Discourse on Method appears with La Géométrie

Catholic states adopted the reform first, while other societies accepted, adapted or resisted it at different times; calendar history was not a single global switch.

In several Catholic territories, Thursday 4 October was followed by Friday 15 October 1582. Ten numbered dates were omitted to realign calendar and season.

Century years became leap years only when divisible by 400, producing a mean year closer to the tropical year than the Julian rule.

Events near the reform may have Old Style and New Style dates. Databases must identify the calendar before comparing dates.

European empires later carried Gregorian dating into colonies, while many communities retained religious and Indigenous calendars alongside it.

The work helped establish methods later called Cartesian geometry, although modern coordinate notation developed gradually.

Publication in French rather than only Latin widened access while still excluding many people from formal scholarly networks.

Descartes built within traditions that included Greek geometry and algebra transmitted and extended through Arabic and European scholarship.

Jeremiah Horrocks predicted and observed Venus crossing the Sun; William Crabtree made an independent observation nearby.

Horrocks revised existing astronomical tables and used mathematical reasoning to predict a transit others had not expected.