mdnahas / peano_book

English translation with original Latin for "Arithmetices Principia, Nova Methodo Exposita" by Giuseppe Peano

English Translation of "Arithmetices Principia, Nova Methodo Exposita"

This repository holds an English translation, with original Latin, of Guiseppe Peano's "Arithmetices Principia, Nova Methodo Exposita" or "The Principles of Arithmetic, Presented by a New Method". This treatise is from 1889 and it laid out the axioms of elementary arithmetic that are still used today.

A recent PDF is available.

License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Compiling to PDF

If you missed it above, there is a recent pre-compiled PDF. But if you want the most up-to-date version, or you want to modify it, or you want it on your paper size (e.g., A4), or you are a masochist, you can compile the document. Here's how you do that:

1. Install LaTeX

2. Start a command prompt or terminal window

3. If you have pdflatex, run:

   pdflatex Peano

3. Otherwise run:

   latex Peano
   dvipdfm Peano

If you run into trouble, look at the Peano.tex file and make sure you've installed all the packages used by it. Also, make sure that your reading in the hyperendnotes.sty style file.

Spellcheck

If you commit changes, please spellcheck.

I used the program "aspell". You can install it with your package manager. While at it, try to install the English (EN) and Latin (LA) dictionaries. My package manager did not support a Latin dictionary. You can downloaded the dictionary(s) here.

To install a dictionary, copy it to a temp directory and run

    bunzip2 aspell6-la-*.tar.bz2
    tar xvf aspell6-la-*.tar
    cd aspell6-la-*[^r]
    ./configure
    make
    sudo make install

The following command will run spellcheck on the LaTeX file using both dictionaries.

    cat Peano.tex | aspell -t --lang=la list | aspell --lang=en list > misspelled_words.txt 

I found this command useful to prioritize mistakes.

   sort misspelled_words.txt | uniq -c | sort -n

Origin of the Translation

Michael Nahas created this repository by coping the LaTeX and PDF files on February 27th, 2018 from:

http://vincentverheyen.com/sites/default/files/documents/node_26/Peano.pdf

http://vincentverheyen.com/sites/default/files/documents/node_26/Peano.tex

http://vincentverheyen.com/sites/default/files/documents/node_26/hyperendnotes.sty

According to http://vincentverheyen.com/about "all content ever published on this website is licensed under [Creative Commons] Attribution-ShareAlike 4.0".

Footnote 6 of the original document says "Written by Vincent Verheyen. Last updated on 17/8/2015. I encourage you to use your reason for good. If you want my support, please contact me via http://vincentverheyen.com/contact. It is possible to contribute to the flourishing of knowledge, even when you have an intelligence like mine. Thank you and good luck studying.

"I would like to thank Mauro Allegranzo and acknowledge his support of this work and his various comments during its creation."

NOTE: The website VincentVerheyen.com was expected to be deleted 2018-03-26. The webpages may be available via the Internet Archive's WaybackMachine at https://web.archive.org/web/*/http://VincentVerheyen.com/node/26

peano_book's Issues

Symbols (), [], {} never defined as grouping symbols

On section "I. Punctuation.", page 8 of the pdf, the passage containing:

"we use parentheses, as in algebra"

is greyed out, meaning it is irrelevant, although the symbols used there, (), [], {}, where never defined in its new usage as grouping symbols. Since the original work and also this translation is nicely "self contained" (any new usage of a symbol is defined), I would have added a red note with something like: "To aid visualisation, the precedence grouping of symbols is according to the traditional use of parentheses, brackets and braces like in algebra, instead of only parentheses."

Original "implies" symbol still present

The original circular "deducitur" symbol is still present instead of its modern equivalent "right arrow" once on page 20 of the pdf, section "Remarks." on the last line of the page ("the form α Cβ, where α and β are propositions..."), and twice in the continuation of that paragraph on the start of the next page.