of knowledge in the Middle Ages and early Renaissance. It contained all the knowledge that students were supposed to learn about and was used as the main textbook in universities.

The author of the Margarita Philosophica was someone called Gregorius Reisch. Gregorius Reisch was a monk and taught in the University of Freiburg that is in the south of Germany. Freiburg University was opened on the 26th April, 1460. When it was opened it only had seven teachers for 214 students. It also only had four different departments: a theology department (for studying religion), a law department, a medical department and an arts department.

Surprisingly, in medieval universities maths was taught in the arts department. Courses in the arts department usually lasted three years. The arts course was broken down into two parts called the 'trivium' and the 'quadrivium'. The trivium was the easiest.

It is where we get the word 'trivial' from. In the trivium students had to study grammar, rhetoric (speaking) and logic. In the quadrivium students studied arithmetic, geometry, astronomy and music. Put together the trivium and the quadrivium made what were called the 'seven liberal arts'. These were called 'liberal' because to begin with they were studied mainly to improve student's mental abilities rather than to teach them practical skills. The seven liberal arts were compulsory for all university students. If they passed the arts course students could then move on to the harder subjects like theology, law and medicine.

The mathematical appendix to the Margarita Philosophica that this illustration comes from was added to it nine years after it was first published. The first part of the Margarita Philosophica was mostly to do with the theory of geometry called 'speculative geometry'. The appendix however was all about the practical problems that could be solved using geometric principles.

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