First issue of Philosophical Transactions appears

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.

Horrocks and Crabtree worked outside major academies, showing that knowledge circulated through correspondence and local observation as well as institutions.

Serial publication helped establish priority, criticism and cumulative discussion among dispersed correspondents.

Problems, observations, instruments and calculations could circulate more rapidly than through large books alone.

Its global reports often depended on colonial travel and unequal access; readers should distinguish wide geographic reach from equal participation.

Leibniz presented a model of his stepped reckoner to the Royal Society, aiming to mechanize repeated arithmetic.

The design could support addition, subtraction, multiplication and division through controlled movement of gears.