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Questions about Philosophiæ Naturalis Principia Mathematica

Short answers, pulled from the story.

When was Philosophiæ Naturalis Principia Mathematica published?

The book appeared in July 1687 after Halley covered all costs from his own pocket. The first edition printed 750 copies appeared on the 5th of July 1686 authorized by Samuel Pepys.

Who financed the printing of Philosophiæ Naturalis Principia Mathematica?

Edmond Halley personally financed the printing of Philosophiae Naturalis Principia Mathematica. He bore publication costs after the Royal Society spent its budget on a fish history book and received leftover copies instead of his promised salary.

What mathematical concepts does Book One of Philosophiæ Naturalis Principia Mathematica cover?

Book One opens with mathematical lemmas on vanishingly small shapes that form a geometrical version of infinitesimal calculus. Propositions one through three establish relationships between centripetal forces and areas swept out by planets while propositions five through ten describe orbits as conic sections.

How did Philosophiæ Naturalis Principia Mathematica refute Cartesian vortex theory?

The book largely refuted Cartesian vortex theory which claimed planetary motions resulted from whirling fluid vortices filling interplanetary space. Newton concluded this hypothesis was completely at odds with astronomical phenomena and stated it served not to explain but to confuse observations.

When were the second and third editions of Philosophiæ Naturalis Principia Mathematica published?

The second edition published June 1713 required extensive revisions edited by Roger Cotes under the weight of priority disputes. The third edition published the 25th of March 1726 revised by Henry Pemberton M.D. followed after Newton began revising in autumn 1723 following serious illness in 1722.