Halley supports publication of the Principia

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.

The machine sought to transfer routine calculation from human operators to a device, anticipating later debates about automation.

Instrument makers, metalworkers and workshop techniques were essential to realizing designs often credited only to a philosopher-mathematician.

The Mathematical Principles of Natural Philosophy presented laws of motion and universal gravitation in a geometric mathematical framework.

The work argued that the same quantitative laws could explain falling bodies, planetary paths and tides.

Astronomical and geographic data came through imperial and maritime networks; its achievement was mathematical but not socially isolated.

Seki's death provides an exact date for a body of independent Japanese work in algebra, determinants, elimination and numerical calculation.

Seki developed procedures for systems of equations independently of contemporary European approaches.

His notation and teaching shaped wasan, the mathematical tradition cultivated during the Edo period.