Greek geometers were the model for mathematicians when Descartes revolutionized geometry by introducing coordinates, making it possible to approach geometry through algebraic methods. Cartesian geometry was born.
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Almost two thousand years of geometry! That is how long it took, with Descartes, to develop the first tools for studying those mathematical objects we all think we know: curves. How far we have come since the tentative explorations of ancient Greek scholars!
François Viète ranks among those scholars celebrated for their considerable contribution to mathematics. He did not invent algebra, but his work propelled the discipline forward spectacularly.
Mathematical writings contain words, but also signs, symbols and figures. Texts are therefore meant to be looked at as much as read, as works of geometry from antiquity to the present day attest.
Some geometric figures are a delight to behold: a host of skilfully arranged lines, intertwined with a graceful curve that seems barely to touch each one. What mathematical theory lies behind them? The theory of envelopes of lines.
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