---
title: "Arithmetices principia, nova methodo exposita"
authors:
  - "Giuseppe Peano"
year: 1889
venue: "Fratres Bocca, Turin"
arxiv: null
doi: null
source: "https://archive.org/details/arithmeticespri00peangoog"
topics:
  - arithmetic
  - axioms
  - peano
seed_rank: 490
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: foundations-of-computing
cites:
  - title: "Begriffsschrift"
    url: "https://gdz.sub.uni-goettingen.de/id/PPN538957069"
    year: 1879
see:
  - "489-begriffsschrift"
---

# Arithmetices principia, nova methodo exposita

## One-sentence takeaway

Peano's 1889 pamphlet axiomatizes the natural numbers with 0, successor, and induction, written in a symbolic Latin that treats arithmetic as a formal object rather than a collection of obvious truths.

## Why it matters here

PA/PRA are the default formal arithmetics when Broadside discusses proof, totality, and computable functions; this is the source text, later Dedekind–Peano formulations notwithstanding.

## Key ideas

- Primitive signs for zero and successor; axioms that successor is injective and misses zero; induction as the defining property of \(\mathbb{N}\).
- Explicit aim: write proofs so that each step is a permitted transformation of symbols.
- Bridge from 19th-century foundations (Dedekind, Frege, Grassmann) to the Hilbert-era metamathematics that takes PA as the test theory.
- Forty-odd pages, Latin, Bocca 1889; the Harvard/IA scan `arithmeticespri00peangoog` is the usual open copy.

## Caveats

## Links

- Internet Archive: https://archive.org/details/arithmeticespri00peangoog