Mathematical knowledge has puzzled philosophers for millennia. The LSE’s own Imre Lakatos coined the term “Euclidean Programme” for the historically dominant way of thinking about this phenomenon. In ...

Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been ...

About a month ago, I discussed how the axiomatic system developed by Euclid to study geometry (and later employed by giants such as Johannes Kepler and Issac Newton) became the intellectual ...

Many ancient societies knew important mathematical facts, but only one discovered mathematics—which is not a collection of accurate rules of thumb, but a body of knowledge organized deductively, by ...

Euclid flourished about 50 years after Aristotle and was certainly familiar with Aristotle's Logic. Euclid's organisation of the work of earlier geometers was truly innovative. His results depended ...

Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

This article studies Ibn al-Haytham's treatment of the common notions from Euclid's Elements (usually referred to today as the axioms). We argue that Ibn al-Haytham initiated a new approach with ...

THIS work will be found really valuable by all students of geometry, especially by those who know little or nothing of the non-Euclidean theories. First of all we have a discussion of the elementary ...

IT is interesting to compare the attitudes of the two most recent writers in English who deal with Euclidean geometry. Sir Thomas Heath, in the second edition of his three-volume translation of the ...