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Library / Mathematics / An essay on the foundations of geometry / Braille

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 · 4,470 unrepresentable characters omitted

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

These are the same pages the .brf download embosses — form-feed breaks and all. BRF opens in braille software (Duxbury, BrailleBlaster), on embossers, and on refreshable displays.