The purpose of this note is to remind readers of information at times well-known and at times almost forgotten, namely that for several centuries in the modern West Euclid’s Elements was simultaneously regarded as the epitome of knowledge and as flawed and confused. It is well known that many mathematicians brought up on Euclid and other Greek geometers complained that they found themselves compelled to accept the conclusions but not instructed in how to do geometry, and the long struggle with the parallel postulate has also been frequently discussed. The confusion discussed here is different, and relates to the concepts of straightness and shortest distance. It will also be suggested that the growing awareness of the defects in Euclid’s presentation by the end of the 18th century contributed to the creation of the new geometries of the 19th century: projective geometry and non-Euclidean geometry.
...MoreBook De Risi, Vincenzo (2015) Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age.
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