We met to discuss “The Great Philosophers” programme on Descartes.  His projects included how to go forward with the scientific ideas of Aristotle in a sound manner.  His "Discourse on the Method of Rightly Conducting One's Reason” addressed this - and by the way he appended a book on his analytical geometry.  As the title suggests, he favoured reason over observation, because sometimes we are misled by what we see.  So his task was to work back through any beliefs which were in any way open to doubt, and through his “Meditations” he arrived at “Cogito ergo sum” - even if I doubt everything I believe, this doubting proves I exist.  Various arguments of circularity in his argument have been debated, but it is generally agreed to be great philosophy.  His proposal that the mind and the body are two distinct substances, and that reality is the mind, stemming from God, and bodies and substances are mere extensions to express the mind started a long-running debate.  The “In our time” episode, and Stanford Encyclopedia entries on "Descartes’ Life and Works” and the “Cogito”, and a longer entry than most in The Dorling Kinnersley “The Philosophy Book by Will Cunningham  (“The Yellow Book”) were all helpful.  You can even read his “Meditations" on Project Gutenberg - the first two go through his process of scepticism.