{"id": "card_chain_mercator_1668", "kind": "reference", "title": "Mercator 1668 — Logarithmotechnia", "body": "N. Mercator (1668). Logarithmotechnia. London, 1668. 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: log(1 + x) = x - x^2/2 + x^3/3 - ... : the logarithm as a series.", "source": {"label": "N. Mercator (1668), London, 1668", "url": "", "domain": "mathematics", "authority_tier": "reference"}, "shelf": "codex", "box": "chain", "bands": ["chain", "record", "1668", "mercator", "mathematics"], "subject": "Logarithmotechnia", "connections": [{"to_card_id": "card_chain_saint_vincent_1647", "relationship": "builds_on", "evidence": "log(1 + x) = x - x^2/2 + x^3/3 - ... : the logarithm as a series"}, {"to_card_id": "card_chain_euler_1748", "relationship": "enables", "evidence": "e, and the exponential and the logarithm as inverse functions: the table-logarithm of Napier and the hyperbola-logarithm of Saint-Vincent are one function"}, {"to_card_id": "card_chain_euler_1737", "relationship": "enables", "evidence": "the Euler product over the primes; its logarithm turns the product into a sum, and the sum of 1/p diverges like log log x"}], "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": ["1668", "mathematics", "mercator", "record"]}, "presentation": {"glyph": "•", "kind_label": "chain", "by": "N. Mercator (1668), London, 1668", "authority": "reference", "posted": "", "standing": ""}, "neighbors": [{"id": "card_chain_saint_vincent_1647", "title": "Saint-Vincent 1647 — Opus geometricum quadraturae circuli et sectionum coni", "relationship": "builds on", "why": "log(1 + x) = x - x^2/2 + x^3/3 - ... : the logarithm as a series", "href": "/card/card_chain_saint_vincent_1647", "resolved": true}, {"id": "card_chain_euler_1748", "title": "Euler 1748 — Introductio in analysin infinitorum (E101-E102)", "relationship": "enables", "why": "e, and the exponential and the logarithm as inverse functions: the table-logarithm of Napier and the hyperbola-logarithm of Saint-Vincent are one function", "href": "/card/card_chain_euler_1748", "resolved": true}, {"id": "card_chain_euler_1737", "title": "Euler 1737 — Variae observationes circa series infinitas (E72)", "relationship": "enables", "why": "the Euler product over the primes; its logarithm turns the product into a sum, and the sum of 1/p diverges like log log x", "href": "/card/card_chain_euler_1737", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_chain_mercator_1668", "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_mercator_1668"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}