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

Grade 2 — contracted English braille (EBAE-compatible subset). Translated on this server by our own braille engine (BRF — Braille Ready Format, Library of Congress fdd000551). View Grade 1 instead.

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430,699 braille cells · 453 embossed pages at 40×25 · 2,394 unrepresentable characters omitted

⠊⠝⠙⠑⠏⠢⠙⠢⠉⠑⠀⠃⠕⠹⠀⠷⠀⠠⠗⠊⠑⠍⠁⠝⠝⠀⠀⠯⠀⠷⠀
⠠⠇⠕⠃⠁⠞⠡⠑⠺⠎⠅⠽⠲⠀⠠⠓⠑⠇⠍⠓⠕⠇⠞⠵⠀⠊⠎⠀⠃⠽⠀⠋⠜⠀⠮⠀⠍⠕⠌⠀
⠺⠊⠙⠑⠇⠽⠀⠗⠑⠁⠙⠀⠷⠀⠁⠇⠇⠀⠀⠺⠗⠊⠞⠻⠎⠀⠕⠝⠀
⠠⠍⠑⠞⠁⠛⠑⠕⠍⠑⠞⠗⠽⠂⠀⠯⠀⠦⠀⠺⠗⠊⠞⠬⠎⠂⠀⠁⠇⠍⠕⠌⠀⠁⠇⠕⠝⠑⠂⠀
⠗⠑⠏⠗⠑⠎⠢⠞⠀⠀⠞⠕⠀⠏⠓⠊⠇⠕⠎⠕⠏⠓⠻⠎⠀⠮⠀⠍⠕⠙⠻⠝⠀
⠍⠁⠮⠍⠁⠞⠊⠉⠁⠇⠀⠌⠯⠏⠕⠔⠞⠀⠕⠝⠀⠹⠊⠎⠀⠎⠥⠃⠚⠑⠉⠞⠲⠀⠀⠠⠃⠀⠦⠀
⠊⠍⠏⠕⠗⠞⠁⠝⠉⠑⠀⠊⠎⠀⠍⠥⠡⠀⠛⠗⠑⠁⠞⠻⠂⠀⠔⠀⠹⠊⠎⠀⠙⠕⠍⠁⠔⠂⠀⠵
⠀⠁⠀⠏⠓⠊⠇⠕⠎⠕⠏⠓⠻⠀⠀⠹⠁⠝⠀⠵⠀⠁⠀⠍⠁⠮⠍⠁⠞⠊⠉⠊⠁⠝⠆⠀
⠁⠇⠍⠕⠌⠀⠦⠀⠕⠝⠇⠽⠀⠕⠗⠊⠛⠔⠁⠇⠀⠍⠁⠮⠍⠁⠞⠊⠉⠁⠇⠀⠀⠗⠑⠎⠥⠇⠞⠂
⠀⠵⠀⠗⠑⠛⠜⠙⠎⠀⠠⠛⠑⠕⠍⠑⠞⠗⠽⠂⠀⠊⠎⠀⠦⠀⠏⠗⠕⠷⠀⠷⠀
⠠⠗⠊⠑⠍⠁⠝⠝⠄⠎⠀⠿⠍⠥⠇⠁⠀⠿⠀⠀⠮⠀⠊⠝⠋⠔⠊⠞⠑⠎⠊⠍⠁⠇⠀⠁⠗⠉⠂⠀
⠯⠀⠑⠧⠢⠀⠹⠊⠎⠀⠏⠗⠕⠷⠀⠴⠀⠋⠜⠀⠋⠀⠗⠊⠛⠊⠙⠂⠀⠥⠝⠞⠊⠇⠀⠀⠠⠇⠊⠑
⠀⠗⠑⠿⠍⠫⠀⠭⠀⠃⠽⠀⠦⠀⠍⠑⠹⠕⠙⠀⠷⠀⠉⠕⠝⠞⠔⠥⠳⠎⠀⠛⠗⠳⠏⠎⠲⠀⠠⠔
⠀⠹⠊⠎⠀⠡⠁⠏⠞⠻⠂⠀⠀⠮⠗⠑⠿⠑⠂⠀⠕⠝⠇⠽⠀⠞⠺⠕⠀⠷⠀⠦⠀⠺⠗⠊⠞⠬⠎⠀
⠝⠑⠫⠀⠕⠉⠉⠥⠏⠽⠀⠥⠂⠀⠝⠁⠍⠑⠇⠽⠀⠮⠀⠞⠺⠕⠀⠀⠁⠗⠞⠊⠉⠇⠑⠎⠀⠔⠀⠮
⠀⠠⠺⠊⠎⠎⠢⠎⠡⠁⠋⠞⠇⠊⠡⠑⠀⠠⠁⠃⠓⠯⠇⠥⠝⠛⠢⠂⠀⠠⠧⠕⠇⠲⠀
⠠⠠⠊⠊⠲⠂⠀⠑⠝⠞⠊⠞⠇⠫⠀⠀⠗⠑⠎⠏⠑⠉⠞⠊⠧⠑⠇⠽⠀⠠⠥⠑⠃⠻⠀⠙⠊⠑⠀
⠹⠁⠞⠎⠡⠇⠊⠡⠢⠀⠠⠛⠗⠥⠝⠙⠇⠁⠛⠢⠀⠙⠻⠀⠠⠛⠑⠕⠍⠑⠞⠗⠊⠑⠂⠀⠀
⠼⠁⠓⠋⠋⠀⠶⠏⠲⠀⠼⠋⠁⠚⠀⠋⠋⠲⠶⠂⠀⠯⠀⠠⠥⠑⠃⠻⠀⠙⠊⠑⠀
⠠⠹⠁⠞⠎⠁⠡⠢⠂⠀⠙⠊⠑⠀⠙⠻⠀⠠⠛⠑⠕⠍⠑⠞⠗⠊⠑⠀⠵⠥⠍⠀⠀⠠⠛⠗⠥⠝⠙⠑
⠀⠇⠊⠑⠛⠢⠂⠀⠼⠁⠓⠋⠓⠀⠶⠏⠲⠀⠼⠋⠁⠓⠀⠋⠋⠲⠶⠲⠀⠀⠀⠀⠼⠃⠑⠲⠀⠠⠔⠀
⠮⠀⠋⠊⠗⠌⠀⠷⠀⠘⠮⠂⠀⠱⠊⠡⠀⠊⠎⠀⠡⠊⠑⠋⠇⠽⠀
⠏⠓⠊⠇⠕⠎⠕⠏⠓⠊⠉⠁⠇⠂⠀⠀⠠⠓⠑⠇⠍⠓⠕⠇⠞⠵⠀⠛⠊⠧⠑⠎⠀⠓⠔⠞⠎⠀⠷⠀
⠦⠀⠮⠝⠀⠥⠝⠉⠕⠍⠏⠇⠑⠞⠫⠀⠍⠁⠮⠍⠁⠞⠊⠉⠁⠇⠀⠐⠺⠂⠀⠀⠃⠀⠔⠀⠮⠀
⠍⠁⠔⠀⠉⠕⠝⠞⠢⠞⠎⠀⠓⠊⠍⠎⠑⠇⠋⠀⠾⠀⠁⠀⠌⠁⠞⠑⠍⠢⠞⠀⠷⠀

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