Many historians praised Saccheri's book of 39 theorems. ... In his 33rd theorem is where his flaw can be found. ... Even though his book came to an abrupt conclusion, Saccheri's investigation was a crucial step in the evolving of non- Eluclidian geometries. His major achievement was to break ground for the later geometers who now were free to investigate the new geometries. ...
This art is geometry "the measuring of Earth. ... In thirteen books he collected The Elements of geometry, starting from the most basic concepts, "a point is that which has no part- and "a line is breadthless length-. ... Although I think that we should never renounce reality in our search for philosophical answers, I'm persuaded that it is in a universe similar in nature to the world of geometry that Euclid opens up for us, where Beauty herself exists. ... This theorem is named after its first observer, Pythagoras, but it was Euclid's insight what made it clear enough to becom...