{"id": "card_chain_legendre_1798", "kind": "reference", "title": "Legendre 1798 — Essai sur la théorie des nombres", "body": "A.-M. Legendre (1798). Essai sur la théorie des nombres. Paris, 1798 (2nd ed. 1808). Cited by its record. License as found: public domain (the author died more than a century ago, or the work was published before 1930). What it gave the chain: the first published guess at the prime count: pi(x) is about x / (log x - 1.08366).", "source": {"label": "A.-M. Legendre (1798), Paris, 1798 (2nd ed. 1808)", "url": "", "domain": "mathematics", "authority_tier": "reference"}, "shelf": "codex", "box": "chain", "bands": ["chain", "record", "1798", "legendre", "mathematics"], "subject": "Essai sur la théorie des nombres", "connections": [{"to_card_id": "card_floor_riemann", "relationship": "part_of", "evidence": "a root of this chain - one of the two trees it began from"}, {"to_card_id": "card_chain_gauss_1849", "relationship": "enables", "evidence": "the logarithmic integral li(x) as the count of primes - read off the log tables he counted primes in"}, {"to_card_id": "card_chain_chebyshev_1852", "relationship": "enables", "evidence": "pi(x) is between 0.92 and 1.11 times x / log x; Bertrand's postulate proven"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.chain", "facets": {"subject": ["1798", "legendre", "mathematics", "record"]}, "presentation": {"glyph": "•", "kind_label": "chain", "by": "A.-M. Legendre (1798), Paris, 1798 (2nd ed. 1808)", "authority": "reference", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_riemann", "title": "The Riemann chain - from Euler's product and Legendre's count to the critical line", "relationship": "part of", "why": "a root of this chain - one of the two trees it began from", "href": "/card/card_floor_riemann", "resolved": true}, {"id": "card_chain_gauss_1849", "title": "Gauss 1849 — Letter to Encke, 24 December 1849 (the count made in 1792–93)", "relationship": "enables", "why": "the logarithmic integral li(x) as the count of primes - read off the log tables he counted primes in", "href": "/card/card_chain_gauss_1849", "resolved": true}, {"id": "card_chain_chebyshev_1852", "title": "Chebyshev 1852 — Mémoire sur les nombres premiers", "relationship": "enables", "why": "pi(x) is between 0.92 and 1.11 times x / log x; Bertrand's postulate proven", "href": "/card/card_chain_chebyshev_1852", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_chain_legendre_1798", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_chain_legendre_1798"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}