Treccani History of Science
The age of Enlightenment
G3 – Astronomy, analytical mechanics and mathematics
Edited by Michael Hoskin, Ivor Grattan-Guinness
The astronomy of the solar system from Newton to Laplace
• 1. Astronomy in the Principia
• 2. Controversy on the figure of the Earth.
• 3. Celestial mechanics becomes algebraically analytical
• 4. The motion of the lunar apse and the inverse square law
• 5. The return of Halley’s comet in 1759
• 6. Solar parallax and the transits of Venus of 1761 and 1769
• 7. Secular equations from Euler to Lagrange
• 8. The Laplace-Lagrange rivalry
• 9. The major anomalies explained: Laplace, 1785-1787
• 10. Astronomy in an «elevated state of flourishing maturity»
Stellar astronomy
• 1. Variable stars
• 2. Movements of stars and the direction of the solar motion
• 3. The scale of inter-stellar distances
• 4. The recognition of binary stars
• 5. The system of the stars
• 6. William Herschel and the riddle of the Nebulae
• 7. Retrospect: The reorientation of astronomy
The instrumentation of astronomy
• 1. Observing.
• 2. Measuring.
• 3. Astronomical instruments for non-astronomers.
• 4. Achromatic refractors.
• 5. Equatorials and circles.
• 6. Reflecting telescopes.
Pure and applied mathematics in the 18th century
• 1. Versions of the calculi.
• 2. Versions of mechanics.
• 3. Geometry, subject and role.
• 4. The art of the approximate.
• 5. Algebra, including number theory.
• 6. Probability theory and some statistics.
• 7. Four main figures.
• 8. Education and publications.
• 9. Philosophy and the Enlightenment.
• 10. History, mainly Montucla.
• 11. Effects of the French Revolution.
Institutional aspects of mathematics
• 1. Overview of development of institutions in the. 16th and 17th century
• 2. The different status of mathematics in national education systems
• 3. Tradition and innovations in the 18th century
The developments of calculus in Great Britain
• 1. A decline in British mathematics?
• 2. The Leibnizian formation of the first fluxionists
• 3. The problem of the foundations: the controversy with Leibniz and Berkeley
• 4. The Newtonian school: The stage of development and decline
• 5. The Philomaths, the Royal Society and the military schools
• 6. Towards the reform of the British calculus