Skip to contentSkip to Braille Studio

Library / Mathematics / The First 498 Bernoulli Numbers / Braille

The First 498 Bernoulli Numbers ⠃⠗⠋ 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.

Download .brf — Grade 2 Download .brf — Grade 1 Plain-text reader .txt

89,968 braille cells · 126 embossed pages at 40×25 · 4 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.