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A Test: Is a Picture is Worth a Thousand Words?

In Paris in 1764, Abbé De la Caille wrote this 277-page text Leçons élémentaires de Mathematiques ou élémens d'Algebre et de Géométrie. The book has six great folding plates, filled with ideas that linked algebra and geometry.

Try to determine what fascinating mathematical ideas are being explored via the diagrams on these folding plates: