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An essay on the foundations of geometry ⠃⠗⠋ braille edition

Grade 1 — uncontracted, letter-for-letter. Translated on this server by our own braille engine (BRF — Braille Ready Format, Library of Congress fdd000551). View Grade 2 instead.

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504,362 braille cells · 533 embossed pages at 40×25 · 2,394 unrepresentable characters omitted

⠉⠕⠝⠉⠑⠊⠧⠑⠀⠁⠝⠙⠀⠙⠑⠎⠉⠗⠊⠃⠑⠂⠀⠁⠀⠎⠏⠁⠉⠑⠀⠙⠊⠋⠋⠑⠗⠑⠝⠞
⠀⠋⠗⠕⠍⠀⠞⠓⠁⠞⠀⠺⠑⠀⠁⠉⠞⠥⠁⠇⠇⠽⠀⠀⠓⠁⠧⠑⠂⠀⠠⠇⠁⠝⠙⠀⠊⠎⠂⠀
⠊⠝⠀⠍⠽⠀⠕⠏⠊⠝⠊⠕⠝⠂⠀⠥⠝⠟⠥⠑⠎⠞⠊⠕⠝⠁⠃⠇⠽⠀⠊⠝⠀⠞⠓⠑⠀
⠗⠊⠛⠓⠞⠲⠀⠠⠋⠕⠗⠀⠁⠀⠀⠏⠥⠗⠑⠀⠠⠅⠁⠝⠞⠊⠁⠝⠂⠀⠺⠓⠕⠀
⠍⠁⠊⠝⠞⠁⠊⠝⠎⠂⠀⠺⠊⠞⠓⠀⠠⠇⠁⠝⠙⠂⠀⠞⠓⠁⠞⠀⠝⠕⠝⠑⠀⠕⠋⠀⠞⠓⠑⠀
⠁⠭⠊⠕⠍⠎⠀⠉⠁⠝⠀⠀⠃⠑⠀⠏⠗⠕⠧⠑⠙⠂⠀⠞⠓⠊⠎⠀⠟⠥⠑⠎⠞⠊⠕⠝⠀⠊⠎⠀
⠕⠋⠀⠛⠗⠑⠁⠞⠀⠊⠍⠏⠕⠗⠞⠁⠝⠉⠑⠲⠀⠠⠃⠥⠞⠀⠊⠋⠂⠀⠁⠎⠀⠠⠊⠀⠓⠁⠧⠑
⠀⠀⠍⠁⠊⠝⠞⠁⠊⠝⠑⠙⠂⠀⠎⠕⠍⠑⠀⠕⠋⠀⠞⠓⠑⠀⠁⠭⠊⠕⠍⠎⠀⠁⠗⠑⠀
⠎⠥⠎⠉⠑⠏⠞⠊⠃⠇⠑⠀⠕⠋⠀⠁⠀⠞⠗⠁⠝⠎⠉⠑⠝⠙⠑⠝⠞⠁⠇⠀⠀⠏⠗⠕⠕⠋⠂⠀
⠺⠓⠊⠇⠑⠀⠞⠓⠑⠀⠕⠞⠓⠑⠗⠎⠀⠉⠁⠝⠀⠃⠑⠀⠧⠑⠗⠊⠋⠊⠑⠙⠀
⠑⠍⠏⠊⠗⠊⠉⠁⠇⠇⠽⠂⠀⠞⠓⠑⠀⠟⠥⠑⠎⠞⠊⠕⠝⠀⠀⠊⠎⠀⠋⠗⠑⠑⠙⠀⠋⠗⠕⠍
⠀⠏⠎⠽⠉⠓⠕⠇⠕⠛⠊⠉⠁⠇⠀⠊⠍⠏⠇⠊⠉⠁⠞⠊⠕⠝⠎⠂⠀⠁⠝⠙⠀⠞⠓⠑⠀
⠊⠍⠁⠛⠊⠝⠁⠃⠊⠇⠊⠞⠽⠀⠕⠗⠀⠀⠝⠕⠝⠤⠊⠍⠁⠛⠊⠝⠁⠃⠊⠇⠊⠞⠽⠀⠕⠋⠀
⠍⠑⠞⠁⠛⠑⠕⠍⠑⠞⠗⠊⠉⠁⠇⠀⠎⠏⠁⠉⠑⠎⠀⠃⠑⠉⠕⠍⠑⠎⠀
⠥⠝⠊⠍⠏⠕⠗⠞⠁⠝⠞⠲⠀⠀⠀⠀⠼⠋⠊⠲⠀⠠⠺⠑⠀⠉⠕⠍⠑⠀⠝⠕⠺⠀⠞⠕⠀⠞⠓⠑
⠀⠞⠓⠊⠗⠙⠀⠁⠝⠙⠀⠍⠕⠎⠞⠀⠊⠍⠏⠕⠗⠞⠁⠝⠞⠀⠟⠥⠑⠎⠞⠊⠕⠝⠂⠀⠞⠓⠑⠀
⠗⠑⠇⠁⠞⠊⠕⠝⠀⠕⠋⠀⠠⠛⠑⠕⠍⠑⠞⠗⠽⠀⠞⠕⠀⠠⠍⠑⠉⠓⠁⠝⠊⠉⠎⠲⠀
⠠⠞⠓⠑⠗⠑⠀⠁⠗⠑⠀⠞⠓⠗⠑⠑⠀⠎⠑⠝⠎⠑⠎⠀⠊⠝⠀⠺⠓⠊⠉⠓⠀⠀
⠠⠓⠑⠇⠍⠓⠕⠇⠞⠵⠄⠎⠀⠁⠏⠏⠑⠁⠇⠀⠞⠕⠀⠗⠊⠛⠊⠙⠀⠃⠕⠙⠊⠑⠎⠀⠍⠁⠽⠀
⠃⠑⠀⠞⠁⠅⠑⠝⠒⠀⠞⠓⠑⠀⠋⠊⠗⠎⠞⠂⠀⠠⠊⠀⠞⠓⠊⠝⠅⠂⠀⠀⠊⠎⠀⠞⠓⠑⠀
⠎⠑⠝⠎⠑⠀⠊⠝⠀⠺⠓⠊⠉⠓⠀⠓⠑⠀⠕⠗⠊⠛⠊⠝⠁⠇⠇⠽⠀⠊⠝⠞⠑⠝⠙⠑⠙⠀
⠊⠞⠆⠀⠞⠓⠑⠀⠎⠑⠉⠕⠝⠙⠀⠎⠑⠑⠍⠎⠀⠀⠞⠕⠀⠃⠑⠀⠞⠓⠑⠀⠎⠑⠝⠎⠑⠀
⠺⠓⠊⠉⠓⠀⠓⠑⠀⠁⠙⠕⠏⠞⠑⠙⠀⠊⠝⠀⠓⠊⠎⠀⠙⠑⠋⠑⠝⠉⠑⠀⠁⠛⠁⠊⠝⠎⠞⠀
⠠⠇⠁⠝⠙⠆⠀⠺⠓⠊⠇⠑⠀⠀⠞⠓⠑⠀⠞⠓⠊⠗⠙⠀⠊⠎⠀⠁⠙⠍⠊⠞⠞⠑⠙⠀⠃⠽⠀
⠠⠇⠁⠝⠙⠂⠀⠁⠝⠙⠀⠺⠊⠇⠇⠀⠃⠑⠀⠁⠙⠍⠊⠞⠞⠑⠙⠀⠊⠝⠀⠞⠓⠑⠀

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