These ideas provide our starting point. We shall see in later chapters that matters take a very different turn in the nineteenth century.
Nineteenth century mathematicians realized that the eighteenth century certainty of geometry was mistaken. Geometry was an empirical science. It reported the way our space happened to to be, not the way it had to be. If that was so, were possible and our experience of space might well have been different. In the nineteenth century, these were regarded as possibilities that were unrealized. Nature had many choices but, they thought, she chose Euclid's system.
In the seventeenth century, with new-found confidence, natural philosophers rebuilt all learning from scratch, discarding the wisdom of antiquity as flawed. In that effusion of new investigation, one achievement stood unchallenged. That was Euclid's . Indeed its premier position was reinforced when the structure it gave to geometrical knowledge was to codify his new mechanics. Like Euclid, Newton listed definitions and, where Euclid gave axioms and postulates, Newton gave his celebrated three laws of motion. Euclid's became the template for organizing knowledge, be it a new science such as Newton's or even knowledge outside science.
The First Six Books of The Elements of Euclid (1847) – …
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Euclid - Ancient History Encyclopedia
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Euclid's Elements by Euclid - Goodreads
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In 1968 at age 7 in Grade 2, Jonathan J. Crabtree noticed Euclid's definition of multiplication made no sense. Two added to itself three times is 8, not 6, as people have said for centuries. (HINT 2 added to itself once is 4.)
Jonathan went on to explore hundreds of original source mathematics books & manuscripts spanning 16 languages. Euclid's definition of multiplication had been incorrectly translated into English in 1570 and was NEVER corrected!
Jonathan's recent and titled, reveals when why and how western mathematics education came to be filled with mis-truths, contradictions and inconsistencies.