Coordinates transform relations between algebra and geometry

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.

Descartes published La Géométrie as an appendix to his Discourse, linking algebraic equations with geometric curves.

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.

Later astronomers used Venus transits and geometry to estimate the scale of distances between Earth, Venus and the Sun.